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	<id>https://murray.cds.caltech.edu/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Apandey</id>
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	<updated>2026-06-03T19:19:56Z</updated>
	<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Lars_Nielsen,_March_2023&amp;diff=25464</id>
		<title>Lars Nielsen, March 2023</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Lars_Nielsen,_March_2023&amp;diff=25464"/>
		<updated>2023-03-11T02:44:06Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* 13 Mar (Mon) */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Lars Nielsen from Linkoping University in Sweden will visit Caltech on 13-17 March 2023.&lt;br /&gt;
__NOTOC__&lt;br /&gt;
&lt;br /&gt;
{| width=100% border=1 &lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=20% |&lt;br /&gt;
=== 13 Mar (Mon) ===&lt;br /&gt;
* 8:30 am: Richard, 109 Steele Lab&lt;br /&gt;
* 9:30 am: Michael Dickinson (204R BBB)&lt;br /&gt;
* 10:30 am: Apurva Badithela (Red Door)&lt;br /&gt;
* 11:15 am: open&lt;br /&gt;
* 12:00 pm: Lunch: Richard + Faculty&lt;br /&gt;
* 1:15 pm: John Doyle&lt;br /&gt;
* 2:00 pm: Seminar: 121 Annenberg&lt;br /&gt;
* 3:15 pm: Ayush Pandey (Annenberg 2nd floor lobby)&lt;br /&gt;
* 4:00 pm: open&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 14 Mar (Tue) ===&lt;br /&gt;
* 9:00 am: open&lt;br /&gt;
* 10:00 am: Biocircuits meeting (optional)&lt;br /&gt;
* 12:00 pm: Lunch: students&lt;br /&gt;
* 1:15 pm: Soon-Jo Chung (235 Guggenheim)&lt;br /&gt;
* 2:00 pm: open&lt;br /&gt;
* 2:45 pm: open&lt;br /&gt;
* 3:30 pm: Joel Burdick (245 Gates-Thomas)&lt;br /&gt;
* 4:15 pm: open&lt;br /&gt;
* 6:00 pm: Dinner with Richard and RuthAnne&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 15 Mar (Wed) ===&lt;br /&gt;
* 1:00 pm: Markus Meister&lt;br /&gt;
* 1:45 pm: open&lt;br /&gt;
* 3:00 pm: CDS Tea&lt;br /&gt;
* 3:45 pm: open&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 16 Mar (Thu) ===&lt;br /&gt;
* Dinner with Richard and graduate students&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 17 Mar (Fri) ===&lt;br /&gt;
* 4:00 pm: wrap up with Richard&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Seminar information === &lt;br /&gt;
&lt;br /&gt;
Force-Centric Perspectives on Autonomous Vehicle Safety-Maneuvers&lt;br /&gt;
&lt;br /&gt;
Lars Nielsen, Division of Vehicular Systems, Linköping University &amp;lt;br&amp;gt;&lt;br /&gt;
(postdoc at Caltech 85-86)&lt;br /&gt;
&lt;br /&gt;
13 March, 2-3 pm OR 15 Mar, 2-3 pm&amp;lt;br&amp;gt;&lt;br /&gt;
213 Anneberg&lt;br /&gt;
 &lt;br /&gt;
Abstract:&lt;br /&gt;
Real-time avoidance maneuvers for vehicles have been developed using a force-centric perspective,&lt;br /&gt;
where the founding principles are obtained from studies of optimal maneuvers. The&lt;br /&gt;
developed optimization framework, the different criteria used, and the obtained solutions give&lt;br /&gt;
insight into how to control the forces on the vehicle. A highlight in this presentation is the first&lt;br /&gt;
algorithm not needing a tire-road friction estimate.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Lars_Nielsen,_March_2023&amp;diff=25463</id>
		<title>Lars Nielsen, March 2023</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Lars_Nielsen,_March_2023&amp;diff=25463"/>
		<updated>2023-03-11T02:43:49Z</updated>

		<summary type="html">&lt;p&gt;Apandey: add meeting with Ayush&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Lars Nielsen from Linkoping University in Sweden will visit Caltech on 13-17 March 2023.&lt;br /&gt;
__NOTOC__&lt;br /&gt;
&lt;br /&gt;
{| width=100% border=1 &lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=20% |&lt;br /&gt;
=== 13 Mar (Mon) ===&lt;br /&gt;
* 8:30 am: Richard, 109 Steele Lab&lt;br /&gt;
* 9:30 am: Michael Dickinson (204R BBB)&lt;br /&gt;
* 10:30 am: Apurva Badithela (Red Door)&lt;br /&gt;
* 11:15 am: open&lt;br /&gt;
* 12:00 pm: Lunch: Richard + Faculty&lt;br /&gt;
* 1:15 pm: John Doyle&lt;br /&gt;
* 2:00 pm: Seminar: 121 Annenberg&lt;br /&gt;
* 3:15 pm: Meeting with Ayush Pandey (Annenberg 2nd floor lobby)&lt;br /&gt;
* 4:00 pm: open&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 14 Mar (Tue) ===&lt;br /&gt;
* 9:00 am: open&lt;br /&gt;
* 10:00 am: Biocircuits meeting (optional)&lt;br /&gt;
* 12:00 pm: Lunch: students&lt;br /&gt;
* 1:15 pm: Soon-Jo Chung (235 Guggenheim)&lt;br /&gt;
* 2:00 pm: open&lt;br /&gt;
* 2:45 pm: open&lt;br /&gt;
* 3:30 pm: Joel Burdick (245 Gates-Thomas)&lt;br /&gt;
* 4:15 pm: open&lt;br /&gt;
* 6:00 pm: Dinner with Richard and RuthAnne&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 15 Mar (Wed) ===&lt;br /&gt;
* 1:00 pm: Markus Meister&lt;br /&gt;
* 1:45 pm: open&lt;br /&gt;
* 3:00 pm: CDS Tea&lt;br /&gt;
* 3:45 pm: open&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 16 Mar (Thu) ===&lt;br /&gt;
* Dinner with Richard and graduate students&lt;br /&gt;
| width=20% |&lt;br /&gt;
&lt;br /&gt;
=== 17 Mar (Fri) ===&lt;br /&gt;
* 4:00 pm: wrap up with Richard&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Seminar information === &lt;br /&gt;
&lt;br /&gt;
Force-Centric Perspectives on Autonomous Vehicle Safety-Maneuvers&lt;br /&gt;
&lt;br /&gt;
Lars Nielsen, Division of Vehicular Systems, Linköping University &amp;lt;br&amp;gt;&lt;br /&gt;
(postdoc at Caltech 85-86)&lt;br /&gt;
&lt;br /&gt;
13 March, 2-3 pm OR 15 Mar, 2-3 pm&amp;lt;br&amp;gt;&lt;br /&gt;
213 Anneberg&lt;br /&gt;
 &lt;br /&gt;
Abstract:&lt;br /&gt;
Real-time avoidance maneuvers for vehicles have been developed using a force-centric perspective,&lt;br /&gt;
where the founding principles are obtained from studies of optimal maneuvers. The&lt;br /&gt;
developed optimization framework, the different criteria used, and the obtained solutions give&lt;br /&gt;
insight into how to control the forces on the vehicle. A highlight in this presentation is the first&lt;br /&gt;
algorithm not needing a tire-road friction estimate.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Yan_Zhang,_28_Mar_2022&amp;diff=24693</id>
		<title>Yan Zhang, 28 Mar 2022</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Yan_Zhang,_28_Mar_2022&amp;diff=24693"/>
		<updated>2022-03-24T05:34:01Z</updated>

		<summary type="html">&lt;p&gt;Apandey: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Yan Zhang, a PhD student at Georgia Tech will visit on 28 Mar 2022.&lt;br /&gt;
&lt;br /&gt;
Schedule:&lt;br /&gt;
* 8:30 am: Richard Murray, 109 Steele&lt;br /&gt;
* 9:00 am: Open&lt;br /&gt;
* 10:00 am: Group meeting presentation&lt;br /&gt;
* 12:00 pm: Lunch with Chelsea, Michaelle&lt;br /&gt;
* 1:15 pm: Open&lt;br /&gt;
* 2:00 pm: Meet with Ayush at Red Door&lt;br /&gt;
* 2:45 pm: Open&lt;br /&gt;
* 3:30 pm: Open&lt;br /&gt;
* 4:15 pm: Open&lt;br /&gt;
* 5:00 pm: Richard Murray, 109 Steele&lt;br /&gt;
&lt;br /&gt;
Research interests:&lt;br /&gt;
* Developed a new diagnostic platform interfacing cell-free biosensors with biphasic polymer systems for simultaneous detection of diverse classes of analytes that are robust to human biofluids and field-deployable.&lt;br /&gt;
* Integrated cell-free biosensors to a personal glucose monitor for rapid and reliable biomarker quantification at the point of need&lt;br /&gt;
* Designed, characterized, and optimized cell-free bacterial biosensors to detect micronutrient deficiencies, pathogenic bacterial infections, and heavy metal environment contaminants&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Yan_Zhang,_28_Mar_2022&amp;diff=24692</id>
		<title>Yan Zhang, 28 Mar 2022</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Yan_Zhang,_28_Mar_2022&amp;diff=24692"/>
		<updated>2022-03-24T05:32:40Z</updated>

		<summary type="html">&lt;p&gt;Apandey: add Ayush meeting&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Yan Zhang, a PhD student at Georgia Tech will visit on 28 Mar 2022.&lt;br /&gt;
&lt;br /&gt;
Schedule:&lt;br /&gt;
* 8:30 am: Richard Murray, 109 Steele&lt;br /&gt;
* 9:00 am: Open&lt;br /&gt;
* 10:00 am: Group meeting presentation&lt;br /&gt;
* 12:00 pm: Lunch with Chelsea, Michaelle&lt;br /&gt;
* 1:15 pm: Open&lt;br /&gt;
* 2:00 pm: Ayush&lt;br /&gt;
* 2:45 pm: Open&lt;br /&gt;
* 3:30 pm: Open&lt;br /&gt;
* 4:15 pm: Open&lt;br /&gt;
* 5:00 pm: Richard Murray, 109 Steele&lt;br /&gt;
&lt;br /&gt;
Research interests:&lt;br /&gt;
* Developed a new diagnostic platform interfacing cell-free biosensors with biphasic polymer systems for simultaneous detection of diverse classes of analytes that are robust to human biofluids and field-deployable.&lt;br /&gt;
* Integrated cell-free biosensors to a personal glucose monitor for rapid and reliable biomarker quantification at the point of need&lt;br /&gt;
* Designed, characterized, and optimized cell-free bacterial biosensors to detect micronutrient deficiencies, pathogenic bacterial infections, and heavy metal environment contaminants&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_discussions,_Feb_2021&amp;diff=24047</id>
		<title>SURF discussions, Feb 2021</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_discussions,_Feb_2021&amp;diff=24047"/>
		<updated>2021-01-28T20:06:12Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* 1 Feb (Mon) */ add Rosita/Ayush&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Slots for talking with applicants and co-mentors about SURF projects.  Please sign up for one of the slots below.  All times are PST. __NOTOC__&lt;br /&gt;
&lt;br /&gt;
In preparation for our conversation, please do the following:&lt;br /&gt;
* SURF students should work with their co-mentors to find a time the meeting/Skype call.  (For Skype calls, co-mentors should initiate.)&lt;br /&gt;
* Please make sure you have read the material in the description of your project, so that you are prepared to talk about what the project is about and we can narrow in on the key ideas that will be the basis of your proposal&lt;br /&gt;
* Please take a look at the [[SURF GOTChA chart]] page, which is the format that we will use for the first iteration of your project proposal.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| border=1 width=100%&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=25% |&lt;br /&gt;
==== 1 Feb (Mon) ====&lt;br /&gt;
* 5:00 pm PST: Rosita/Ayush&lt;br /&gt;
* 5:30 pm PST: open&lt;br /&gt;
| width=25% |&lt;br /&gt;
&lt;br /&gt;
==== 2 Feb (Tue) ====&lt;br /&gt;
* 4:00 pm PST: Christian/Josefine&lt;br /&gt;
* 4:30 pm PST: open&lt;br /&gt;
| width=25% |&lt;br /&gt;
&lt;br /&gt;
==== 3 Feb (Wed) ====&lt;br /&gt;
* 9:00 am PST: Manisha/Hannah&lt;br /&gt;
* 9:30 am PST: open&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The agenda for the phone call is (roughly):&lt;br /&gt;
&lt;br /&gt;
# Description of the basic idea behind the project (based on applicant&#039;s understanding)&lt;br /&gt;
# Discussion about approaches, things to read, variations to consider, etc&lt;br /&gt;
# Discussion of the format of the proposal&lt;br /&gt;
# Questions and discussion about the process&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2020:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23996</id>
		<title>SURF 2020: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2020:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23996"/>
		<updated>2020-12-22T04:19:26Z</updated>

