View source for CDS 112/Ae 103b, Winter 2023

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<font color='blue' size='+2'>Optimal Control and Estimation</font>__NOTOC__
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'''Instructors'''
* Richard Murray (CDS/BE), murray@cds.caltech.edu
* Lectures: MWF, 2-3 pm, 213 ANB
* Office hours: Wed, 3-3:30 pm (at CDS tea)
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'''Teaching Assistants'''
* Carmen Amo Alonso, Ioannis Mandralis
* Office hours: Mon, 3-4 pm and Tue, 3-4 pm in 110 Steele Lab
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This is the course homepage for CDS 112 (and Ae 103b), Winter 2023.  This course is intended for undergraduates and graduate students interested in optimization-based methods in control.  After completion of the course, students will understand the key principles of state-space based controller design, including optimal estimation and control techniques.

=== Catalog Description ===

'''CDS 112. Optimal Control and Estimation.''' 9 units (3-0-6): second term. Prerequisites: CDS 110 (or equivalent) and CDS 131. Optimization-based design of control systems, including optimal control and receding horizon control. Introductory random processes and optimal estimation. Kalman filtering and nonlinear filtering methods for autonomous systems.

'''Ae 103 b. Aerospace Control Systems.''' 9 units (3-0-6): second term. Prerequisites: Ae 103a. Optimization-based design of control systems, including optimal control and receding horizon control. Introductory random processes and optimal estimation. Kalman filtering and nonlinear filtering methods for autonomous systems.

=== Lecture Schedule ===

{| class="mw-collapsible wikitable" width=100% border=1 cellpadding=5
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| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''

