Murray Wiki - User contributions [en]

CDS 110b: Robust Performance

2006-03-08T01:16:32Z

Gillula:

{{cds110b-wi06}}
This lecture describes ???. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> ???
</ol>

== Lecture Materials ==
* Lecture Notes??? (MP3???)
* Reading: ???
* {{cds110b-pdfs|hw8.pdf|HW #8}} (due 8 Mar)

== References and Further Reading ==

== Frequently Asked Questions ==
'''Q: Is problem 3 impossible?'''
<blockquote>
<p>It might be -- we're not sure. As a general recommendation, if you think a problem is impossible, explain why you think it is impossible, and then relax the specifications and try to solve it again. As long as you don't make it trivial, you'll likely get a decent amount of partial credit.</p>
</blockquote>

CDS 110b: Robust Stability

2006-02-28T19:26:04Z

Gillula: /* Frequently Asked Questions */

{{cds110b-wi06}}
This lecture describes how to model uncertainty in <math>H_\infty</math> control and provides conditions for checking robust stability in this framework. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Modeling uncertainty
<li> Robust stability
<li> Preview: robust performance
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L8-1_robstab.pdf|Lecture notes}} ({{cds110b-pdfs|L8-1_robstab.mp3|MP3}})
* Reading: DFT, Chapter 4
* {{cds110b-pdfs|hw7.pdf|HW #7}} (due 1 Mar)

== References and Further Reading ==

== Frequently Asked Questions ==
'''Q: Is there any way to bode plot (exp(-ts)-1) in MATLAB?'''
<blockquote>
<p>You can't use the 'bode' command, since the exponential makes that expression not a polynomial transfer function. If all you're interested in is the magnitude though, (as in this week's homework set) you can plot that explicitly, as follows. (This should look familiar for those of you who took 110A, since we had you do a bode plot without using the bode command a long time ago.)</p>

<pre>
omega = logspace(some_start, some_end, some_num);
loglog(omega, abs(exp(-t*i*omega)-1));
</pre>

<p>I recommend doing help logspace and help loglog to understand what those functions do -- they're not too tricky.</p>
</blockquote>

CDS 110b: Robust Stability

2006-02-28T19:25:34Z

Gillula: /* Frequently Asked Questions */

{{cds110b-wi06}}
This lecture describes how to model uncertainty in <math>H_\infty</math> control and provides conditions for checking robust stability in this framework. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Modeling uncertainty
<li> Robust stability
<li> Preview: robust performance
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L8-1_robstab.pdf|Lecture notes}} ({{cds110b-pdfs|L8-1_robstab.mp3|MP3}})
* Reading: DFT, Chapter 4
* {{cds110b-pdfs|hw7.pdf|HW #7}} (due 1 Mar)

== References and Further Reading ==

== Frequently Asked Questions ==
'''Q: Is there any way to bode plot (exp(-ts)-1) in MATLAB?'''
<blockquote>
You can't use the 'bode' command, since the exponential makes that expression not a polynomial transfer function. If all you're interested in is the magnitude though, (as in this week's homework set) you can plot that explicitly, as follows. (This should look familiar for those of you who took 110A, since we had you do a bode plot without using the bode command a long time ago.)

omega = logspace(some_start, some_end, some_num);
loglog(omega, abs(exp(-t*i*omega)-1));

I recommend doing help logspace and help loglog to understand what those functions do -- they're not too tricky.
</blockquote>

CDS 110b: Sensor Fusion

2006-02-12T05:19:10Z

Gillula: /* Frequently Asked Questions */

{{cds110b-wi06}}
In this lecture we show how the Kalman filter can be used for sensor fusion and explore some variations on the basic Kalman filter, including the extended Kalman filter. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Sensor fusion using Kalman filters
<li> The extended Kalman filter
* Ducted fan example: {{cds110b-pdfs|dfan_kf.m|dfan_kf.m}}, {{cds110b-pdfs|pvtol.m|pvtol.m}}
<li> Parameter estimation using EKF
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L6-1_fusion.pdf|Lecture presentation}} ({{cds110b-pdfs|L6-1_fusion.mp3|MP3}})
* {{cds110b-pdfs|kalman.pdf|Lecture Notes on Kalman Filters}}
* Reading: Friedland, Chapter 11
* {{cds110b-pdfs|hw5.pdf|HW #5}}, due 13 Feb (Mon)
** [http://www.nsd.es.northropgrumman.com/Html/LN-200/ LN-200 IMU data sheet]

== References and Further Reading ==

== Frequently Asked Questions ==
'''Q: How do you deal with time correlated noise (eg, GPS jumps on Alice)?'''
<blockquote>
<p>Correlated noise can be put into the Kalman filtering framework by using a (linear) filter to give a correlated noise source with a given correlation function (or spectral density). Suppose that <math>H(s)</math> is a transfer function that filters Gaussian white noise and provides the desired correlation. Let <math>(A_f, B_f, C_f)</math> be a state space representation for the filter. Then the entire system can be written as
<center>
{|
|-
| <math>
\left[\begin{matrix} x \\ z \end{matrix}\right] =
\left[\begin{matrix} A & F C_f \\ 0 & A_f \end{matrix}\right] \left[\begin{matrix} x \\ z \end{matrix}\right] +
\left[\begin{matrix} B \\ 0 \end{matrix}\right] u +
\left[\begin{matrix} 0 \\ B_f \end{matrix}\right] v
</math>
|-
| <math>
y = \left[\begin{matrix} C & 0 \end{matrix}\right] \left[\begin{matrix} x \\ z \end{matrix}\right] + w
</math>
|}
</center>
This system takes a Guassian white noise input <math>v</math>, filters it to give the desired spectrum, and uses it to drive the system.</p>