		<summary type="html">&lt;p&gt;Apandey: Apandey moved page SURF 2020: Modeling tools for design and analysis of synthetic biological circuits to SURF 2021: Modeling tools for design and analysis of synthetic biological circuits: move to surf 2021&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;#REDIRECT [[SURF 2021: Modeling tools for design and analysis of synthetic biological circuits]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23995</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23995"/>
		<updated>2020-12-22T04:19:26Z</updated>

		<summary type="html">&lt;p&gt;Apandey: Apandey moved page SURF 2020: Modeling tools for design and analysis of synthetic biological circuits to SURF 2021: Modeling tools for design and analysis of synthetic biological circuits: move to surf 2021&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2021|SURF 2021]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. We are working on developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and the identified models can be used to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis to propose a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23994</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23994"/>
		<updated>2020-12-22T04:18:28Z</updated>

		<summary type="html">&lt;p&gt;Apandey: update for surf 2021&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2021|SURF 2021]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. We are working on developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and the identified models can be used to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis to propose a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23627</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23627"/>
		<updated>2020-04-27T01:49:34Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Lecture Schedule */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): Thu, 3-4:30 pm PDT&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): Tue, 3-4:30 pm PDT&lt;br /&gt;
* Office hours (individual help via Slack): Fri, 1-5 pm PDT&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week of the course will cover a different topic and/or tool.  The first class meeting of the week (Thu session) will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week (the following Tue) will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered between the lectures to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Notes&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 31 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| [[http:www.anaconda.com|Anaconda]], [[http:jupyter.org|Jupyter]], [[http:github.com|GitHub]]&lt;br /&gt;
| [[Media:W1_setup-31Mar2020.pdf|Computer setup instructions]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 7 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W2_bioscrape.ipynb|W2_bioscrape.ipynb]] (Jupyter notebook)&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 16 Apr&lt;br /&gt;
| Intro to SBML and non-mass-action propensities &amp;amp; rules in bioscrape&lt;br /&gt;
| Ayush&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p1.ipynb|W3_sbml_p1.ipynb]], [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p2.ipynb|W3_sbml_p2.ipynb]] (Jupyter notebook), [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/repressilator_sbml.xml|repressilator_sbml.xml]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4&amp;amp;nbsp;-&amp;amp;nbsp;23&amp;amp;nbsp;Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| BioCRNpyler&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W4_biocrnpyler.ipynb|W4_biocrnpyler.ipynb]] (Jupyter notebook), [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/parameters.txt|parameters.txt]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 30 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 7 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 14 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 21 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9&amp;amp;nbsp;-&amp;amp;nbsp;28&amp;amp;nbsp;May&amp;amp;nbsp;&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 4 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23626</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23626"/>
		<updated>2020-04-27T01:47:59Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Lecture Schedule */ added biocrnpyler&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): Thu, 3-4:30 pm PDT&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): Tue, 3-4:30 pm PDT&lt;br /&gt;
* Office hours (individual help via Slack): Fri, 1-5 pm PDT&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week of the course will cover a different topic and/or tool.  The first class meeting of the week (Thu session) will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week (the following Tue) will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered between the lectures to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Notes&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 31 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| [[http:www.anaconda.com|Anaconda]], [[http:jupyter.org|Jupyter]], [[http:github.com|GitHub]]&lt;br /&gt;
| [[Media:W1_setup-31Mar2020.pdf|Computer setup instructions]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 7 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W2_bioscrape.ipynb|W2_bioscrape.ipynb]] (Jupyter notebook)&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 16 Apr&lt;br /&gt;
| Intro to SBML and non-mass-action propensities &amp;amp; rules in bioscrape&lt;br /&gt;
| Ayush&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p1.ipynb|W3_sbml_p1.ipynb]], [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p2.ipynb|W3_sbml_p2.ipynb]] (Jupyter notebook), [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/repressilator_sbml.xml|repressilator_sbml.xml]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4&amp;amp;nbsp;-&amp;amp;nbsp;23&amp;amp;nbsp;Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| [[https://github.com/BuildACell/biocrnpyler|BioCRNpyler]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W4_biocrnpyler.ipynb|W4_biocrnpyler.ipynb]] (Jupyter notebook), [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/parameters.txt|parameters.txt]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 30 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 7 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 14 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 21 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9&amp;amp;nbsp;-&amp;amp;nbsp;28&amp;amp;nbsp;May&amp;amp;nbsp;&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 4 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23621</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23621"/>
		<updated>2020-04-17T01:22:13Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Lecture Schedule */ fixed a typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): Thu, 3-4:30 pm PDT&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): Tue, 3-4:30 pm PDT&lt;br /&gt;
* Office hours (individual help via Slack): Fri, 1-5 pm PDT&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week of the course will cover a different topic and/or tool.  The first class meeting of the week (Thu session) will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week (the following Tue) will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered between the lectures to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Notes&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 31 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| [[http:www.anaconda.com|Anaconda]], [[http:jupyter.org|Jupyter]], [[http:github.com|GitHub]]&lt;br /&gt;
| [[Media:W1_setup-31Mar2020.pdf|Computer setup instructions]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 7 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W2_bioscrape.ipynb|W2_bioscrape.ipynb]] (Jupyter notebook)&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 16 Apr&lt;br /&gt;
| Intro to SBML and non-mass-action propensities &amp;amp; rules in bioscrape&lt;br /&gt;
| Ayush&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p1.ipynb|W3_sbml_p1.ipynb]], [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W3_sbml_p2.ipynb|W3_sbml_p2.ipynb]] (Jupyter notebook), [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/repressilator_sbml.xml|repressilator_sbml.xml]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4&amp;amp;nbsp;-&amp;amp;nbsp;23&amp;amp;nbsp;Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| BioCRNpyler&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 30 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 7 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 14 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 21 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9&amp;amp;nbsp;-&amp;amp;nbsp;28&amp;amp;nbsp;May&amp;amp;nbsp;&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 4 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23616</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23616"/>
		<updated>2020-04-16T03:29:08Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Lecture Schedule */ updated title of week 3 lecture&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): Thu, 3-4:30 pm PDT&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): Tue, 3-4:30 pm PDT&lt;br /&gt;
* Office hours (individual help via Slack): Fri, 1-5 pm PDT&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week of the course will cover a different topic and/or tool.  The first class meeting of the week (Thu session) will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week (the following Tue) will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered between the lectures to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Notes&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 31 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| [[http:www.anaconda.com|Anaconda]], [[http:jupyter.org|Jupyter]], [[http:github.com|GitHub]]&lt;br /&gt;
| [[Media:W1_setup-31Mar2020.pdf|Computer setup instructions]]&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 7 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
| [[http:www.cds.caltech.edu/~murray/courses/be240/sp2020/W2_bioscrape.ipynb|W2_bioscrape.ipynb]] (Jupyter notebook)&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 16 Apr&lt;br /&gt;
| Intro to SBML and non-mass-action propensities &amp;amp; rules in bioscrape&lt;br /&gt;
| Ayush&lt;br /&gt;
| [[http:github.com/ananswam/bioscrape/wiki|Bioscrape]]&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4&amp;amp;nbsp;-&amp;amp;nbsp;23&amp;amp;nbsp;Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| BioCRNpyler&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 30 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 7 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 14 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 21 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9&amp;amp;nbsp;-&amp;amp;nbsp;28&amp;amp;nbsp;May&amp;amp;nbsp;&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 4 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23572</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23572"/>
		<updated>2020-03-27T21:03:46Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Lecture Schedule */ minor typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): TBD&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): TBD&lt;br /&gt;
* Office hours (individual help via Slack): TBD&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week of the course will cover a different topic and/or tool.  The first class meeting of the week will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered after the second lecture to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 30 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| Anaconda, Jupyter, Git&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 6 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 13 Apr&lt;br /&gt;
| Model reduction in bioscrape via non-mass-action propensities and rules&lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4 - 20 Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| BioCRNpyler&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 27 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 4 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 11 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 18 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9 - 25 May&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 1 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23571</id>
		<title>BE 240, Spring 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=BE_240,_Spring_2020&amp;diff=23571"/>
		<updated>2020-03-27T21:02:38Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added TA emails&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Open Source Tools for Biological Circuit Design&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Ayush Pandey (CDS), apandey@caltech.edu&lt;br /&gt;
* Cindy Ren (CDS), xrren@caltech.edu&lt;br /&gt;
* William Poole (CNS), wpoole@caltech.edu&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Class meeting times&#039;&#039;&#039;&lt;br /&gt;
* Lectures (overview of the tool via Zoom): TBD&lt;br /&gt;
* Recitations (group debugging of student examples via Zoom): TBD&lt;br /&gt;
* Office hours (individual help via Slack): TBD&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for BE 240, Spring 2020.&lt;br /&gt;
&lt;br /&gt;
This course covers the use of open source tools developed at Caltech for use in modeling and simulation of engineered biological circuits.  Participants in the course will develop working knowledge of modeling, simulation, and design tools that are available for biological circuits and apply that knowledge to a circuit relevant to your research.  Students will also gain insights into modeling and design choices, including what level of detail to include in a model based on the questions you are trying to ask.  Finally, the course aims to expand the available applications of model-based design of biological circuits and/or the available tools for biological circuit design through open source implementations.&lt;br /&gt;
&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
Each week fo the course will cover a different topic and/or tool.  The first class meeting of the week will be a description of the use of that tool on a representative problem, carried out using a Jupyter notebook that students can download and follow along with the instructor.  The second class meeting of the week will consist of problems brought forth by students in the class as they have tried to implement the tools on their own problems.  These problems will be discussed and solved in a group setting.  Weekly office hours will be offered after the second lecture to allow students to ask questions about individual tools and problem and receive help via Slack and/or Zoom.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Lecturer&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Tools&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W1 - 30 Mar&lt;br /&gt;
| Organizational week&lt;br /&gt;
| Richard&lt;br /&gt;
| Anaconda, Jupyter, Git&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W2 - 6 Apr&lt;br /&gt;
| CRNs and simulating them with Bioscrape &lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W3 - 13 Apr&lt;br /&gt;
| Model reduction in bioscrape via non-mass-action propensities and rules&lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W4 - 20 Apr&lt;br /&gt;
| BioCRNpyler for generating large CRN models from parts&lt;br /&gt;
| William&lt;br /&gt;
| BioCRNpyler&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W5 - 27 Apr&lt;br /&gt;
| Compartments as orthogonal CRNs connected by diffusion reactions and SubSBML &lt;br /&gt;
| Ayush&lt;br /&gt;
| Sub-SBML&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W6 - 4 May&lt;br /&gt;
| Spatial systems and signalling&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W7 - 11 May&lt;br /&gt;
| Cells and Growth/death regulation&lt;br /&gt;
| Cindy&lt;br /&gt;
| Gro&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W8 - 18 May&lt;br /&gt;
| System ID: Bioscrape inference tools &lt;br /&gt;
| Ayush&lt;br /&gt;
| Bioscrape Inference&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W9 - 25 May&lt;br /&gt;
| Bioscrape Lineages as a well-mixed version of GRO&lt;br /&gt;
| William&lt;br /&gt;
| Bioscrape Lineages&lt;br /&gt;
|- valign=top&lt;br /&gt;
| W10 - 1 Jun&lt;br /&gt;
| Advanced: Automated Model Reduction &lt;br /&gt;
| Ayush&lt;br /&gt;
| Auto-Reduce&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
&lt;br /&gt;