|- valign=top
| '''Week 1'''<br>
4 Jan <br>  6 Jan <br>
| Introduction and review
* Course introduction and logistics
* Overview: control architectures
* [[http:python-control.org|Python Control Systems Library]]
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-intro|29Dec2022|Chapter 1}}
* Lecture slides: {{cds112 wi2023 pdf|L1-1_intro-04Jan2023.pdf|Mon}}
* Jupyter notebook: {{cds112 wi2023 pdf|W1_python-control.ipynb}} ({{cds112 wi2023 pdf|W1_python-control.pdf|PDF}})
* [https://simons.berkeley.edu/control-theory Feedback Control Theory video tutorial (Simons Institute)]
| {{cds112 wi2023 pdf|hw1-wi2023.pdf|HW #1}} <br>
* {{cds112 wi2023 pdf|servomech-python_template.ipynb}}
* {{cds112 wi2023 pdf|servomech.py}}
Out: 4 Jan <br>
Due: 11 Jan <br>
{{cds112 wi2023 pdf|caltech/hw1-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 2'''<br>
9 Jan <br>  11 Jan <br> 13 Jan
| Two degree of freedom control design
* Trajectory generation
* Differential flatness
* Gain scheduling
* Implementation in Python
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-trajgen|08Jan2023|Chapter 2}}
* Background: FBS2e, Section 8.5
* Theory: [[http:fbswiki.org/wiki/index.php/Supplement:_Linear_Systems_Theory|LST]], Sections 3.1, 3.2
* Jupyter notebooks: {{cds112 wi2023 pdf|W2_flatness.ipynb}} ({{cds112 wi2023 pdf|W2_flatness.pdf|PDF}}), {{cds112 wi2023 pdf|W2_gainsched.ipynb}} ({{cds112 wi2023 pdf|W2_gainsched.pdf|PDF}})
| {{cds112 wi2023 pdf|hw2-wi2023.pdf|HW #2}} <br>
Out: 11 Jan <br>
Due: 18 Jan <br>
{{cds112 wi2023 pdf|caltech/hw2-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 3'''<br>
<s>16 Jan</s> <br>  18 Jan <br> 20 Jan*
| Optimal control
* Maximum principle
* Implementation in Python
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-optimal|14Jan2023|Chapter 3}}
* Theory: [http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html Liberzon, 2010]
* Jupyter notebooks: {{cds112 wi2023 pdf|W3_linquad.ipynb}} ({{cds112 wi2023 pdf|W3_linquad.pdf|PDF}}), {{cds112 wi2023 pdf|W3_optimal.ipynb}} ({{cds112 wi2023 pdf|W3_linquad.pdf|PDF}}), {{cds112 wi2023 pdf|kincar.py}} 
| {{cds112 wi2023 pdf|hw3-wi2023.pdf|HW #3}} <br>
Out: 18 Jan <br>
Due: 25 Jan <br>
* {{cds112 wi2023 pdf|pvtol.py}}
{{cds112 wi2023 pdf|caltech/hw3-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 4'''<br>
23 Jan <br>  25 Jan <br> 27 Jan*
| Linear quadratic regulators
* Problem formulation and solution
* Choosing LQR Weights
* Incorporating integral feedback
* Implementation in Python
* Lyapunov functions
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-optimal|14Jan2023|Chapter 3}}
* [[http:fbswiki.org/wiki/index.php/Feedback_Systems:_An_Introduction_for_Scientists_and_Engineers|FBS]], [[http:www.cds.caltech.edu/~murray/books/AM08/pdf/fbs-dynamics_24Jul2020.pdf|Section 5.4]] (Lyapunov Stability Analysis) 
* Theory: [http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html Liberzon, 2010]
* Jupyter notebooks (Wed): {{cds112 wi2023 pdf|W4_lqr-tracking.ipynb}} ({{cds112 wi2023 pdf|W4_lqr-tracking.pdf|PDF}}), {{cds112 wi2023 pdf|W4_pvtol-lqr.ipynb}} ({{cds112 wi2023 pdf|W4_pvtol-lqr.pdf|PDF}}), {{cds112 wi2023 pdf|pvtol.py}}
| {{cds112 wi2023 pdf|hw4-wi2023.pdf|HW #4}} <br>
Out: 25 Jan <br>
Due: 1 Feb <br>
{{cds112 wi2023 pdf|caltech/hw4-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 5'''<br>
30 Jan <br>  1 Feb <br> 3 Feb
| Receding horizon control
* Problem formulation and solution
* Receding horizon control using differential flatness
* Example: Caltech ducted fan
* Implementation in Python
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-rhc|28Jan2023|Chapter 4}}
* Theory: [https://sites.engineering.ucsb.edu/~jbraw/mpc/ Model Predictive Control (2012)] by Rawlings, Mayne, Diehl
* Lecture slides: {{cds112 wi2023 pdf|L5-2_rhc-dfan-01Feb2023.pdf|Wed}}, {{cds112 wi2023 pdf|L5-3_re-intro-03Feb2023.pdf|Fri}}
* Jupyter notebooks: {{cds112 wi2023 pdf|W5_rhc-doubleint.ipynb}} ({{cds112 wi2023 pdf|W5_rhc-doubleint.pdf|PDF}})
| {{cds112 wi2023 pdf|hw5-wi2023.pdf|HW #5}} <br>
Out: 1 Feb <br>
Due: 8 Feb <br>
{{cds112 wi2023 pdf|caltech/hw5-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 6'''<br>
6 Feb <br>  8 Feb <br> 10 Feb
| Stochastic systems
* Review of random variables
* Introduction to random processes
* Continuous-time, vector-valued random processes
* Linear stochastic systems
* Random processes in the frequency domain
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-stochastic|05Feb2023|Chapter 5}}
* Jupyter notebook: {{cds112 wi2023 pdf|W6_stochastic-linsys.ipynb}} ({{cds112 wi2023 pdf|W6_stochastic-linsys.pdf|PDF}})
| {{cds112 wi2023 pdf|hw6-wi2023.pdf|HW #6}} 
Out: 8 Feb <br>
Due: 15 Feb <br>
{{cds112 wi2023 pdf|caltech/hw6-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 7'''<br>
13 Feb <br>  15 Feb <br> 17 Feb*
| Kalman filtering
* Linear quadratic estimators
* Extensions of the Kalman filter
* LQG control
* Example: vectored thrust aircraft
* Implementation in Python
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-kalman|20Feb2023|Chapter 6}} (updated, 20 Feb 2023)
* Jupyter notebooks: {{cds112 wi2023 pdf|W7_kalman-pvtol.ipynb}} ({{cds112 wi2023 pdf|W7_kalman-pvtol.pdf|PDF}})
| {{cds112 wi2023 pdf|hw7-wi2023.pdf|HW #7}} <br>
Out: 15 Feb <br>
Due: 22 Feb <br>
{{cds112 wi2023 pdf|caltech/hw7-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 8'''<br>
<s>20 Feb</s> <br> 22&nbsp;Feb <br> 24 Feb
| Sensor fusion
* Discrete-time stochastic systems
* Kalman filters in discrete time
* Predictor-corrector form
* Combining information from multiple sensors (information filters)
* Implementation in Python
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-fusion|20Feb2023|Chapter 7}}
* Jupyter notebook: {{cds112 wi2023 pdf|W8_fusion-kincar.ipynb}} ({{cds112 wi2023 pdf|W8_fusion-kincar.pdf|PDF}}), {{cds112 wi2023 pdf|kincar.py}}
* [[http:www.cds.caltech.edu/~murray/courses/cds110/wi07/gro02_infofilter.pdf|Appendix]] from [[http:ses.library.usyd.edu.au/handle/2123/796|Ben Grocholsky's thesis]] on information filter
| {{cds112 wi2023 pdf|hw8-wi2023.pdf|HW #8}} <br>
Out: 20 Feb <br>
Due: 27 Feb <br>
{{cds112 wi2023 pdf|caltech/hw8-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week 9'''<br>
27 Feb <br>  1 Mar <br> 3 Mar
| Advanced estimation and sensor fusion techniques
* Motivation, examples, and approaches (IF, UKF, PF, ML)
* Moving horizon estimation (MHE)
* Unscented Kalman filters
* Implementation in Python (UKF, MHE)
| 
* [[http:fbswiki.org/OBC|OBC]], {{OBC pdf|obc-fusion|26Feb2023|Chapter 7}}
* Lecture slides/notes: {{cds112 wi2023 pdf|L9-1_kfexts-27Feb2023.pdf|Mon}}, {{cds112 wi2023 pdf|ukf_notes-01Mar2023.pdf|Wed (UKF)}}
* Rawlings, Mayne, Diehl: [[http:sites.engineering.ucsb.edu/~jbraw/mpc|Model Predictive Control: Theory, Computation, and Design]] (2nd edition)
* Jupyter notebook: {{cds112 wi2023 pdf|W9_ukf-dinvpend.ipynb}} ({{cds112 wi2023 pdf|W9_ukf-dinvpend.pdf|PDF}}), {{cds112 wi2023 pdf|ukf.py}}, {{cds112 wi2023 pdf|dinvpend.py}} {{cds112 wi2023 pdf|W9_mhe-pvtol.ipynb}} ({{cds112 wi2023 pdf|W9_mhe-pvtol.pdf|PDF}}), {{cds112 wi2023 pdf|ctrlutil.py}}, {{cds112 wi2023 pdf|pvtol.py}} (updated)
| {{cds112 wi2023 pdf|hw9-wi2023.pdf|HW #9}}
* {{cds112 wi2023 pdf|lorenz.py}}
* {{cds112 wi2023 pdf|ctrlutil.py}}
* {{cds112 wi2023 pdf|pvtol-complete_template.ipynb}}
Out: 1 Mar <br>
Due: 8 Mar <br>
{{cds112 wi2023 pdf|caltech/hw9-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only)