<p>For Alice, the most correct approach would be to model the noise as something other than a Gaussian process (in which case the theory we have studied doesn't directly apply). However, we can also take data from the sensor and develop the correlation function numerically, then determine the linear system that best models the correlation.</p>
</blockquote>

'''Q: In problem 1(a), can we assume <math>\alpha</math> and <math>\beta</math> as given in homework #2 when doing our plots? Can we also assume them when doing the calculations?'''
<blockquote>
Getting an expression first in terms of <math>\alpha</math> and <math>\beta</math> would be good, and then plugging in the values from homework #2. (And as always, if you used different values, please be sure to clearly state that.)
</blockquote>

'''Q: In problem 1(b), what transfer function should we use to calculate the gain margin? I know we want open loop, but do we want to break the loop such that it's SISO?'''
<blockquote>
Yes, break the loop so it's SISO. In the coming weeks we'll make clear exactly where we'd want to break the loop and why based on precisely where the disturbances and noise are, but for now...just pick a SISO break spot.
</blockquote>

'''Q: In dfan_kf.m, shouldn’t P22 be y1(:,20) and P33 be y1(:,27)?'''
<blockquote>
Good catch! There is a mistake in the file. You need to add 7 to each entry to go from one diagonal entry to the next. The code as written will plot the first column of the P matrix.
</blockquote>

'''Q: What's up with the units of the power spectral density on the LN200 datasheet? Why is it in degrees/sqrt(hr)?'''
<blockquote>
Sometimes, the square root of the PSD is given instead of the PSD, as in this case. Thus, to get the PSD, you'll need to square the given value. (Also, remember that the units of PSD are not the same as the units of the covariance, e.g. <math>\sigma^2</math>. Because integrating the PSD over a band of frequencies will give you the correlation in the frequency band, the units of the PSD should be the units of <math>\sigma^2</math>divided by Hz.)
</blockquote>

CDS 110b: Sensor Fusion

2006-02-11T20:18:16Z

Gillula: /* Frequently Asked Questions */

CDS 110b: Sensor Fusion

2006-02-11T07:32:28Z

Gillula: /* Frequently Asked Questions */

CDS 110b, Winter 2006

2006-02-10T23:52:00Z

Gillula: /* Announcements */

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

<table width=80%>
<tr valign=top>
<td>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 4-5 pm
<td>
'''Teaching Assistants''' ([mailto:cds110-tas@cds.caltech.edu cds110-tas@cds])
* [[User:Gillula|Jeremy Gillula]], jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
* Office hours: Fri, 4-5p & Sun 4-6p in 110 STL
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 6 Feb: {{cds110b-pdfs|hw5.pdf|HW #5}} is now posted ([http://www.nsd.es.northropgrumman.com/Html/LN-200/ datasheet here]). Due 13 Feb (Mon)
* 3 Feb: Please remember to turn in the {{cds110b-pdfs|mtsurvey.pdf|midterm survey}}
* 3 Feb: HW 4 [[Media:Hw4sol.pdf|solutions]] are now posted.

== Course Syllabus ==

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

* [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-students cds110-students mailing list] - all students in the class should be signed up on this list ([http://listserv.cds.caltech.edu/pipermail/cds110-students/ archive])

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. ([http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Google Books])
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>{{cds110b-pdfs|LS95-optimal.pdf|LS95, 3.1-3.2}} <td rowspan=3> {{cds110b-pdfs|hw1.pdf|HW 1}}, {{cds110b-pdfs|soln1.pdf|Solns}}
<tr><td>6 Jan (F) <td> [[CDS 110b: Control Implementation|Course Project overview]] (optional) <td>

<tr><td rowspan=3 valign=middle>

===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>{{cds110b-pdfs|hw2.pdf|HW 2}}, {{cds110b-pdfs|soln2.pdf|Solns}}
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> [http://www.cds.caltech.edu/~murray/papers/2001n_mur+03-sec.html Murray et al, 2003] <td rowspan=3>{{cds110b-pdfs|hw3.pdf|HW 3}}, {{cds110b-pdfs|soln3.pdf|Solns}}

<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> [[CDS 110b: Observability and Estimators|Observability and Estimators]] <td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> [[CDS 110b: Random Processes|Random Processes]] <td rowspan=2> Friedland, Ch 10 <td rowspan=2>{{cds110b-pdfs|hw4.pdf|HW 4}}, [[Media:Hw4sol.pdf|Solns]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> [[CDS 110b: Stochastic Systems|Stochastic Systems]]
<tr><td> 1 Feb (W) <td> [[CDS 110b: Kalman Filtering|Kalman Filters]] <td> Friedland, Ch 11 <td rowspan=2> Midterm (due 7 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b:Sensor Fusion|Sensor Fusion]] <td> Friedland, Ch 11 + notes <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}}