This class is graded pass/fail.  To pass the class, you must participate in at least 80% of the lectures and recitations and submit a final project report consisting of a Jupyter notebook demonstrating the use of two or more of the tools in the class on a problem of interest to your research.&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration is encouraged in figuring out how to use all of the tools of this course.  The final project report should represent your individual understanding of how to apply the tools demonstrated in this course to a problem of interest to your research.  Obtaining feedback and advice from the instructors, course participants, or others on the final project is allowed, but the final code included in the project should be written up individually, citing any sources of code snippets that are included in the notebook.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=David_Garcia,_13_Feb_2020&amp;diff=23384</id>
		<title>David Garcia, 13 Feb 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=David_Garcia,_13_Feb_2020&amp;diff=23384"/>
		<updated>2020-02-11T19:25:26Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Schedule */  added meeting with Ayush&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;David Garcia, a PhD student working at Oak Ridge National Laboratory (ORNL) will visit Caltech on 13 Feb (Thu).  If you would like to meet with him, sign up here (using your IMSS credentials).&lt;br /&gt;
&lt;br /&gt;
=== Schedule ===&lt;br /&gt;
* 9:15 am: Richard (107 Steele Lab)&lt;br /&gt;
* 10:00 am: Seminar&lt;br /&gt;
* 11:00 am: Zoila&lt;br /&gt;
* 11:45 am: Lunch (Michaelle, Chelsea)&lt;br /&gt;
* 1:00 pm: Open&lt;br /&gt;
* 1:45 pm: Chelsea&lt;br /&gt;
* 2:30 pm: Open&lt;br /&gt;
* 3:15 pm: John Marken&lt;br /&gt;
* 4:00 pm: Ayush&lt;br /&gt;
* 4:45 pm: Wrap up meet with Richard&lt;br /&gt;
&lt;br /&gt;
=== Seminar ===&lt;br /&gt;
&lt;br /&gt;
Cell-Free Enabled Bioproduction and Biological Discovery &amp;lt;br&amp;gt;&lt;br /&gt;
David Garcia, The University of Tennessee, Knoxville and Oak Ridge National Laboratory&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
13 Feb (Thu), 10a-11a, 114 Steele&lt;br /&gt;
&lt;br /&gt;
As our understanding of the microbial world has progressed, so too has the backlog of information and open questions generated from the thousands uncharacterized proteins and metabolites with potential applications as biofuels, therapeutics, and biomaterials. To address this problem, new tools need to be developed in order to rapidly test and take advantage of uncharacterized proteins and metabolites. Cell-free systems have developed into a high-throughput and scalable tool for synthetic biology and metabolic engineering with applications across multiple disciplines. The work presented in this talk leverages cell-free systems as a conduit for the exploration of protein function and metabolite production using two complementary approaches. The first elucidates interaction networks associated with secondary metabolite production using a computationally assisted pathway description pipeline that employs bioinformatic searches of genome databases, structural modeling, and ligand-docking simulations to predict the gene products most likely to be involved in a metabolic pathway. In vitro reconstructions of the pathway are then modularly assembled and chemically verified in Escherichia coli lysates in order to differentiate between active and inactive pathways. The second takes a systems and synthetic biology approach to engineer E. coli extracts capable of directing flux towards specific metabolites. Using growth and genome engineering-based methods, we produced cell-free proteomes capable of creating unconventional metabolic states with minimal impact on the cell in vivo. As a result of this work, we have significantly expanded our ability to use cell extracts outside of their native context to solve metabolic engineering problems and provide engineers new tools that can rapidly explore the functions of proteins and test novel metabolic pathways.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_discussions,_Jan_2020&amp;diff=23321</id>
		<title>SURF discussions, Jan 2020</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_discussions,_Jan_2020&amp;diff=23321"/>
		<updated>2020-01-23T18:18:50Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* 28 Jan (Tue) */ added time slot for Alicia&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Slots for talking with applicants and co-mentors about SURF projects.  Please sign up for one of the slots below.  All times are PST. __NOTOC__&lt;br /&gt;
&lt;br /&gt;
In preparation for our conversation, please do the following:&lt;br /&gt;
* SURF students should work with their co-mentors to find a time the meeting/Skype call.  (For Skype calls, co-mentors should initiate.)&lt;br /&gt;
* Please make sure you have read the material in the description of your project, so that you are prepared to talk about what the project is about and we can narrow in on the key ideas that will be the basis of your proposal&lt;br /&gt;
* Please take a look at the [[SURF GOTChA chart]] page, which is the format that we will use for the first iteration of your project proposal.&lt;br /&gt;
* Please read through the [[http:sfp.caltech.edu/students/proposal/surf_and_amgen_proposals|SURF proposal information page]] to see what the SURF office requires (and when)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| border=1 width=100%&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=25% |&lt;br /&gt;
==== 24 Jan (Fri) ====&lt;br /&gt;
* 2:00 pm PST: open&lt;br /&gt;
* 2:30 pm PST: Rory/Joe&lt;br /&gt;
&amp;lt;hr&amp;gt;&lt;br /&gt;
* 4:30 pm PST: Karena, Giovanna&lt;br /&gt;
* 5:00 pm PST: Chelsea, Katherine&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(Richard is off campus on Fri; all meetings via Skype)&lt;br /&gt;
| width=25% |&lt;br /&gt;
&lt;br /&gt;
==== 28 Jan (Tue) ====&lt;br /&gt;
* 1:30 pm PST: Alicia and Ayush&lt;br /&gt;
&amp;lt;hr&amp;gt;&lt;br /&gt;
* 5:00 pm PST: Bruno and Francesca&lt;br /&gt;
* 5:30 pm PST: Ivy and Apurva&lt;br /&gt;
| width=25% |&lt;br /&gt;
&lt;br /&gt;
==== 30 Jan (Wed) ====&lt;br /&gt;
* 8:00 am PST: Albert A?&lt;br /&gt;
* 8:30 am PST: Tom and Josefine&lt;br /&gt;
| width=25% |&lt;br /&gt;
&lt;br /&gt;
==== 3 Feb (Mon, if needed) ====&lt;br /&gt;
* 9:00 am PST: Open&lt;br /&gt;
* 9:30 am PST: Open&lt;br /&gt;
&amp;lt;hr&amp;gt;&lt;br /&gt;
* 5:00 pm PST: Open&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Please only use these slots of none of the others work (it is a bit late in the timeline for proposals)&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The agenda for the phone call is (roughly):&lt;br /&gt;
&lt;br /&gt;
# Description of the basic idea behind the project (based on applicant&#039;s understanding)&lt;br /&gt;
# Discussion about approaches, things to read, variations to consider, etc&lt;br /&gt;
# Discussion of the format of the proposal&lt;br /&gt;
# Questions and discussion about the process&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_GOTChA_chart&amp;diff=23304</id>
		<title>SURF GOTChA chart</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_GOTChA_chart&amp;diff=23304"/>
		<updated>2020-01-22T00:04:55Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Contents of a GOTChA chart */  typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;GOTChA charts are a simple proposal planning tool that we use for planning out SURF projects. A GOTChA chart is an attempt to summarize in one page what you are trying to do on a project.  The idea for GOTChA charts comes from Pratt and Whitney Corporation, which makes jet engines.  Richard Murray learned about them when he spent two years working for United Technologies, the parent company for Pratt. __NOTOC__&lt;br /&gt;
&lt;br /&gt;
== Contents of a GOTChA chart ==&lt;br /&gt;
&lt;br /&gt;
A GOTChA chart has four main elements:&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;&amp;lt;u&amp;gt;G&amp;lt;/u&amp;gt;oal&#039;&#039; - a high level description of what you want to accomplish, in plain English.  This should be written as a 2-3 sentence abstract for the paper that you would like to eventually write, stating what the probem is and what the contributions of the paper are.  Write it as if the project wewe done and it was completely successful.  It should be written without a lot of detail and in a way that would be accessible to researchers in your discipline, without having them necessarily be experts on the deatilis of your project.&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;&amp;lt;u&amp;gt;O&amp;lt;/u&amp;gt;bjectives&#039;&#039; - a concrete specification of what you want to accomplish, with numbers and dates, when appropriate.  Objectives are something that you can measure whether or not it has been completed.  They should support the overall goal, but should be much more specific and concrete.  A sample objective is &amp;quot;Demonstrate autonomous driving for 10 miles at an average speed of 5 miles per hour by the end of summer&amp;quot;.  You should have 2-4 objectives, with a few of them ones that you can accomplish by mid-summer and the others to be done by the end of the summer.  The last objective might be a bit of a stretch for what you think is possible.&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;&amp;lt;u&amp;gt;T&amp;lt;/u&amp;gt;echnical &amp;lt;u&amp;gt;Ch&amp;lt;/u&amp;gt;allenges&#039;&#039; - a list of the &amp;quot;hard parts&amp;quot; of accomplishing your goals and objectives.  Try to keep the list fairly short (3-5) items and focus on those parts of the problem that are the true showstoppers.  A sample technical challenge is &amp;quot;Getting stereo vision to work sufficiently fast that we can recognize obstacles in time to stop&amp;quot;.  You should make sure that your technical challenges are such that if you overcome them, you will be able to complies your objectives (which will let you accomplish your overall goals!).&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;&amp;lt;u&amp;gt;A&amp;lt;/u&amp;gt;pproach&#039;&#039; - a list of activities or strategies that you plan to implement to overcome the technical challenges.  These activities should provide the justification for why you think you can achieve your goals and objectives in the face of the technical challenges you have described.  Think of this as your plan for the summer: what will you do before you arrive, what will you do in the first few weeks, by mid summer, and toward the end of the summer.  Your approach should address the technical challenges, since if you don&#039;t overcome your technical challenges then you can&#039;t accomplish your objectives and you won&#039;t achieve your goals for the summer -:(.&lt;br /&gt;
&lt;br /&gt;
This information is most easily presented in the form of a &#039;&#039;quad chart&#039;&#039;, which can be laid out in powerpoint or HTML (or wiki):&lt;br /&gt;
&amp;lt;center&amp;gt;&lt;br /&gt;
&amp;lt;h3&amp;gt;Project title, name and date &amp;lt;/h3&amp;gt;&lt;br /&gt;
{| border=1 width=&amp;quot;80%&amp;quot;&lt;br /&gt;
|- valign=top&lt;br /&gt;
|width=&amp;quot;50%&amp;quot;| &#039;&#039;&#039;Goal:&#039;&#039;&#039; The first sentence should describe/motivate the project and its scope, to set the frame of reference for the rest of the GOTChA chart.  The next 1-2 sentences should describe the contributions of the project, written assuming that it is successful.  Write this paragraph as if the work as already been done.&lt;br /&gt;
|width=&amp;quot;50%&amp;quot;| &#039;&#039;&#039;Technical Challenges&#039;&#039;&#039;&lt;br /&gt;
* Challenge 1&lt;br /&gt;
* Challenge 2&lt;br /&gt;
* Challenge 3&lt;br /&gt;
* Challenge 4&lt;br /&gt;
* Challenge 5&lt;br /&gt;
|- valign=top&lt;br /&gt;
|width=&amp;quot;50%&amp;quot;| &#039;&#039;&#039;Objectives&#039;&#039;&#039;&lt;br /&gt;
* Objective 1&lt;br /&gt;
* Objective 2&lt;br /&gt;
* Objective 3&lt;br /&gt;
* Objective 4&lt;br /&gt;
* Objective 5&lt;br /&gt;
|width=&amp;quot;50%&amp;quot;| &#039;&#039;&#039;Approach&#039;&#039;&#039;&lt;br /&gt;
* Approach 1&lt;br /&gt;
* Approach 2&lt;br /&gt;
* Approach 3&lt;br /&gt;
* Approach 4&lt;br /&gt;
* Approach 5&lt;br /&gt;
|}&lt;br /&gt;
&amp;lt;/center&amp;gt;&lt;br /&gt;
&#039;&#039;&#039;It is important that you GOTChA chart fit on a single sheet of paper&#039;&#039;&#039;.  The purpose of this format is to create a concise description of your project and focus on the key aspects that you will focus on.  If your description at this stage is longer than a page, something is wrong.&lt;br /&gt;
&lt;br /&gt;
= Frequently Asked Questions =&lt;br /&gt;
&lt;br /&gt;
=== What&#039;s the difference between a goal and an objective? ===&lt;br /&gt;
Goals describe what you plan to do in plain English.  Thinks of this as the type of thing you might use to describe what the team is doing to one of your friends who is not part of the project.  The intent of the goals section of a GOTChA chart is to capture the high level vision of what you plan to get done.&lt;br /&gt;
&lt;br /&gt;
Objectives are concrete and measurable.  They should be something that you can say that you either accomplished or didn&#039;t, and there won&#039;t be any disagreement.&lt;br /&gt;
&lt;br /&gt;
Examples:&lt;br /&gt;
* Goal: complete integration of all sensors that will be used for the race&lt;br /&gt;
* Objective: mount all stereo camera pairs on vehicle by 6/1/05 and verify they meet project specifications for range and angle.&lt;br /&gt;
&lt;br /&gt;
=== How does the GOTChA chart compare to the SURF proposal? ===&lt;br /&gt;
Once you have your GOTChA chart in final form, it will map fairly naturally to the items that you are supposed to address in your project proposal.  Roughly speaking, you will turn the bullets in your GOTChA chart into paragraphs in your SURF proposal.  You should follow the SURF guidelines for the layout and contents of your proposal, but the information on the GOTChA chart will drive the contents.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23233</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23233"/>
		<updated>2019-12-12T04:29:42Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Research overview: */ typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. We are working on developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and the identified models can be used to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis to propose a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23232</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23232"/>
		<updated>2019-12-12T04:28:29Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Research overview: */ typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. We are working on developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and the identified models can be used to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23231</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23231"/>
		<updated>2019-12-12T04:26:44Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Research overview: */ typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. We are working on developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and use the identified models to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23230</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23230"/>
		<updated>2019-12-12T04:23:17Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Introduction: */ typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges such as biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. A possible project could involve developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and use the identified models to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23227</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23227"/>
		<updated>2019-12-12T01:36:39Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Research directions for the SURF project include: */  removed heading format&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges due to the biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. A possible project could involve developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and use the identified models to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23226</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23226"/>
		<updated>2019-12-12T01:36:05Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added heading format&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Introduction:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges due to the biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research overview:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
&lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. A possible project could involve developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and use the identified models to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;&#039;Research directions for the SURF project include:&#039;&#039;&#039; ==&lt;br /&gt;
&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
&lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23225</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23225"/>
		<updated>2019-12-12T01:34:04Z</updated>