|- valign=top
| '''Week&nbsp;10'''<br>
6 Mar <br>  8 Mar <br> 10 Mar
| Course wrap-up and review
* Supervisory (feedback) control systems
* Introduction to safety-critical systems
* Review for final
| 
* Lecture slides: {{cds112 wi2023 pdf|L10-1_supervisory-06Mar2023.pdf|Mon}}
* [http://www.cds.caltech.edu/~murray/papers/2012z_wtm12-us.html Synthesis of Control Protocols for Autonomous Systems], N. Wongpiromsarn, U. Topcu and R. M. Murray.  ''Unmanned Systems'', 2013 (optional)
* [[http:www.youtube.com/watch?v=Wi8Y---ce28|Can We Really Use Machine Learning in Safety Critical Systems? (IPAM talk)]]
| {{cds112 wi2023 pdf|final-wi2023_cover.pdf|Final (cover page)}} <br>
Out: 10 Mar <br>
Due: 17 Mar, 5 pm <br>
<!-- {{cds112 wi2023 pdf|caltech/final-wi2023_solns.pdf|Solns}}&nbsp;(Caltech&nbsp;only) -->

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=== Grading ===
The final grade will be based on homework sets and a final exam: 

*''Homework (70%):'' Homework sets will be handed out weekly and due on Wednesdays by 2 pm using GradeScope.  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).

:The lowest homework set grade will be dropped when computing your final grade.

* ''Final exam (30%):''  The final exam will be handed out on the last day of class (10 Mar) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).

=== Collaboration Policy ===

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).

No collaboration is allowed on the final exam.

=== Course Text and References ===

The primary course texts are
* <span id="OBC">[OBC]</span> R. M. Murray, "Optimization-Based Control", 2023. [https://fbswiki.org/wiki/index.php/Supplement:_Optimization-Based_Control Online access]

The following additional references may also be useful:

* [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org ''Feedback Systems: An Introduction for Scientists and Engineers''], Princeton University Press, Second Edition*, 2020.
* [LST] Richard M. Murray, [https://fbswiki.org/wiki/index.php/Supplement:_Linear_Systems_Theory Feedback Systems: Notes on Linear Systems Theory], 2020. (Updated 30 Oct 2020)

<!--
* [Lew03] A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [https://mast.queensu.ca/~andrew/teaching/pdf/332-notes.pdf Online access].
<!--
* J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), ''Schaum's Outline of Feedback and Control Systems'', 2nd Edition, 2013.  
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.
-->
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.

[[Category: Courses]]