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]] <td rowspan=3>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td>
<tr> <td> 22 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}
<tr><td> 1 Mar (W) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=3>[[CDS 110b: Homework 8|HW 8]]

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M)
<tr><td> 8 Mar (W) <td> [[CDS 110b: Design Example|Design Example]] <td> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}}
<tr><td> 10 Mar <td> Final review (optional) <td> <td> Final (due 17 Mar)
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a description of the (nonlinear) model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

A special set of lectures on [[CDS 110b: Control Implementation|control implementation]] will be given for students interested in purusing the course project.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

== Old Announcements ==
* 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele
* 4 Jan 05: Please turn in {{cds110b-pdfs|scheduling.pdf|course scheduling form}} by 6 Jan (Fri), 5 pm
* 4 Jan 05: {{cds110b-pdfs|hw1.pdf|HW #1}} is now available; due 11 Jan (Wed)
* 4 Jan 05: <font color=red>No class on Monday (9 Jan)</font>; the next regularly schedule class is Wed from 1:30-3:00 pm
* 7 Jan 05: Office hours will be on Sun from 4-5 pm and Tue from 4-6 pm in <s>125</s> 110 Steele ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000005.html details])
* 6 Jan 05: There will be a [[CDS 110b: Control Implementation|course project]] information session today (Fri) at 2 pm in 125 Steele
* 10 Jan 05: Office hours will now be in 110 Steele, same times as before (check 125 Steele if nobody is in 110 Steele)
* 11 Jan 05: {{cds110b-pdfs|hw2.pdf|HW #2}} is now available; due 18 Jan (Wed)
* 12 Jan 05: Lectures are now available in MP3 format; see individual lecture pages for link
* 15 Jan 05: {{cds110b-pdfs|hw2.pdf|HW #2}} has been updated with some improved notation ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000006.html details])
* 15 Jan 05: A new mailing list, [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-project cds110-project], has been set up for students participating in the course project
* 18 Jan 05: {{cds110b-pdfs|soln1.pdf|HW #1 Solutions}} are now posted. Average = 27/30
* 18 Jan 05: Next week's lectures will be on Mon and Wed from '''2-3 pm''' in 102 Steele
* 18 Jan 05: {{cds110b-pdfs|hw3.pdf|HW #3}} has been posted
* 25 Jan 05: {{cds110b-pdfs|soln2.pdf|HW #2 Solutions}} are now posted. Average = 31/40
* 25 Jan 05: {{cds110b-pdfs|hw4.pdf|HW #4}} is now posted. Due 1 Feb @ 5 pm

User:Gillula

2006-02-09T06:06:14Z

Gillula: /* Jeremy Gillula */

[[Image:Gillula.PNG|right|frame|I look vaguely like this]]
= Jeremy Gillula =
* Position: Lab TA for [[Cds110b|CDS 110B]] for 2005-2006 winter term. (It may say lab TA, but I'm happy to help with anything 110B related)
* Contact Info: jeremy@caltech.edu
* Office Hours: Fri, 4-5pm, 125 Steele; or by appointment - just email me

CDS 110b: State Estimation

2006-01-24T15:30:17Z

Gillula: Fixing a broken link

{{cds110b-wi06}}
This lecture presents an introduction to state estimation and observers. Beginning with a definition of observability, we provide conditions under which a linear system is observable and show how to construct an observer in the case where there is no noise. We then prove the ''separation principle'', which shows how to combine state regulation with state estimation. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Observability
* Definition of observability (full nonlinear system)
* Observability conditions for linear processes: intuition + proof
<li> State Estimation
* Luenberger observer
* Example: ducted fan
<li> Separation Principle
* Proof of the separation principle
* Transfer function representation
* Example: ducted fan
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L4-1_observability.pdf|Lecture Presentation}} ({{cds110b-pdfs|L4-1_observers.mp3|MP3}})
* Reading: {{am05|Chapter_6_-_Output_Feedback|Sec 6.1-6.3}}
* {{cds110b-pdfs|obs_dfan.m|obs_dfan.m}} - sample computations for Caltech ducted fan

== References and Further Reading ==
* Friedland, Chapters 7 and 8

== Frequently Asked Questions ==

'''Q: Is there any relationship between observability and differential flatness?'''
<blockquote>
<p>There is indeed a relationship, of sorts. Strictly speaking, when we talk about differential flatness, we do so independent of the specific outputs for the system. A system is flat if ''there exist'' outputs such that we can characterize the trajectories of the system (states and inputs) as a function of the flat outputs and their derivatives. As one might imagine, with this choice of outputs, the system is ''always'' observable.</p>