		<summary type="html">&lt;p&gt;Apandey: filled in all information&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
Introduction:&lt;br /&gt;
&lt;br /&gt;
This SURF project is about modeling, simulations, and analysis methods and tools used in engineering biological circuits. Figure 1 shows a brief overview of the pipeline starting at the design phase where biological controllers are designed to be implemented either &#039;&#039;in vivo&#039;&#039; or &#039;&#039;in vitro&#039;&#039; to achieve certain biological / chemical function. To specify the performance specifications, to predict signalling levels, and to analyze these biological circuits, mathematical models are built. Control theoretic methods [1] can be used to study the stability and performance using these mathematical models. Similar to other engineering disciplines, experimental data is used to identify the model parameters in order to make design decisions. However, unlike other engineering disciplines there are various challenges due to the biological complexity, context dependence, and lack of understanding of various interactions in a biological system that obscure the use of models as the predictive design tools. Hence, this is an active area of research [2] with various interesting directions of research as suggested in Figure 1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Research overview:&lt;br /&gt;
&lt;br /&gt;
A 10-12 week project on modeling and analysis tools for biological circuits is possible in various research directions. As shown in Figure 1, modeling plays an important role in the standard design-build-test cycle for synthetic biology. This role can be divided into three parts as shown in the figure viz. theory based design of biological circuits, building and selecting models that represent a given circuit, and finally using experimental data to identify parameters of the models and study the related properties using simulations and other analysis tools. Each of these is discussed briefly in the following bullets:&lt;br /&gt;
* Biological feedback controllers can be designed at molecular and/or at cell population level. Control theory principles and analysis tools for stability and performance are commonly used to study the various properties that can be expected from a circuit and also to assess new design ideas. For example, in order to design a genetic oscillator, it is important to study the multi stability properties of the proposed nonlinear circuit models. Similarly, we have been exploring the question of studying how these properties arise from the particular nonlinear structure of chemical reaction network models. &lt;br /&gt;
* From the parts and components description of a biological circuit, creating models that represent the circuit functions and the dynamics is an important task. Automated tools such as TX-TLsim [3] and iBioSim [4] can be used to create chemical reaction network models of a circuit. We have been working on developing a similar Python based chemical reaction network compiler called BioCRNpyler [6]. It can be used to quickly create models for biological circuits given the parts, components, and mechanism description. The models of all the submodules can then be assembled together by other tools such as Sub-SBML [7]. BioCRNpyler is primarily aimed at creating models for cell-free systems but can also be used to create subsystem models of circuits &#039;&#039;in vivo&#039;&#039;. A possible project could involve developing these tools further and using them to model and simulate synthetic cell vesicles and cell-free circuits.&lt;br /&gt;
* To validate and quantify the models for a circuit, experimental data is used to identify the model parameters. Often for biological systems a big challenge is that the output measurements cannot be used to identify all the model parameters uniquely. A set of parameter identification tools is available in a Cython based fast stochastic simulator toolbox called bioscrape [5]. Various kinds of data from different experiments can be used to validate these tools and use the identified models to study system properties of these circuits. Moreover, signalling levels can be predicted and used for circuit improvements and design with the identified models. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Research directions for the SURF project include:&lt;br /&gt;
* Modeling and simulations of cell-free (sub)systems and synthetic cells (vesicles) consisting of cell-free extracts and circuits. &lt;br /&gt;
* Using some of the cell-free extract and TX-TL data, modeling and identifying model parameters using parameter identification tools. Studying structural parameter identifiability for these nonlinear models is another related direction.&lt;br /&gt;
* For a given circuit model, using tools such as global sensitivity analysis and parameter identifiability analysis, proposing a decomposition of the circuit using the model so that methodical system identification by parts can be performed. A related direction of research could be to study reduced order models and their mapping back and forth to full order models.&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Myers, Chris J., et al. &amp;quot;iBioSim: a tool for the analysis and design of genetic circuits.&amp;quot; Bioinformatics 25.21 (2009): 2848-2849.&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23222</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23222"/>
		<updated>2019-12-11T06:32:59Z</updated>

		<summary type="html">&lt;p&gt;Apandey: structure complete. need to fill in details&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
Intro about modeling in synthetic biology and the pipeline in the figure.&lt;br /&gt;
&lt;br /&gt;
Intro about the project(s) possible.&lt;br /&gt;
&lt;br /&gt;
Particular details on modeling work going on in the lab. &lt;br /&gt;
&lt;br /&gt;
Research directions for the SURF project include:&lt;br /&gt;
* Modeling of cell-free systems&lt;br /&gt;
* System identification by parts, global sensitivity analysis, model decomposition, reduced models&lt;br /&gt;
* Using extract and tx-tl data&lt;br /&gt;
* Subsystem modeling of a build a cell project&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. Experience with programming in Python and an understanding of feedback control systems are a bonus. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Hsiao, Victoria, Anandh Swaminathan, and Richard M. Murray. &amp;quot;Control theory for synthetic Biology: Recent advances in system characterization, control design, and controller implementation for synthetic biology.&amp;quot; IEEE Control Systems Magazine 38.3 (2018): 32-62.&lt;br /&gt;
# Del Vecchio, Domitilla, Aaron J. Dy, and Yili Qian. &amp;quot;Control theory meets synthetic biology.&amp;quot; Journal of The Royal Society Interface 13.120 (2016): 20160380.&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23221</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23221"/>
		<updated>2019-12-11T06:25:15Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added github links to toolboxes&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in the synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
Research directions for the SURF project include:&lt;br /&gt;
* Modeling of cell-free systems&lt;br /&gt;
* System identification by parts, global sensitivity analysis, model decomposition, reduced models&lt;br /&gt;
* Using extract and tx-tl data&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Swaminathan, Anandh, et al. &amp;quot;Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape.&amp;quot; (2017). [https://github.com/ananswam/bioscrape/ Github link]&lt;br /&gt;
# BioCRNPyler - Biomolecular Chemical Reaction Network Compiler : A Python toolbox to create CRN models in SBML for biomolecular mechanisms. [https://github.com/BuildACell/BioCRNPyler Github link]&lt;br /&gt;
# Sub-SBML : A Python based toolbox to create, edit, combine, and model interactions among multiple Systems Biology Markup Language (SBML) models. [https://github.com/ayush9pandey/subsbml Github link]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23220</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23220"/>
		<updated>2019-12-11T06:20:35Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added image, formatted&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg|thumb|500px|right|Figure 1: Modeling and analysis tools in synthetic biology pipeline]]&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
Research directions for the SURF project include:&lt;br /&gt;
* Modeling of cell-free systems&lt;br /&gt;
* System identification by parts, global sensitivity analysis, model decomposition, reduced models&lt;br /&gt;
* Using extract and tx-tl data&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Bioscrape&lt;br /&gt;
# BioCRNpyler&lt;br /&gt;
# Sub-SBML&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=File:SynBioModelingPipeline.jpg&amp;diff=23219</id>
		<title>File:SynBioModelingPipeline.jpg</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=File:SynBioModelingPipeline.jpg&amp;diff=23219"/>
		<updated>2019-12-11T06:08:36Z</updated>

		<summary type="html">&lt;p&gt;Apandey: Modeling tools for synthetic biology and their use in the design build test cycle&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Modeling tools for synthetic biology and their use in the design build test cycle&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23217</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23217"/>
		<updated>2019-12-11T06:06:58Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added research directions&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|SURF 2020]] project description&#039;&#039;&#039;&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SynBioModelingPipeline.jpg]]&lt;br /&gt;
&lt;br /&gt;
Research directions for the SURF project include:&lt;br /&gt;
* Modeling of cell-free systems&lt;br /&gt;
* System identification by parts, global sensitivity analysis, model decomposition, reduced models&lt;br /&gt;
* Using extract and tx-tl data&lt;br /&gt;
* &lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
# Tuza, Zoltan A., et al. &amp;quot;An in silico modeling toolbox for rapid prototyping of circuits in a biomolecular “breadboard” system.&amp;quot; 52nd IEEE Conference on Decision and Control. IEEE, 2013. [[An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System| Link]]&lt;br /&gt;
# Bioscrape&lt;br /&gt;
# BioCRNpyler&lt;br /&gt;
# Sub-SBML&lt;br /&gt;
#&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23213</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23213"/>
		<updated>2019-12-11T04:28:46Z</updated>

		<summary type="html">&lt;p&gt;Apandey: skeleton set up for the page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;[[SURF 2020|2020 SURF]] project description&#039;&#039;&#039;&lt;br /&gt;
* Mentor: Richard Murray&lt;br /&gt;
* Co-mentor: Ayush Pandey&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Research directions for a SURF project include:&lt;br /&gt;
&lt;br /&gt;
We are interested in both theoretical and computational directions for this project. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;References:&#039;&#039;&#039;&lt;br /&gt;
#&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Create_new_page&amp;diff=23212</id>
		<title>Create new page</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Create_new_page&amp;diff=23212"/>
		<updated>2019-12-11T04:25:49Z</updated>

		<summary type="html">&lt;p&gt;Apandey: Apandey moved page Create new page to SURF 2020 : Modeling tools for design and analysis of synthetic biological circuits&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;#REDIRECT [[SURF 2020 : Modeling tools for design and analysis of synthetic biological circuits]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23211</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23211"/>
		<updated>2019-12-11T04:25:49Z</updated>

		<summary type="html">&lt;p&gt;Apandey: Apandey moved page Create new page to SURF 2020 : Modeling tools for design and analysis of synthetic biological circuits&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;SURF 2020 project description&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23210</id>
		<title>SURF 2021: Modeling tools for design and analysis of synthetic biological circuits</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=SURF_2021:_Modeling_tools_for_design_and_analysis_of_synthetic_biological_circuits&amp;diff=23210"/>
		<updated>2019-12-11T04:23:20Z</updated>

		<summary type="html">&lt;p&gt;Apandey: started SURF 2020 project page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;SURF 2020 project description&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23042</id>
		<title>CDS 131, Fall 2019</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23042"/>
		<updated>2019-10-15T21:12:53Z</updated>

		<summary type="html">&lt;p&gt;Apandey: reverted back to the original link for HW3&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Linear Systems Theory&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Lectures: MWF, 2-3 pm, 213 Annenberg&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Teaching Assistants&#039;&#039;&#039;&lt;br /&gt;
* [mailto:jch3n@caltech.edu Jiexin (Jessie) Chen (CDS)], [mailto:apandey@caltech.edu Ayush Pandey (CDS)]&lt;br /&gt;
* Office hours: Fri, 4-5; Tue, 4-5 in 243 Annenberg&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for CDS 131, Fall 2019.  This course is intended for first year graduate students in controls, advanced undergraduates in EE, ChE, and ME who have taken a basic controls course (e.g., CDS 110, ChE 105, EE 113), and motivated graduate students in other disciplines would would like to learn more about linear systems and control.  All students taking the course should also have a good understanding of (matrix) differential equations and linear algebra.&lt;br /&gt;
&lt;br /&gt;
=== Catalog Description ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;CDS 131. Linear Systems Theory.&#039;&#039;&#039; 9 units (3-0-6); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; state-space and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and output-feedback. Instructor: Murray.&lt;br /&gt;
&lt;br /&gt;
{| border=0 padding=0 width=100% &lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
There will be 2-3 one hour lectures per week, with the specific days varying from week-to-week.  The lecture days for each week will be announced in class and posted here at least 1 week in advance.&lt;br /&gt;
&lt;br /&gt;
Reading:&lt;br /&gt;
* Opt = optional reading (useful if you are confused and trying to understand the basic concepts)&lt;br /&gt;
* Rec = recommended reading (this is what the homework is based on)&lt;br /&gt;
* Adv = advanced reading (more detailed results, useful if you are interested in learning more)&lt;br /&gt;
&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Announcements ===&lt;br /&gt;
* 14 Oct 2019: Solutions for HW #1 are posted. Access is restricted to the Caltech network (VPN OK).&lt;br /&gt;
* 14 Oct 2019: Revised course notes have been updated to include W3 material ({{cds131 fa19 pdf|fbs-linsys_14Oct2019.pdf|latest version}}; no significant changes in Ch 1-2)&lt;br /&gt;
* 11  Oct 2019: For HW #2, problem 1: assume that the linear system is time invariant.&lt;br /&gt;
* 8 Oct 2019: Fixed bug in definition of linear system in course notes ({{cds131 fa19 pdf|fbs-linsys_08Oct2019.pdf|latest version}})&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Reading&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Homework&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 1&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
30 Sep &amp;lt;br&amp;gt;  2 Oct &amp;lt;br&amp;gt; 4 Oct*&lt;br /&gt;
| Introduction and review&lt;br /&gt;
* Course logistics&lt;br /&gt;
* Norms of signals in continuous (and discrete) time&lt;br /&gt;
* I/O systems, LTI systems&lt;br /&gt;
* Induced system norms&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e&amp;amp;nbsp;Ch 1 and&amp;amp;nbsp;2&lt;br /&gt;
* Rec: FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;1 (or DFT Sec&amp;amp;nbsp;2.1&amp;amp;#8209;2.4)&lt;br /&gt;
* Adv: Sontag, Ch 2&lt;br /&gt;
| {{cds131 fa19 pdf|hw1-fa19.pdf|HW #1}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 2 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
{{cds131 fa19 pdf|caltech/hw1-fa19_solns.pdf|Solns}} (Caltech only)&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 2&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Richard --&amp;gt;&lt;br /&gt;
7 Oct &amp;lt;br&amp;gt; 9 Oct &amp;lt;br&amp;gt; 11 Oct&lt;br /&gt;
| Linear I/O systems&lt;br /&gt;
* Differential and difference equations (with inputs and outputs, including disturbances and noise)&lt;br /&gt;
* Linearized system dynamics&lt;br /&gt;
* Stability of equilibrium points, I/O stability&lt;br /&gt;
* Convolution equation, impulse response&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Ch 3; DFT&amp;amp;nbsp;Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Rec: FBS2e Sec&amp;amp;nbsp;5.1&amp;amp;#8209;5.3, 6.1&amp;amp;#8209;6.3; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;2&lt;br /&gt;
* Adv: Sontag Sec C.4, 2.6&lt;br /&gt;
| {{cds131 fa19 pdf|hw2-fa19.pdf|HW #2}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 3&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
14 Oct &amp;lt;br&amp;gt; 16 Oct &amp;lt;br&amp;gt; 18 Oct*&lt;br /&gt;
| Reachability&lt;br /&gt;
* Definitions (reachability, stabilizability)&lt;br /&gt;
* Characterization and rank tests (Grammian, PBH)&lt;br /&gt;
* Decomposition into reachable/unreachable subspaces&lt;br /&gt;
* Eigenvalue placement theorem&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 7.1,&amp;amp;nbsp;7.2; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;3&lt;br /&gt;
* Adv: FBS2e Sec&amp;amp;nbsp;7.3; Sontag Sec&amp;amp;nbsp;3.1&amp;amp;#8209;3.3,&amp;amp;nbsp;3.5&lt;br /&gt;
| {{cds131 fa19 pdf|hw3-fa19.pdf|HW #3}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 4&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
21 Oct &amp;lt;br&amp;gt; 23 Oct &amp;lt;br&amp;gt; 25 Oct*&lt;br /&gt;
| State feedback&lt;br /&gt;
* Optimization and optimal control&lt;br /&gt;
* Linear quadratic regulator (including Ricatti equation)&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e  Sec 7.5&lt;br /&gt;
* Rec: FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;4 (= OBC Ch&amp;amp;nbsp;2)&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;8.1&amp;amp;#8209;8.3, 9.1,&amp;amp;nbsp;9.2&lt;br /&gt;
| {{cds131 fa19 pdf|hw4-fa19.pdf|HW #4}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 5&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
28 Oct &amp;lt;br&amp;gt; 30 Oct* &amp;lt;br&amp;gt; 1 Nov&lt;br /&gt;
| Observability and state estimation&lt;br /&gt;
* Definitions (observability, observable subspace)&lt;br /&gt;
* Characterization and rank tests&lt;br /&gt;
* Kalman decomposition&lt;br /&gt;
* Linear observers (full-state)&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 8.1-8.3; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;5&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;6.1&amp;amp;#8209;6.3, 7.1&lt;br /&gt;
|  {{cds131 fa19 pdf|hw5-fa19.pdf|HW #5}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 6&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Nov &amp;lt;br&amp;gt; 6 Nov &amp;lt;br&amp;gt; 8 Nov*&lt;br /&gt;
| Frequency domain modeling&lt;br /&gt;
* Control system transfer functions&lt;br /&gt;
* State space realizations, minimal realizations&lt;br /&gt;
* Poles and zeros&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS23 Ch 2&lt;br /&gt;
* Rec: FBS2e Ch&amp;amp;nbsp;9; DFT Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Adv: Lewis Ch 3 and 4&lt;br /&gt;
&amp;lt;!-- * Adv: [[http:web.mit.edu/6.242/www/images/lec5_6242_2004.pdf|Notes on balanced truncation (Megretski, 2004)]] --&amp;gt;&lt;br /&gt;
|  {{cds131 fa19 pdf|hw6-fa19.pdf|HW #6}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 7&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
11 Nov &amp;lt;br&amp;gt; 13 Nov &amp;lt;br&amp;gt; 15 Nov*&lt;br /&gt;
| Frequency domain analysis&lt;br /&gt;
* Internal stability&lt;br /&gt;
* Tracking, disturbance rejection&lt;br /&gt;
* I/O performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.1-10.2, Sec&amp;amp;nbsp;12.1-12.2&lt;br /&gt;
* Rec: DFT Ch 3&lt;br /&gt;
* Adv: Lewis Ch 5-8&lt;br /&gt;
| {{cds131 fa19 pdf|hw7-fa19.pdf|HW #7}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;8&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
18 Nov &amp;lt;br&amp;gt; 20 Nov* &amp;lt;br&amp;gt; 22 Nov&lt;br /&gt;
| Uncertainty and robustness&lt;br /&gt;
* Types of uncertainty: parametric, operator, disturbances/noise&lt;br /&gt;
* Robust stability and robust performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.3, Sec&amp;amp;nbsp;13.1-13.3&lt;br /&gt;
* Rec: DFT Ch 4&lt;br /&gt;
|  {{cds131 fa19 pdf|hw8-fa19.pdf|HW #8}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 27 Nov  &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;9&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
25 Nov &amp;lt;br&amp;gt; 27 Nov* &amp;lt;br&amp;gt; &amp;lt;s&amp;gt;29 Nov&amp;lt;/s&amp;gt; &amp;lt;br&amp;gt; 2 Dec &lt;br /&gt;
| Fundamental limits&lt;br /&gt;
* Algebraic limits&lt;br /&gt;
* Bode&#039;s integral formula&lt;br /&gt;
* Maximum modulus principle&lt;br /&gt;
|&lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;14.3-14.5&lt;br /&gt;
* Rec: DFT Ch 6&lt;br /&gt;
* Adv: Lewis, Ch 9&lt;br /&gt;
| {{cds131 fa19 pdf|hw9-fa19.pdf|HW #9}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 27 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Dec (Fri) &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;10&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Dec &amp;lt;br&amp;gt; 6 Dec*&lt;br /&gt;
| Review for final&lt;br /&gt;
| Final&lt;br /&gt;
| &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
The final grade will be based on homework sets, a midterm exam, and a final exam: &lt;br /&gt;
&lt;br /&gt;
*&#039;&#039;Homework (70%):&#039;&#039; Homework sets will be handed out weekly and due on Wednesdays by 2 pm either in class or in the labeled box across from 107 Steele Lab.  Each student is allowed up to two extensions of no more than 2 days each over the course of the term.  Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean.  MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).&lt;br /&gt;
&lt;br /&gt;
:The lowest homework set grade will be dropped when computing your final grade.&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;Final exam (30%):&#039;&#039;  The final exam will be handed out on the last day of class (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing.  Any computer code that is used to solve homework problems is considered part of your writeup and should be done individually (you can share ideas, but not code).&lt;br /&gt;
&lt;br /&gt;
No collaboration is allowed on the final exam.&lt;br /&gt;
&lt;br /&gt;
=== Course Text and References ===&lt;br /&gt;
&lt;br /&gt;
The primary course texts are&lt;br /&gt;
* [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org &#039;&#039;Feedback Systems: An Introduction for Scientists and Engineers&#039;&#039;], Princeton University Press, Second Edition*, 2019.&lt;br /&gt;
* [FBS2s] Richard M. Murray, &#039;&#039;{{cds131 fa19 pdf|fbs-linsys_14Oct2019.pdf|Feedback Systems:  Notes on Linear Systems Theory}}&#039;&#039;, 2019. (Updated 14 Oct 2019)&lt;br /&gt;
* [DFT] J. Doyle, B. Francis and A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.pdf &#039;&#039;Feedback Control Theory&#039;&#039;], Dover, 2009 (originally published by Macmillan, 1992).&lt;br /&gt;
* [OBC] R. M. Murray, &amp;quot;Optimization-Based Control&amp;quot;, 2010. [http://www.cds.caltech.edu/~murray/amwiki/index.php?title=OBC:Main_Page Online access]&lt;br /&gt;
* [Son98] E. D. Sontag, &#039;&#039;Mathematical Control Theory&#039;&#039;, Springer, 1998. [http://www.math.rutgers.edu/~sontag/mct.html Online access]&lt;br /&gt;
&amp;lt;nowiki&amp;gt;*&amp;lt;/nowiki&amp;gt; Please make sure to use the &#039;&#039;second&#039;&#039; edition [FBS2e].&lt;br /&gt;
&lt;br /&gt;
The following additional references may also be useful:&lt;br /&gt;
&lt;br /&gt;
* [Lew03] A. D. Lewis, &#039;&#039;A Mathematical Approach to Classical Control&#039;&#039;, 2003. [https://mast.queensu.ca/~andrew/teaching/pdf/332-notes.pdf Online access].&lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
* J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), &#039;&#039;Schaum&#039;s Outline of Feedback and Control Systems&#039;&#039;, 2nd Edition, 2013.  &lt;br /&gt;
* B. Friedland, &#039;&#039;Control System Design: An Introduction to State-Space Methods&#039;&#039;, McGraw-Hill, 1986.&lt;br /&gt;
--&amp;gt;&lt;br /&gt;
Note: the only sources listed here are those that allow free access to online versions.  Additional textbooks that are not freely available can be obtained from the library.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23041</id>
		<title>CDS 131, Fall 2019</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23041"/>
		<updated>2019-10-15T18:01:10Z</updated>