<p>On the other hand, a system might be observable with a certain set of outputs, but those outputs are not necessarily differentially flat outputs. For example, consider the system
<center><math>
\begin{matrix}
\dot x &= \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} x & + \begin{bmatrix}0 \\ 1 \end{bmatrix} u \\
y &= \begin{bmatrix} 1 & 1 \end{bmatrix} x &
\end{matrix}
</math></center>
This matrix is observable (easy to check by computing the observability matrix), but with the given output, it is not possible to compute the input and state. (Note that you can compute the state given the input; just not the state ''and'' input given the output.)</p>

<p> The basic issue in this example is that the process has a zero and hence there is an input such that the corresponding output is identically zero. </p>
</blockquote>

CDS 110b, Winter 2006

2006-01-19T06:16:46Z

Gillula: /* Old Announcements */

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

<table width=80%>
<tr valign=top>
<td>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 4-5 pm
<td>
'''Teaching Assistants''' ([mailto:cds110-tas@cds.caltech.edu cds110-tas@cds])
* [[User:Gillula|Jeremy Gillula]], jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
* Office hours: Sun, 4-5p & Tue 4-6p in 110 STL
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 18 Jan 05: {{cds110b-pdfs|hw3.pdf|HW #3}} has been posted
* 18 Jan 05: Next week's lectures will be on Mon and Wed from '''2-3 pm''' in 102 Steele
* 18 Jan 05: {{cds110b-pdfs|soln1.pdf|HW #1 Solutions}} are now posted. Average = 27/30
* 15 Jan 05: A new mailing list, [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-project cds110-project], has been set up for students participating in the course project

== Course Syllabus ==

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

* [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-students cds110-students mailing list] - all students in the class should be signed up on this list ([http://listserv.cds.caltech.edu/pipermail/cds110-students/ archive])

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. ([http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Google Books])
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>{{cds110b-pdfs|LS95-optimal.pdf|LS95, 3.1-3.2}} <td rowspan=3> {{cds110b-pdfs|hw1.pdf|HW 1}}, {{cds110b-pdfs|soln1.pdf|Solns}}
<tr><td>6 Jan (F) <td> [[CDS 110b: Control Implementation|Course Project overview]] (optional) <td>

<tr><td rowspan=3 valign=middle>

===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>{{cds110b-pdfs|hw2.pdf|HW 2}}
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> [http://www.cds.caltech.edu/~murray/papers/2001n_mur+03-sec.html Murray et al, 2003] <td rowspan=3>{{cds110b-pdfs|hw3.pdf|HW 3}} (due 25 Jan)

<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> Observability and Estimators<td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> Introduction to Random Processes <td> Friedland, Ch 10 <td rowspan=2> [[CDS 110b: Homework 4|HW 4]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> Linear Quadratic Estimators (LQE) <td rowspan=2> Friedland, Ch 11
<tr><td> 1 Feb (W) <td> Kalman Filtering <td rowspan=2> Midterm (due 6 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}} <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]]

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td> <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]
<tr><td> 22 Feb (W) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=2>[[CDS 110b: Homework 8|HW 8]]
<tr><td> 1 Mar (W)

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M) <td rowspan=2> [[CDS 110b: Design Example|Design Example]] <td rowspan=2> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}} <td rowspan=3> Final (due 17 Mar)
<tr><td> 8 Mar (W)
<tr><td> 10 Mar <td> Final review (optional) <td>
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a description of the (nonlinear) model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

A special set of lectures on [[CDS 110b: Control Implementation|control implementation]] will be given for students interested in purusing the course project.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

== Old Announcements ==
* 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele
* 4 Jan 05: Please turn in {{cds110b-pdfs|scheduling.pdf|course scheduling form}} by 6 Jan (Fri), 5 pm
* 4 Jan 05: {{cds110b-pdfs|hw1.pdf|HW #1}} is now available; due 11 Jan (Wed)
* 4 Jan 05: <font color=red>No class on Monday (9 Jan)</font>; the next regularly schedule class is Wed from 1:30-3:00 pm
* 7 Jan 05: Office hours will be on Sun from 4-5 pm and Tue from 4-6 pm in <s>125</s> 110 Steele ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000005.html details])
* 6 Jan 05: There will be a [[CDS 110b: Control Implementation|course project]] information session today (Fri) at 2 pm in 125 Steele
* 10 Jan 05: Office hours will now be in 110 Steele, same times as before (check 125 Steele if nobody is in 110 Steele)
* 11 Jan 05: {{cds110b-pdfs|hw2.pdf|HW #2}} is now available; due 18 Jan (Wed)
* 12 Jan 05: Lectures are now available in MP3 format; see individual lecture pages for link
* 15 Jan 05: {{cds110b-pdfs|hw2.pdf|HW #2}} has been updated with some improved notation ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000006.html details])

CDS 110b, Winter 2006

2006-01-19T06:16:24Z

Gillula: /* Announcements */

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

<table width=80%>
<tr valign=top>
<td>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 4-5 pm
<td>
'''Teaching Assistants''' ([mailto:cds110-tas@cds.caltech.edu cds110-tas@cds])
* [[User:Gillula|Jeremy Gillula]], jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
* Office hours: Sun, 4-5p & Tue 4-6p in 110 STL
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 18 Jan 05: {{cds110b-pdfs|hw3.pdf|HW #3}} has been posted
* 18 Jan 05: Next week's lectures will be on Mon and Wed from '''2-3 pm''' in 102 Steele
* 18 Jan 05: {{cds110b-pdfs|soln1.pdf|HW #1 Solutions}} are now posted. Average = 27/30
* 15 Jan 05: A new mailing list, [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-project cds110-project], has been set up for students participating in the course project