		<summary type="html">&lt;p&gt;Apandey: edited hw3 link in wiki?&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Linear Systems Theory&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Lectures: MWF, 2-3 pm, 213 Annenberg&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Teaching Assistants&#039;&#039;&#039;&lt;br /&gt;
* [mailto:jch3n@caltech.edu Jiexin (Jessie) Chen (CDS)], [mailto:apandey@caltech.edu Ayush Pandey (CDS)]&lt;br /&gt;
* Office hours: Fri, 4-5; Tue, 4-5 in 243 Annenberg&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for CDS 131, Fall 2019.  This course is intended for first year graduate students in controls, advanced undergraduates in EE, ChE, and ME who have taken a basic controls course (e.g., CDS 110, ChE 105, EE 113), and motivated graduate students in other disciplines would would like to learn more about linear systems and control.  All students taking the course should also have a good understanding of (matrix) differential equations and linear algebra.&lt;br /&gt;
&lt;br /&gt;
=== Catalog Description ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;CDS 131. Linear Systems Theory.&#039;&#039;&#039; 9 units (3-0-6); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; state-space and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and output-feedback. Instructor: Murray.&lt;br /&gt;
&lt;br /&gt;
{| border=0 padding=0 width=100% &lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
There will be 2-3 one hour lectures per week, with the specific days varying from week-to-week.  The lecture days for each week will be announced in class and posted here at least 1 week in advance.&lt;br /&gt;
&lt;br /&gt;
Reading:&lt;br /&gt;
* Opt = optional reading (useful if you are confused and trying to understand the basic concepts)&lt;br /&gt;
* Rec = recommended reading (this is what the homework is based on)&lt;br /&gt;
* Adv = advanced reading (more detailed results, useful if you are interested in learning more)&lt;br /&gt;
&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Announcements ===&lt;br /&gt;
* 14 Oct 2019: Solutions for HW #1 are posted. Access is restricted to the Caltech network (VPN OK).&lt;br /&gt;
* 14 Oct 2019: Revised course notes have been updated to include W3 material ({{cds131 fa19 pdf|fbs-linsys_14Oct2019.pdf|latest version}}; no significant changes in Ch 1-2)&lt;br /&gt;
* 11  Oct 2019: For HW #2, problem 1: assume that the linear system is time invariant.&lt;br /&gt;
* 8 Oct 2019: Fixed bug in definition of linear system in course notes ({{cds131 fa19 pdf|fbs-linsys_08Oct2019.pdf|latest version}})&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Reading&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Homework&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 1&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
30 Sep &amp;lt;br&amp;gt;  2 Oct &amp;lt;br&amp;gt; 4 Oct*&lt;br /&gt;
| Introduction and review&lt;br /&gt;
* Course logistics&lt;br /&gt;
* Norms of signals in continuous (and discrete) time&lt;br /&gt;
* I/O systems, LTI systems&lt;br /&gt;
* Induced system norms&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e&amp;amp;nbsp;Ch 1 and&amp;amp;nbsp;2&lt;br /&gt;
* Rec: FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;1 (or DFT Sec&amp;amp;nbsp;2.1&amp;amp;#8209;2.4)&lt;br /&gt;
* Adv: Sontag, Ch 2&lt;br /&gt;
| {{cds131 fa19 pdf|hw1-fa19.pdf|HW #1}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 2 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
{{cds131 fa19 pdf|caltech/hw1-fa19_solns.pdf|Solns}} (Caltech only)&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 2&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Richard --&amp;gt;&lt;br /&gt;
7 Oct &amp;lt;br&amp;gt; 9 Oct &amp;lt;br&amp;gt; 11 Oct&lt;br /&gt;
| Linear I/O systems&lt;br /&gt;
* Differential and difference equations (with inputs and outputs, including disturbances and noise)&lt;br /&gt;
* Linearized system dynamics&lt;br /&gt;
* Stability of equilibrium points, I/O stability&lt;br /&gt;
* Convolution equation, impulse response&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Ch 3; DFT&amp;amp;nbsp;Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Rec: FBS2e Sec&amp;amp;nbsp;5.1&amp;amp;#8209;5.3, 6.1&amp;amp;#8209;6.3; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;2&lt;br /&gt;
* Adv: Sontag Sec C.4, 2.6&lt;br /&gt;
| {{cds131 fa19 pdf|hw2-fa19.pdf|HW #2}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 3&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
14 Oct &amp;lt;br&amp;gt; 16 Oct &amp;lt;br&amp;gt; 18 Oct*&lt;br /&gt;
| Reachability&lt;br /&gt;
* Definitions (reachability, stabilizability)&lt;br /&gt;
* Characterization and rank tests (Grammian, PBH)&lt;br /&gt;
* Decomposition into reachable/unreachable subspaces&lt;br /&gt;
* Eigenvalue placement theorem&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 7.1,&amp;amp;nbsp;7.2; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;3&lt;br /&gt;
* Adv: FBS2e Sec&amp;amp;nbsp;7.3; Sontag Sec&amp;amp;nbsp;3.1&amp;amp;#8209;3.3,&amp;amp;nbsp;3.5&lt;br /&gt;
| {{cds131 fa19 pdf|hw3-fa19-removed.pdf|HW #3}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 4&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
21 Oct &amp;lt;br&amp;gt; 23 Oct &amp;lt;br&amp;gt; 25 Oct*&lt;br /&gt;
| State feedback&lt;br /&gt;
* Optimization and optimal control&lt;br /&gt;
* Linear quadratic regulator (including Ricatti equation)&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e  Sec 7.5&lt;br /&gt;
* Rec: FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;4 (= OBC Ch&amp;amp;nbsp;2)&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;8.1&amp;amp;#8209;8.3, 9.1,&amp;amp;nbsp;9.2&lt;br /&gt;
| {{cds131 fa19 pdf|hw4-fa19.pdf|HW #4}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 5&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
28 Oct &amp;lt;br&amp;gt; 30 Oct* &amp;lt;br&amp;gt; 1 Nov&lt;br /&gt;
| Observability and state estimation&lt;br /&gt;
* Definitions (observability, observable subspace)&lt;br /&gt;
* Characterization and rank tests&lt;br /&gt;
* Kalman decomposition&lt;br /&gt;
* Linear observers (full-state)&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 8.1-8.3; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;5&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;6.1&amp;amp;#8209;6.3, 7.1&lt;br /&gt;
|  {{cds131 fa19 pdf|hw5-fa19.pdf|HW #5}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 6&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Nov &amp;lt;br&amp;gt; 6 Nov &amp;lt;br&amp;gt; 8 Nov*&lt;br /&gt;
| Frequency domain modeling&lt;br /&gt;
* Control system transfer functions&lt;br /&gt;
* State space realizations, minimal realizations&lt;br /&gt;
* Poles and zeros&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS23 Ch 2&lt;br /&gt;
* Rec: FBS2e Ch&amp;amp;nbsp;9; DFT Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Adv: Lewis Ch 3 and 4&lt;br /&gt;
&amp;lt;!-- * Adv: [[http:web.mit.edu/6.242/www/images/lec5_6242_2004.pdf|Notes on balanced truncation (Megretski, 2004)]] --&amp;gt;&lt;br /&gt;
|  {{cds131 fa19 pdf|hw6-fa19.pdf|HW #6}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 7&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
11 Nov &amp;lt;br&amp;gt; 13 Nov &amp;lt;br&amp;gt; 15 Nov*&lt;br /&gt;
| Frequency domain analysis&lt;br /&gt;
* Internal stability&lt;br /&gt;
* Tracking, disturbance rejection&lt;br /&gt;
* I/O performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.1-10.2, Sec&amp;amp;nbsp;12.1-12.2&lt;br /&gt;
* Rec: DFT Ch 3&lt;br /&gt;
* Adv: Lewis Ch 5-8&lt;br /&gt;
| {{cds131 fa19 pdf|hw7-fa19.pdf|HW #7}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;8&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
18 Nov &amp;lt;br&amp;gt; 20 Nov* &amp;lt;br&amp;gt; 22 Nov&lt;br /&gt;
| Uncertainty and robustness&lt;br /&gt;
* Types of uncertainty: parametric, operator, disturbances/noise&lt;br /&gt;
* Robust stability and robust performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.3, Sec&amp;amp;nbsp;13.1-13.3&lt;br /&gt;
* Rec: DFT Ch 4&lt;br /&gt;
|  {{cds131 fa19 pdf|hw8-fa19.pdf|HW #8}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 27 Nov  &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;9&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
25 Nov &amp;lt;br&amp;gt; 27 Nov* &amp;lt;br&amp;gt; &amp;lt;s&amp;gt;29 Nov&amp;lt;/s&amp;gt; &amp;lt;br&amp;gt; 2 Dec &lt;br /&gt;
| Fundamental limits&lt;br /&gt;
* Algebraic limits&lt;br /&gt;
* Bode&#039;s integral formula&lt;br /&gt;
* Maximum modulus principle&lt;br /&gt;
|&lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;14.3-14.5&lt;br /&gt;
* Rec: DFT Ch 6&lt;br /&gt;
* Adv: Lewis, Ch 9&lt;br /&gt;
| {{cds131 fa19 pdf|hw9-fa19.pdf|HW #9}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 27 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Dec (Fri) &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;10&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Dec &amp;lt;br&amp;gt; 6 Dec*&lt;br /&gt;
| Review for final&lt;br /&gt;
| Final&lt;br /&gt;
| &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
The final grade will be based on homework sets, a midterm exam, and a final exam: &lt;br /&gt;
&lt;br /&gt;
*&#039;&#039;Homework (70%):&#039;&#039; Homework sets will be handed out weekly and due on Wednesdays by 2 pm either in class or in the labeled box across from 107 Steele Lab.  Each student is allowed up to two extensions of no more than 2 days each over the course of the term.  Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean.  MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).&lt;br /&gt;
&lt;br /&gt;
:The lowest homework set grade will be dropped when computing your final grade.&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;Final exam (30%):&#039;&#039;  The final exam will be handed out on the last day of class (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing.  Any computer code that is used to solve homework problems is considered part of your writeup and should be done individually (you can share ideas, but not code).&lt;br /&gt;
&lt;br /&gt;
No collaboration is allowed on the final exam.&lt;br /&gt;
&lt;br /&gt;
=== Course Text and References ===&lt;br /&gt;
&lt;br /&gt;
The primary course texts are&lt;br /&gt;
* [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org &#039;&#039;Feedback Systems: An Introduction for Scientists and Engineers&#039;&#039;], Princeton University Press, Second Edition*, 2019.&lt;br /&gt;
* [FBS2s] Richard M. Murray, &#039;&#039;{{cds131 fa19 pdf|fbs-linsys_14Oct2019.pdf|Feedback Systems:  Notes on Linear Systems Theory}}&#039;&#039;, 2019. (Updated 14 Oct 2019)&lt;br /&gt;
* [DFT] J. Doyle, B. Francis and A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.pdf &#039;&#039;Feedback Control Theory&#039;&#039;], Dover, 2009 (originally published by Macmillan, 1992).&lt;br /&gt;
* [OBC] R. M. Murray, &amp;quot;Optimization-Based Control&amp;quot;, 2010. [http://www.cds.caltech.edu/~murray/amwiki/index.php?title=OBC:Main_Page Online access]&lt;br /&gt;
* [Son98] E. D. Sontag, &#039;&#039;Mathematical Control Theory&#039;&#039;, Springer, 1998. [http://www.math.rutgers.edu/~sontag/mct.html Online access]&lt;br /&gt;
&amp;lt;nowiki&amp;gt;*&amp;lt;/nowiki&amp;gt; Please make sure to use the &#039;&#039;second&#039;&#039; edition [FBS2e].&lt;br /&gt;
&lt;br /&gt;
The following additional references may also be useful:&lt;br /&gt;
&lt;br /&gt;
* [Lew03] A. D. Lewis, &#039;&#039;A Mathematical Approach to Classical Control&#039;&#039;, 2003. [https://mast.queensu.ca/~andrew/teaching/pdf/332-notes.pdf Online access].&lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
* J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), &#039;&#039;Schaum&#039;s Outline of Feedback and Control Systems&#039;&#039;, 2nd Edition, 2013.  &lt;br /&gt;
* B. Friedland, &#039;&#039;Control System Design: An Introduction to State-Space Methods&#039;&#039;, McGraw-Hill, 1986.&lt;br /&gt;
--&amp;gt;&lt;br /&gt;
Note: the only sources listed here are those that allow free access to online versions.  Additional textbooks that are not freely available can be obtained from the library.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23016</id>
		<title>CDS 131, Fall 2019</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=CDS_131,_Fall_2019&amp;diff=23016"/>
		<updated>2019-10-09T01:13:52Z</updated>