== Course Syllabus ==

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

* [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-students cds110-students mailing list] - all students in the class should be signed up on this list ([http://listserv.cds.caltech.edu/pipermail/cds110-students/ archive])

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. ([http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Google Books])
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>{{cds110b-pdfs|LS95-optimal.pdf|LS95, 3.1-3.2}} <td rowspan=3> {{cds110b-pdfs|hw1.pdf|HW 1}}, {{cds110b-pdfs|soln1.pdf|Solns}}
<tr><td>6 Jan (F) <td> [[CDS 110b: Control Implementation|Course Project overview]] (optional) <td>

<tr><td rowspan=3 valign=middle>

===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>{{cds110b-pdfs|hw2.pdf|HW 2}}
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> [http://www.cds.caltech.edu/~murray/papers/2001n_mur+03-sec.html Murray et al, 2003] <td rowspan=3>{{cds110b-pdfs|hw3.pdf|HW 3}} (due 25 Jan)

<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> Observability and Estimators<td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> Introduction to Random Processes <td> Friedland, Ch 10 <td rowspan=2> [[CDS 110b: Homework 4|HW 4]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> Linear Quadratic Estimators (LQE) <td rowspan=2> Friedland, Ch 11
<tr><td> 1 Feb (W) <td> Kalman Filtering <td rowspan=2> Midterm (due 6 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}} <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]]

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td> <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]
<tr><td> 22 Feb (W) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=2>[[CDS 110b: Homework 8|HW 8]]
<tr><td> 1 Mar (W)

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M) <td rowspan=2> [[CDS 110b: Design Example|Design Example]] <td rowspan=2> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}} <td rowspan=3> Final (due 17 Mar)
<tr><td> 8 Mar (W)
<tr><td> 10 Mar <td> Final review (optional) <td>
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a description of the (nonlinear) model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

A special set of lectures on [[CDS 110b: Control Implementation|control implementation]] will be given for students interested in purusing the course project.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

== Old Announcements ==
* 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele
* 4 Jan 05: Please turn in {{cds110b-pdfs|scheduling.pdf|course scheduling form}} by 6 Jan (Fri), 5 pm
* 4 Jan 05: {{cds110b-pdfs|hw1.pdf|HW #1}} is now available; due 11 Jan (Wed)
* 4 Jan 05: <font color=red>No class on Monday (9 Jan)</font>; the next regularly schedule class is Wed from 1:30-3:00 pm
* 7 Jan 05: Office hours will be on Sun from 4-5 pm and Tue from 4-6 pm in <s>125</s> 110 Steele ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000005.html details])
* 6 Jan 05: There will be a [[CDS 110b: Control Implementation|course project]] information session today (Fri) at 2 pm in 125 Steele
* 10 Jan 05: Office hours will now be in 110 Steele, same times as before (check 125 Steele if nobody is in 110 Steele)
* 11 Jan 05: {{cds110b-pdfs|hw2.pdf|HW #2}} is now available; due 18 Jan (Wed)
* 12 Jan 05: Lectures are now available in MP3 format; see individual lecture pages for link

CDS 110b, Winter 2006

2006-01-10T18:54:43Z

Gillula:

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

<table width=80%>
<tr valign=top>
<td>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 4-5 pm
<td>
'''Teaching Assistants''' ([mailto:cds110-tas@cds.caltech.edu cds110-tas@cds])
* [[User:Gillula|Jeremy Gillula]], jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
* Office hours: Sun, 4-5p & Tue 4-6p in 110 STL (or check 125 STL)
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 10 Jan 05: Office hours will now be in 110 Steele, same times as before (check 125 Steele if nobody is in 110 Steele)
* 7 Jan 05: Office hours will be on Sun from 4-5 pm and Tue from 4-6 pm in 125 Steele ([http://listserv.cds.caltech.edu/pipermail/cds110-students/2006-January/000005.html details])
* 6 Jan 05: There will be a [[CDS 110b: Control Implementation|course project]] information session today (Fri) at 2 pm in 125 Steele
* 4 Jan 05: <font color=red>No class on Monday (9 Jan)</font>; the next regularly schedule class is Wed from 1:30-3:00 pm
* 4 Jan 05: {{cds110b-pdfs|hw1.pdf|HW #1}} is now available; due 11 Jan (Wed)

== Course Syllabus ==

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

* [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-students cds110-students mailing list] - all students in the class should be signed up on this list ([http://listserv.cds.caltech.edu/pipermail/cds110-students/ archive])

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. ([http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Google Books])
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>{{cds110b-pdfs|LS95-optimal.pdf|LS95, 3.1-3.2}} <td rowspan=3> {{cds110b-pdfs|hw1.pdf|HW 1}} (due 11 Jan)
<tr><td>6 Jan (F) <td> [[CDS 110b: Control Implementation|Course Project overview]] (optional) <td>

<tr><td rowspan=3 valign=middle>

===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>[[CDS 110b: Homework 2|HW 2]]
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> Handout <td rowspan=3>[[CDS 110b: Homework 3|HW 3]]
<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> Observability and Estimators<td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> Introduction to Random Processes <td> Friedland, Ch 10 <td rowspan=2> [[CDS 110b: Homework 4|HW 4]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> Linear Quadratic Estimators (LQE) <td rowspan=2> Friedland, Ch 11
<tr><td> 1 Feb (W) <td> Kalman Filtering <td rowspan=2> Midterm (due 6 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}} <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]]

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td> <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]
<tr><td> 22 Feb (W) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=2>[[CDS 110b: Homework 8|HW 8]]
<tr><td> 1 Mar (W)

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M) <td rowspan=2> [[CDS 110b: Design Example|Design Example]] <td rowspan=2> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}} <td rowspan=3> Final (due 17 Mar)
<tr><td> 8 Mar (W)
<tr><td> 10 Mar <td> Final review (optional) <td>
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a description of the (nonlinear) model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

A special set of lectures on [[CDS 110b: Control Implementation|control implementation]] will be given for students interested in purusing the course project.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

== Old Announcements ==
* 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele
* 4 Jan 05: Please turn in {{cds110b-pdfs|scheduling.pdf|course scheduling form}} by 6 Jan (Fri), 5 pm

CDS 110b: Optimal Control

2006-01-08T00:55:01Z

Gillula: /* Frequently Asked Questions */

{{cds110b-wi06}}
This lecture provides an overview of optimal control theory. Beginning with a review of optimization, we introduce the notion of Lagrange multipliers and provide a summary of the Pontryagin's maximum principle. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Introduction: two degree of freedom design and trajectory generation
<li> Review of optimization: necessary conditions for extrema, with and without constraints
<li> Optimal control: Pontryagin Maximum Principle
<li> Examples: bang-bang control and Caltech ducted fan (if time)
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L1-2_Optimal.pdf|Lecture Presentation}}
* {{cds110b-pdfs|optimal.pdf|Lecture notes on optimal control}}
* {{cds110b-pdfs|hw1.pdf|Homework 1}}

== References and Further Reading ==
* {{cds110b-pdfs|LS95-optimal.pdf|Excerpt from LS95 on optimal control}} - This excerpt is from [http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Lewis and Syrmos, 1995] and gives a derivation of the necessary conditions for optimaliity. A few pages have been left out from the middle that contained some additional examples (which you can find in similar books in the library, if you are interested). Other parts of the book can be searched via [http://books.google.com Google Books] and purchased online.
* [http://www.cds.caltech.edu/~macmardg/cds110b/pontryagin.pdf Notes on Pontryagin's Maximum Principle] (courtesy of Doug MacMynowski) - this comes from a book on dynamic programming (DP) and uses a slightly different notation than we used in class.

== Frequently Asked Questions ==

'''Q: Notation question for you: In the Lecture notes from Wednesday, I'm assuming that <math>T</math> is the final time and <sup><math>T</math></sup> (superscript T) is a transpose operation. Am I correct in my assumption?'''

<blockquote>
<p>Yes, you are correct.</p>

<p>Jeremy Gillula, 07 Jan 05</p>
</blockquote>

'''Q: What do you mean by penalizing something, from Q>=0 "penalizes" state error?'''

<blockquote>
<p>According to the form of the quadratic cost function <math>J</math>, there are three quadratic terms such
as <math>x^T Q x</math>, <math>u^T R u</math>, and <math>x(T)^T P_1 x(T)</math>. When <math>Q \geq 0</math> and if <math>Q</math> is relative big, the value of <math>x</math> will have bigger contribution to the value of <math>J</math>. In order to keep <math>J</math> small, <math>x</math> must be relatively small. So selecting a big <math>Q</math> can keep <math>x</math> in small value regions. This is what the "penalizing" means.</p>

<p>So in the optimal control design, the relative values of <math>Q</math>, <math>R</math>, and <math>P_1</math> represent how important <math>X</math>, <math>U</math>, and <math>X(T)</math> are in the designer's concerns.</p>

<p>Zhipu Jin,13 Jan 03</p>
</blockquote>

User:Gillula

2006-01-07T21:18:16Z

Gillula: /* Jeremy Gillula */

[[Image:Gillula.PNG|right|frame|I look vaguely like this]]
= Jeremy Gillula =
* Position: Lab TA for [[Cds110b|CDS 110B]] for 2005-2006 winter term. (It may say lab TA, but I'm happy to help with anything 110B related)
* Contact Info: jeremy@caltech.edu
* Office Hours: Sun, 4-5pm, 125 Steele; or by appointment - just email me

User:Gillula

2006-01-04T23:54:59Z

Gillula: /* Jeremy Gillula */

CDS 110b, Winter 2006

2006-01-04T23:54:09Z

Gillula:

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

<table width=80%>
<tr valign=top>
<td width=50%>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 3-4 pm
<td width=50%>
'''Teaching Assistants''' ([mailto:cds110-tas@cds.caltech.edu cds110-tas@cds])
* [[User:Gillula|Jeremy Gillula]], jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 4 Jan 05: Please turn in {{cds110b-pdfs|scheduling.pdf|course scheduling form}} by 6 Jan (Fri), 5 pm
* 4 Jan 05: {{cds110b-pdfs|hw1.pdf|HW #1}} is now available; due 11 Jan (Wed)
* 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele

== Course Syllabus ==

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

* [http://listserv.cds.caltech.edu/mailman/listinfo/cds110-students cds110-students mailing list] - all students in the class should be signed up on this list ([http://listserv.cds.caltech.edu/pipermail/cds110-students/ archive])

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. ([http://books.google.com/books?ie=UTF-8&hl=en&vid=ISBN0471033782&id=jkD37elP6NIC Google Books])
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>{{cds110b-pdfs|LS95-optimal.pdf|LS95, 3.1-3.2}} <td rowspan=3> {{cds110b-pdfs|hw1.pdf|HW 1}} (due 11 Jan)
<tr><td>6 Jan (F) <td> Course Project overview (optional) <td>

<tr><td rowspan=3 valign=middle>

===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>[[CDS 110b: Homework 2|HW 2]]
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> Handout <td rowspan=3>[[CDS 110b: Homework 3|HW 3]]
<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> Observability and Estimators<td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> Introduction to Random Processes <td> Friedland, Ch 10 <td rowspan=2> [[CDS 110b: Homework 4|HW 4]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> Linear Quadratic Estimators (LQE) <td rowspan=2> Friedland, Ch 11
<tr><td> 1 Feb (W) <td> Kalman Filtering <td rowspan=2> Midterm (due 6 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}} <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]]

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td> <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]
<tr><td> 22 Feb (W) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=2>[[CDS 110b: Homework 8|HW 8]]
<tr><td> 1 Mar (W)

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M) <td rowspan=2> [[CDS 110b: Design Example|Design Example]] <td rowspan=2> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}} <td rowspan=3> Final (due 17 Mar)
<tr><td> 8 Mar (W)
<tr><td> 10 Mar <td> Final review (optional) <td>
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a derivation of a nonlinear model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

== Old Announcements ==

User:Gillula

2006-01-04T23:52:25Z

Gillula: /* Jeremy Gillula */

[[Image:Gillula.PNG|right|frame|I look vaguely like this]]
= Jeremy Gillula =
* Position: Lab TA for [[Cds110b|CDS 110B]] (But happy to help with anything 110B related)
* Contact Info: jeremy@caltech.edu
* Office Hours: TBD

File:Gillula.PNG

2006-01-04T23:49:42Z

Gillula: Mug shot of Jeremy Gillula for CDS110B page

Mug shot of Jeremy Gillula for CDS110B page

User:Gillula

2006-01-04T23:46:26Z

Gillula:

= Jeremy Gillula =
* Position: Lab TA for [[Cds110b|CDS 110B]] (But happy to help with anything 110B related)
* Contact Info: jeremy@caltech.edu
* Office Hours: TBD

CDS 110b, Winter 2006

2006-01-03T18:27:03Z

Gillula: Made wording more consistent, fixed typo

{{cds110b-wi06}}
<table align=right border=1 width=20% cellpadding=6>
<tr bgcolor=lightgreen><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Text and References]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006. __NOTOC__ [[Category:Courses]]

'''Course Desciption and Goals:''' CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of taking the midterm and final. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.

<table width=100%>
<tr valign=top>
<td width=50%>
'''Instructor'''
* [[User:Murray|Richard Murray]], murray@cds.caltech.edu
* Office hours: Fridays, 3-4 pm
<td width=50%>
'''Teaching Assistants'''
* Jeremy Gillula, jeremy@caltech.edu
* James Martin, duck@caltech.edu
* Shaunak Sen, shaunak@cds.caltech.edu
</table>

=== Grading ===
The final grade will be based on homework sets, a midterm exam and a final exam:
* '''Homework: 50%''' <br> Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. <i>Late homework will not be accepted without'' <b>prior</b> permission from the instructor.</i><br>
* '''Midterm: 20%''' <br> A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.<br>
* '''Final: 30%''' <br>The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.<br>

Note: students working on the [[#Course Project|course project]] will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.

No collaboration is allowed on the midterm of final exams.

=== Course Text and References ===

The recommended course texts are:
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', Dover, 2004. Available in the Caltech bookstore.
* K. J. {{Astrom}} and R. M. Murray, [http://www.cds.caltech.edu/~murray/books/AM05/wiki ''Design and Analysis of Feedback Systems''], Preprint, 2006. Available online.
* J. Doyle, B. Francis, A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.html ''Feedback Control Theory''], Macmillan, 1992. Available online.

You may find the following texts useful as well:
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.
* N. E. Leonard and W. S. Levine, ''Using Matlab to Analyze and Design Control Systems'', Benjamin/Cummings, 1992.
* A. D. Lewis, [http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control], 2003.