		<summary type="html">&lt;p&gt;Apandey: added emails for TAs&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| width=100%&lt;br /&gt;
|-&lt;br /&gt;
| colspan=2 align=center |&lt;br /&gt;
&amp;lt;font color=&#039;blue&#039; size=&#039;+2&#039;&amp;gt;Linear Systems Theory&amp;lt;/font&amp;gt;__NOTOC__&lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Instructors&#039;&#039;&#039;&lt;br /&gt;
* Richard Murray (CDS/BE), murray@cds.caltech.edu&lt;br /&gt;
* Lectures: MWF, 2-3 pm, 213 Annenberg&lt;br /&gt;
| width=50% |&lt;br /&gt;
&#039;&#039;&#039;Teaching Assistants&#039;&#039;&#039;&lt;br /&gt;
* [mailto:jch3n@caltech.edu Jiexin (Jessie) Chen (CDS)], [mailto:apandey@caltech.edu Ayush Pandey (CDS)]&lt;br /&gt;
* Office hours: Fri, 4-5; Tue, 4-5 in 243 Annenberg&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This is the course homepage for CDS 131, Fall 2019.  This course is intended for first year graduate students in controls, advanced undergraduates in EE, ChE, and ME who have taken a basic controls course (e.g., CDS 110, ChE 105, EE 113), and motivated graduate students in other disciplines would would like to learn more about linear systems and control.  All students taking the course should also have a good understanding of (matrix) differential equations and linear algebra.&lt;br /&gt;
&lt;br /&gt;
=== Catalog Description ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;CDS 131. Linear Systems Theory.&#039;&#039;&#039; 9 units (3-0-6); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; state-space and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and output-feedback. Instructor: Murray.&lt;br /&gt;
&lt;br /&gt;
{| border=0 padding=0 width=100% &lt;br /&gt;
|- valign=top&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Lecture Schedule ===&lt;br /&gt;
&lt;br /&gt;
There will be 2-3 one hour lectures per week, with the specific days varying from week-to-week.  The lecture days for each week will be announced in class and posted here at least 1 week in advance.&lt;br /&gt;
&lt;br /&gt;
Reading:&lt;br /&gt;
* Opt = optional reading (useful if you are confused and trying to understand the basic concepts)&lt;br /&gt;
* Rec = recommended reading (this is what the homework is based on)&lt;br /&gt;
* Adv = advanced reading (more detailed results, useful if you are interested in learning more)&lt;br /&gt;
&lt;br /&gt;
| width=50% |&lt;br /&gt;
=== Announcements ===&lt;br /&gt;
* 8 Oct 2019: Fixed bug in definition of linear system in course notes ({{cds131 fa19 pdf|fbs-linsys_08Oct2019.pdf|latest version}})&lt;br /&gt;
* 6 Oct 2019: Course notes have been updated; please download the {{cds131 fa19 pdf|fbs-linsys_08Oct2019.pdf|latest version}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible wikitable&amp;quot; width=100% border=1 cellpadding=5&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Date&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Topic&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Reading&#039;&#039;&#039;&lt;br /&gt;
| &#039;&#039;&#039;Homework&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 1&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
30 Sep &amp;lt;br&amp;gt;  2 Oct &amp;lt;br&amp;gt; 4 Oct*&lt;br /&gt;
| Introduction and review&lt;br /&gt;
* Course logistics&lt;br /&gt;
* Norms of signals in continuous (and discrete) time&lt;br /&gt;
* I/O systems, LTI systems&lt;br /&gt;
* Induced system norms&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e&amp;amp;nbsp;Ch 1 and&amp;amp;nbsp;2&lt;br /&gt;
* Rec: FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;1 (or DFT Sec&amp;amp;nbsp;2.1&amp;amp;#8209;2.4)&lt;br /&gt;
* Adv: Sontag, Ch 2&lt;br /&gt;
| {{cds131 fa19 pdf|hw1-fa19.pdf|HW #1}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 2 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;!-- {{cds131 fa19 pdf|caltech/hw1-fa19_solns.pdf|Solns}} (Caltech only) --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 2&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Richard --&amp;gt;&lt;br /&gt;
7 Oct &amp;lt;br&amp;gt; 9 Oct &amp;lt;br&amp;gt; 11 Oct&lt;br /&gt;
| Linear I/O systems&lt;br /&gt;
* Differential and difference equations (with inputs and outputs, including disturbances and noise)&lt;br /&gt;
* Linearized system dynamics&lt;br /&gt;
* Stability of equilibrium points, I/O stability&lt;br /&gt;
* Convolution equation, impulse response&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Ch 3; DFT&amp;amp;nbsp;Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Rec: FBS2e Sec&amp;amp;nbsp;5.1&amp;amp;#8209;5.3, 6.1&amp;amp;#8209;6.3; FBS2s&amp;amp;nbsp;Ch&amp;amp;nbsp;2&lt;br /&gt;
* Adv: Sontag Sec C.4, 2.6&lt;br /&gt;
| {{cds131 fa19 pdf|hw2-fa19.pdf|HW #2}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 9 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 3&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
14 Oct &amp;lt;br&amp;gt; 16 Oct &amp;lt;br&amp;gt; 18 Oct*&lt;br /&gt;
| Reachability&lt;br /&gt;
* Definitions (reachability, stabilizability)&lt;br /&gt;
* Characterization and rank tests (Grammian, PBH)&lt;br /&gt;
* Decomposition into reachable/unreachable subspaces&lt;br /&gt;
* Eigenvalue placement theorem&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 7.1,&amp;amp;nbsp;7.2; Sontag Sec&amp;amp;nbsp;3.1&amp;amp;#8209;3.3&lt;br /&gt;
* Adv: FBS2e Sec&amp;amp;nbsp;7.3; Sontag Sec&amp;amp;nbsp;3.5&lt;br /&gt;
| {{cds131 fa19 pdf|hw3-fa19.pdf|HW #3}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 16 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 4&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
21 Oct &amp;lt;br&amp;gt; 23 Oct &amp;lt;br&amp;gt; 25 Oct*&lt;br /&gt;
| State feedback&lt;br /&gt;
* Optimization and optimal control&lt;br /&gt;
* Linear quadratic regulator (including Ricatti equation)&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e  Sec 7.5&lt;br /&gt;
* Rec: OBC Ch&amp;amp;nbsp;2&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;8.1&amp;amp;#8209;8.3, 9.1,&amp;amp;nbsp;9.2&lt;br /&gt;
| {{cds131 fa19 pdf|hw4-fa19.pdf|HW #4}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 23 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 5&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
28 Oct &amp;lt;br&amp;gt; 30 Oct* &amp;lt;br&amp;gt; 1 Nov&lt;br /&gt;
| Observability and state estimation&lt;br /&gt;
* Definitions (observability, observable subspace)&lt;br /&gt;
* Characterization and rank tests&lt;br /&gt;
* Kalman decomposition&lt;br /&gt;
* Linear observers (full-state)&lt;br /&gt;
| &lt;br /&gt;
* Rec: FBS2e Sec 8.1-8.3&lt;br /&gt;
* Adv: Sontag Sec&amp;amp;nbsp;6.1&amp;amp;#8209;6.3, 7.1&lt;br /&gt;
|  {{cds131 fa19 pdf|hw5-fa19.pdf|HW #5}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 30 Oct &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 6&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Nov &amp;lt;br&amp;gt; 6 Nov &amp;lt;br&amp;gt; 8 Nov*&lt;br /&gt;
| Frequency domain modeling&lt;br /&gt;
* Control system transfer functions&lt;br /&gt;
* State space realizations, minimal realizations&lt;br /&gt;
* Poles and zeros&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS23 Ch 2&lt;br /&gt;
* Rec: FBS2e Ch&amp;amp;nbsp;9; DFT Sec&amp;amp;nbsp;2.6&lt;br /&gt;
* Adv: Lewis Ch 3 and 4&lt;br /&gt;
&amp;lt;!-- * Adv: [[http:web.mit.edu/6.242/www/images/lec5_6242_2004.pdf|Notes on balanced truncation (Megretski, 2004)]] --&amp;gt;&lt;br /&gt;
|  {{cds131 fa19 pdf|hw6-fa19.pdf|HW #6}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 6 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week 7&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
11 Nov &amp;lt;br&amp;gt; 13 Nov &amp;lt;br&amp;gt; 15 Nov*&lt;br /&gt;
| Frequency domain analysis&lt;br /&gt;
* Internal stability&lt;br /&gt;
* Tracking, disturbance rejection&lt;br /&gt;
* I/O performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.1-10.2, Sec&amp;amp;nbsp;12.1-12.2&lt;br /&gt;
* Rec: DFT Ch 3&lt;br /&gt;
* Adv: Lewis Ch 5-8&lt;br /&gt;
| {{cds131 fa19 pdf|hw7-fa19.pdf|HW #7}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 13 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;8&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
18 Nov &amp;lt;br&amp;gt; 20 Nov* &amp;lt;br&amp;gt; 22 Nov&lt;br /&gt;
| Uncertainty and robustness&lt;br /&gt;
* Types of uncertainty: parametric, operator, disturbances/noise&lt;br /&gt;
* Robust stability and robust performance&lt;br /&gt;
| &lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;10.3, Sec&amp;amp;nbsp;13.1-13.3&lt;br /&gt;
* Rec: DFT Ch 4&lt;br /&gt;
|  {{cds131 fa19 pdf|hw8-fa19.pdf|HW #8}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 20 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 27 Nov  &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;9&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Jessie --&amp;gt;&lt;br /&gt;
25 Nov &amp;lt;br&amp;gt; 27 Nov* &amp;lt;br&amp;gt; &amp;lt;s&amp;gt;19 Nov&amp;lt;/s&amp;gt; &amp;lt;br&amp;gt; 2 Dec &lt;br /&gt;
| Fundamental limits&lt;br /&gt;
* Algebraic limits&lt;br /&gt;
* Bode&#039;s integral formula&lt;br /&gt;
* Maximum modulus principle&lt;br /&gt;
|&lt;br /&gt;
* Opt: FBS2e Sec&amp;amp;nbsp;14.3-14.5&lt;br /&gt;
* Rec: DFT Ch 6&lt;br /&gt;
* Adv: Lewis, Ch 9&lt;br /&gt;
| {{cds131 fa19 pdf|hw9-fa19.pdf|HW #9}} &amp;lt;br&amp;gt;&lt;br /&gt;
Out: 27 Nov &amp;lt;br&amp;gt;&lt;br /&gt;
Due: 6 Dec (Fri) &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- valign=top&lt;br /&gt;
| &#039;&#039;&#039;Week&amp;amp;nbsp;10&#039;&#039;&#039;&amp;lt;br&amp;gt; &amp;lt;!-- Ayush --&amp;gt;&lt;br /&gt;
4 Dec &amp;lt;br&amp;gt; 6 Dec*&lt;br /&gt;
| Review for final&lt;br /&gt;
| Final&lt;br /&gt;
| &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== Grading ===&lt;br /&gt;
The final grade will be based on homework sets, a midterm exam, and a final exam: &lt;br /&gt;
&lt;br /&gt;
*&#039;&#039;Homework (70%):&#039;&#039; Homework sets will be handed out weekly and due on Wednesdays by 2 pm either in class or in the labeled box across from 107 Steele Lab.  Each student is allowed up to two extensions of no more than 2 days each over the course of the term.  Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean.  MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).&lt;br /&gt;
&lt;br /&gt;
:The lowest homework set grade will be dropped when computing your final grade.&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;Final exam (30%):&#039;&#039;  The final exam will be handed out on the last day of class (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).&lt;br /&gt;
&lt;br /&gt;
=== Collaboration Policy ===&lt;br /&gt;
&lt;br /&gt;
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing.  Any computer code that is used to solve homework problems is considered part of your writeup and should be done individually (you can share ideas, but not code).&lt;br /&gt;
&lt;br /&gt;
No collaboration is allowed on the final exam.&lt;br /&gt;
&lt;br /&gt;
=== Course Text and References ===&lt;br /&gt;
&lt;br /&gt;
The primary course texts are&lt;br /&gt;
* [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org &#039;&#039;Feedback Systems: An Introduction for Scientists and Engineers&#039;&#039;], Princeton University Press, Second Edition*, 2019.&lt;br /&gt;
* [FBS2s] Richard M. Murray, &#039;&#039;{{cds131 fa19 pdf|fbs-linsys_08Oct2019.pdf|Feedback Systems:  Notes on Linear Systems Theory}}&#039;&#039;, 2019. (Updated 8 Oct 2019)&lt;br /&gt;
* [DFT] J. Doyle, B. Francis and A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.pdf &#039;&#039;Feedback Control Theory&#039;&#039;], Dover, 2009 (originally published by Macmillan, 1992).&lt;br /&gt;
* [OBC] R. M. Murray, &amp;quot;Optimization-Based Control&amp;quot;, 2010. [http://www.cds.caltech.edu/~murray/amwiki/index.php?title=OBC:Main_Page Online access]&lt;br /&gt;
* [Son98] E. D. Sontag, &#039;&#039;Mathematical Control Theory&#039;&#039;, Springer, 1998. [http://www.math.rutgers.edu/~sontag/mct.html Online access]&lt;br /&gt;
&amp;lt;nowiki&amp;gt;*&amp;lt;/nowiki&amp;gt; Please make sure to use the &#039;&#039;second&#039;&#039; edition [FBS2e].&lt;br /&gt;
&lt;br /&gt;
The following additional references may also be useful:&lt;br /&gt;
&lt;br /&gt;
* [Lew03] A. D. Lewis, &#039;&#039;A Mathematical Approach to Classical Control&#039;&#039;, 2003. [https://mast.queensu.ca/~andrew/teaching/pdf/332-notes.pdf Online access].&lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
* J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), &#039;&#039;Schaum&#039;s Outline of Feedback and Control Systems&#039;&#039;, 2nd Edition, 2013.  &lt;br /&gt;
* B. Friedland, &#039;&#039;Control System Design: An Introduction to State-Space Methods&#039;&#039;, McGraw-Hill, 1986.&lt;br /&gt;
--&amp;gt;&lt;br /&gt;
Note: the only sources listed here are those that allow free access to online versions.  Additional textbooks that are not freely available can be obtained from the library.&lt;br /&gt;
&lt;br /&gt;
[[Category: Courses]]&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Jake_Beal,_1_Oct_2019&amp;diff=22961</id>
		<title>Jake Beal, 1 Oct 2019</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Jake_Beal,_1_Oct_2019&amp;diff=22961"/>
		<updated>2019-09-30T23:04:48Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Schedule */  added Ayush and Chelsea for 4pm&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Jake Beal will visit Caltech on 1 Oct 2019.  If you would like to meet with him, please sign up below.&lt;br /&gt;
&lt;br /&gt;
=== Schedule ===&lt;br /&gt;
* 9:00a: RMM group meeting, 111 Keck (if interested)&lt;br /&gt;
* 11:00a: James&lt;br /&gt;
* 11:45a: seminar setup&lt;br /&gt;
* 12:00p: Seminar, 111 Keck (abstract below)&lt;br /&gt;
* 1:00p: Lunch with Andrey Shur, Sam Clamons&lt;br /&gt;
* 1:45p: Lab tour and calibration discussion (Andrey, Sam, Mark, Miki)&lt;br /&gt;
* 2:30p: John Marken&lt;br /&gt;
* 3:15p: Elin Larsson &lt;br /&gt;
* 4:00p: Ayush and Chelsea&lt;br /&gt;
* 4:45p: Wrap up with Richard&lt;br /&gt;
&lt;br /&gt;
=== Talk abstract ===&lt;br /&gt;
&lt;br /&gt;
Paths to Resilient Biological Information Processing&amp;lt;br&amp;gt;&lt;br /&gt;
Jake Beal (Raytheon BBN)&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 October (Tue), 12-1 pm, 111 Keck&lt;br /&gt;
&lt;br /&gt;
Engineered information processing in biological organisms has potential revolutionary implications across many application domains. A major barrier, however, has been the fragility of biological information processing devices to changes in their usage, genetic context, or operating environment. Engineering resilient information processing, however, is not just a biological challenge, but a three-way interplay between device performance, measurement quality, and model accuracy. In this talk, I will discuss how the interplay between these three aspects offer multiple paths for improving the resilience of biological information processing, giving examples of recent progress in reproducible and comparable measurement, the development of high-performance devices and insulators, and precision prediction of genetic circuits.&lt;br /&gt;
&lt;br /&gt;
Dr. Jacob Beal is a Senior Scientist at Raytheon BBN Technologies, where he leads research on synthetic biology and distributed systems engineering. His work in synthetic biology includes development of methods for calibrated flow cytometry, precision analysis and design of genetic regulatory networks, engineering of biological information processing devices, standards for representation and communication of biological designs, and signature-based detection of pathogenic sequences.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Paul_Van_den_Hof,_Dec_2018&amp;diff=22277</id>
		<title>Paul Van den Hof, Dec 2018</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Paul_Van_den_Hof,_Dec_2018&amp;diff=22277"/>
		<updated>2018-12-05T02:52:57Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Schedule */  minor typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Paul van den Hof is Full Professor and Chair of the Control Systems (CS) Group at the Department of Electrical Engineering. He is interested in data-driven modeling, control and optimization of dynamic systems in several technological fields: industrial process control, oil reservoir engineering, high-tech mechatronic and cyber-physical systems, etc. His focus is the development of fundamental techniques, such as data-driven modeling, closed-loop and control-oriented identification and data analytics, experimental design and performance monitoring, and model-based control, monitoring and optimization.&lt;br /&gt;
&lt;br /&gt;
=== Schedule ===&lt;br /&gt;
&lt;br /&gt;
* 10 am: Richard Murray, 107 Steele Lab&lt;br /&gt;
* 10:30 am: open&lt;br /&gt;
* 11:00 am: open&lt;br /&gt;
* 11:45 am: Lunch with CDS faculty&lt;br /&gt;
* 1:00 pm: Seminar, 106 Annenberg&lt;br /&gt;
* 2:00 pm: Soon-Jo Chung, 106 Annenberg&lt;br /&gt;
* 2:45 pm: Open&lt;br /&gt;
* 3:30 pm: Richard Murray, 107 Steele Lab&lt;br /&gt;
* 4:00 pm: Chelsea and Ayush, 2nd floor lounge, Annenberg&lt;br /&gt;
* 4:45 pm: Open (if nothing else available)&lt;br /&gt;
* 5:30 pm: Depart&lt;br /&gt;
&lt;br /&gt;
=== Seminar ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Data-driven modeling in linear dynamic networks&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
Friday, December 7th at 1pm, 106 Annenberg&lt;br /&gt;
 &lt;br /&gt;
In many areas of science and technology, the complexity of dynamic systems that are being considered, grows beyond the level of single systems into interconnected networks of dynamic systems. In control and optimization this has led to the development of decentralized and distributed algorithms for control/optimization, as e.g. in multi-agent systems. &lt;br /&gt;
From the modelling perspective, data-driven modelling tools are typically developed for relatively simple open-loop and closed-loop structures, while the opportunities for big data handling in the current data science era, are becoming abundant. As a result there is a strong need for the development of data-driven modelling tools for large-scale interconnected dynamic networks.&lt;br /&gt;
In this seminar we will highlight the main developments and challenges in this area. Besides setting up a modelling framework, we will address problems of local identification of a particular part of the network, including the selection of the appropriate signals to be measured. The concept of network identifiability is highlighted and the role of structural properties of the network, in terms of its topology/graph, is given strong attention. It is also shown how classical closed-loop identification methods need to be generalized to be able to cope with the new situations.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Paul_Van_den_Hof,_Dec_2018&amp;diff=22276</id>
		<title>Paul Van den Hof, Dec 2018</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Paul_Van_den_Hof,_Dec_2018&amp;diff=22276"/>
		<updated>2018-12-05T02:48:53Z</updated>

		<summary type="html">&lt;p&gt;Apandey: /* Schedule */ setting up appointment with Chelsea Hu and Ayush&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Paul van den Hof is Full Professor and Chair of the Control Systems (CS) Group at the Department of Electrical Engineering. He is interested in data-driven modeling, control and optimization of dynamic systems in several technological fields: industrial process control, oil reservoir engineering, high-tech mechatronic and cyber-physical systems, etc. His focus is the development of fundamental techniques, such as data-driven modeling, closed-loop and control-oriented identification and data analytics, experimental design and performance monitoring, and model-based control, monitoring and optimization.&lt;br /&gt;
&lt;br /&gt;
=== Schedule ===&lt;br /&gt;
&lt;br /&gt;
* 10 am: Richard Murray, 107 Steele Lab&lt;br /&gt;
* 10:30 am: open&lt;br /&gt;
* 11:00 am: open&lt;br /&gt;
* 11:45 am: Lunch with CDS faculty&lt;br /&gt;
* 1:00 pm: Seminar, 106 Annenberg&lt;br /&gt;
* 2:00 pm: Soon-Jo Chung, 106 Annenberg&lt;br /&gt;
* 2:45 pm: Open&lt;br /&gt;
* 3:30 pm: Richard Murray, 107 Steele Lab&lt;br /&gt;
* 4:00 pm: Chelsea and Ayush, 2nd floor lounge, Annenberg)&lt;br /&gt;
* 4:45 pm: Open (if nothing else available)&lt;br /&gt;
* 5:30 pm: Depart&lt;br /&gt;
&lt;br /&gt;
=== Seminar ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Data-driven modeling in linear dynamic networks&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
Friday, December 7th at 1pm, 106 Annenberg&lt;br /&gt;
 &lt;br /&gt;
In many areas of science and technology, the complexity of dynamic systems that are being considered, grows beyond the level of single systems into interconnected networks of dynamic systems. In control and optimization this has led to the development of decentralized and distributed algorithms for control/optimization, as e.g. in multi-agent systems. &lt;br /&gt;
From the modelling perspective, data-driven modelling tools are typically developed for relatively simple open-loop and closed-loop structures, while the opportunities for big data handling in the current data science era, are becoming abundant. As a result there is a strong need for the development of data-driven modelling tools for large-scale interconnected dynamic networks.&lt;br /&gt;
In this seminar we will highlight the main developments and challenges in this area. Besides setting up a modelling framework, we will address problems of local identification of a particular part of the network, including the selection of the appropriate signals to be measured. The concept of network identifiability is highlighted and the role of structural properties of the network, in terms of its topology/graph, is given strong attention. It is also shown how classical closed-loop identification methods need to be generalized to be able to cope with the new situations.&lt;/div&gt;</summary>
		<author><name>Apandey</name></author>
	</entry>
</feed>