=== Course Schedule ===
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson ([[Talk:CDS 110b, Winter 2006#Course Scheduling|course scheduling page]]).

<table width=100% border=1 valign=top>
<tr valign=top>
<td> Week <td> Date <td> Topic <td> Reading <td> Homework

<tr><td rowspan=2 valign=middle>
===== 1 =====
<td>4 Jan (W) <td> [[CDS 110b: Course Overview|Course Overview]] + [[CDS 110b: Optimal Control|Optimal Control]] <td>Handout <td rowspan=3> [[CDS 110b: Homework 1|HW1]]
<tr><td>6 Jan (F) <td> Course Project overview (optional) <td>

<tr><td rowspan=3 valign=middle>
===== 2 =====
<td> 9 Jan (M)* <td> No class <td>
<tr><td> 11 Jan (W) <td> [[CDS 110b: Linear Quadratic Regulators|Linear Quadratic Regulators]] <td>Friedland, Ch 9 <td rowspan=3>[[CDS 110b: Homework 2|HW 2]]
<tr><td> 13 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td> {{am05|Chapter_12_-Implementation|Ch 12}}

<tr><td rowspan=3 valign=middle>
===== 3 =====
<td> 16 Jan (M) <td> No class (Institute holiday) <td>
<tr><td> 18 Jan (W) <td> [[CDS 110b: Receding Horizon Control|Receding Horizon Control]] <td> Handout <td rowspan=3>[[CDS 110b: Homework 3|HW 3]]
<tr><td> 20 Jan (F) <td> [[CDS 110b: Control Implementation|Control Implementation]] (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 4 =====
<td> 23 Jan (M) <td> Observability and Estimators<td> {{am05|Chapter_6_-_Output_Feedback|Ch 6}}
<tr><td> 25 Jan (W) <td> Introduction to Random Processes <td> Friedland, Ch 10 <td rowspan=2> [[CDS 110b: Homework 4|HW 4]]

<tr><td rowspan=3 valign=middle>
===== 5 =====
<td> 30 Jan (M) <td> Linear Quadratic Estimators (LQE) <td rowspan=2> Friedland, Ch 11
<tr><td> 1 Feb (W) <td> Kalman Filtering <td rowspan=2> Midterm (due 6 Feb)
<tr><td> 2 Feb (F) <td> Midterm review (optional) <td>

<tr><td rowspan=2 valign=middle>
===== 6 =====
<td> 6 Feb (M) <td> [[CDS 110b: Introduction to Robust Control|Intro to Robust Control]] <td rowspan=2> DFT Ch 1-3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.1}} <td rowspan=2> [[CDS 110b: Homework 5|HW 5]]
<tr><td>8 Feb (W) <td> [[CDS 110b:Norms of Signals and Systems|Norms of Signals and Systems]]

<tr><td rowspan=2 valign=middle>
===== 7 =====
<td> 13 Feb (M) <td> [[CDS 110b: Uncertainty Modeling|Uncertainty Modeling]] <td> DFT 4.1, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}} <td rowspan=2>[[CDS 110b: Homework 6|HW 6]]
<tr><td> 15 Feb (W) <td> [[CDS 110b: Robust Stability|Robust Stability]] <td> DFT 4.2, {{am05|Chapter_11_-_Robust_Performance|Sec 11.2}}

<tr><td rowspan=2 valign=middle>
===== 8 =====
<td> 20 Feb (M) <td> No class (Institute holiday) <td> <td rowspan=2> [[CDS 110b: Homework 7|HW 7]]
<tr><td> 22 Feb (W) <td> [[CDS 110b: Robust Performance|Robust Performance]] <td> DFT 4.3, {{am05|Chapter_11_-_Robust_Performance|Sec 11.3}}

<tr><td rowspan=2 valign=middle>
===== 9 =====
<td> 27 Feb (M) <td rowspan=2> [[CDS 110b: Design Constraints|Design Constraints]] <td rowspan=2> DFT, Ch 6 {{am05|Chapter_11_-_Robust_Performance|Sec 11.4}} <td rowspan=2>[[CDS 110b: Homework 8|HW 8]]
<tr><td> 1 Mar (W)

<tr><td rowspan=3 valign=middle>
===== 10 =====
<td> 6 Mar (M) <td rowspan=2> [[CDS 110b: Design Example|Design Example]] <td rowspan=2> {{am05|Chapter_11_-_Robust_Performance|Sec 11.5}} <td rowspan=3> Final (due 17 Mar)
<tr><td> 8 Mar (W)
<tr><td> 10 Mar <td> Final review (optional) <td>
</table>

=== Course Project ===

Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, [http://gc.caltech.edu/wiki/index.php/Alice Alice].

The following work must be performed as part of the class project:

* '''Midterm report: 20%'''<br> By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a derivation of a nonlinear model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.

* '''Final report: 30%'''<br> By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report describing the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a design, analysis and demonstration of the full system. An estimator must be part of the design. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.

Students who are interested in continuing their work on the course project may wish to apply for the [http://gc.caltech.edu/wiki/index.php/2006_SURF Autonomous Vehicle SURF team]. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).