Difference between revisions of "CDS 131, Fall 2019"
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'''Teaching Assistants'''  '''Teaching Assistants'''  
−  * Jiexin (Jessie) Chen (CDS), Ayush Pandey (CDS)  +  * [mailto:jch3n@caltech.edu Jiexin (Jessie) Chen (CDS)], [mailto:apandey@caltech.edu Ayush Pandey (CDS)] 
−  * Office hours  +  * Office hours: Fri, 45; Tue, 45 in 243 Annenberg 
}  }  
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'''CDS 131. Linear Systems Theory.''' 9 units (306); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; statespace and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and outputfeedback. Instructor: Murray.  '''CDS 131. Linear Systems Theory.''' 9 units (306); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; statespace and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and outputfeedback. Instructor: Murray.  
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+   valign=top  
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=== Lecture Schedule ===  === Lecture Schedule ===  
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* Rec = recommended reading (this is what the homework is based on)  * Rec = recommended reading (this is what the homework is based on)  
* Adv = advanced reading (more detailed results, useful if you are interested in learning more)  * Adv = advanced reading (more detailed results, useful if you are interested in learning more)  
+  
+   width=50%   
+  === Announcements ===  
+  * 31 Oct 2019: Revised course notes with some small updates in Chapter 5 ({{cds131 fa19 pdffbslinsys_31Oct2019.pdflatest version}}.  
+  * 27 Oct 2019: Revised course notes have been updated to include W5 material ({{cds131 fa19 pdffbslinsys_27Oct2019.pdflatest version}}; no significant changes in Ch 14)  
+  * 19 Oct 2019: Revised course notes have been updated to include W4 material ({{cds131 fa19 pdffbslinsys_19Oct2019.pdflatest version}}; no significant changes in Ch 13)  
+  <!  
+  * 11 Oct 2019: For HW #2, problem 1: assume that the linear system is time invariant.  
+  >  
+  }  
{ class="mwcollapsible wikitable" width=100% border=1 cellpadding=5  { class="mwcollapsible wikitable" width=100% border=1 cellpadding=5  
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* Induced system norms  * Induced system norms  
    
−  * Opt: FBS2e Ch 1 and 2  +  * Opt: FBS2e Ch 1 and 2 
−  +  * Rec: FBS2s Ch 1 (or DFT Sec 2.1‑2.4)  
* Adv: Sontag, Ch 2  * Adv: Sontag, Ch 2  
 {{cds131 fa19 pdfhw1fa19.pdfHW #1}} <br>   {{cds131 fa19 pdfhw1fa19.pdfHW #1}} <br>  
Out: 2 Oct <br>  Out: 2 Oct <br>  
Due: 9 Oct <br>  Due: 9 Oct <br>  
−  +  {{cds131 fa19 pdfcaltech/hw1fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
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Out: 9 Oct <br>  Out: 9 Oct <br>  
Due: 16 Oct <br>  Due: 16 Oct <br>  
−  +  {{cds131 fa19 pdfcaltech/hw2fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 3'''<br> <! Jessie >   '''Week 3'''<br> <! Jessie >  
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* Eigenvalue placement theorem  * Eigenvalue placement theorem  
    
−  * Rec: FBS2e Sec 7.1, 7.2;  +  * Rec: FBS2e Sec 7.1, 7.2; FBS2s Ch 3 
−  * Adv: FBS2e Sec 7.3; Sontag Sec 3.5  +  * Adv: FBS2e Sec 7.3; Sontag Sec 3.1‑3.3, 3.5 
 {{cds131 fa19 pdfhw3fa19.pdfHW #3}} <br>   {{cds131 fa19 pdfhw3fa19.pdfHW #3}} <br>  
Out: 16 Oct <br>  Out: 16 Oct <br>  
Due: 23 Oct <br>  Due: 23 Oct <br>  
−  +  {{cds131 fa19 pdfcaltech/hw3fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 4'''<br> <! Ayush >   '''Week 4'''<br> <! Ayush >  
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* Opt: FBS2e Sec 7.5  * Opt: FBS2e Sec 7.5  
−  * Rec: OBC Ch 2  +  * Rec: FBS2s Ch 4 (= OBC Ch 2) 
* Adv: Sontag Sec 8.1‑8.3, 9.1, 9.2  * Adv: Sontag Sec 8.1‑8.3, 9.1, 9.2  
 {{cds131 fa19 pdfhw4fa19.pdfHW #4}} <br>   {{cds131 fa19 pdfhw4fa19.pdfHW #4}} <br>  
Out: 23 Oct <br>  Out: 23 Oct <br>  
Due: 30 Oct <br>  Due: 30 Oct <br>  
−  +  {{cds131 fa19 pdfcaltech/hw4fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 5'''<br> <! Jessie >   '''Week 5'''<br> <! Jessie >  
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* Linear observers (fullstate)  * Linear observers (fullstate)  
    
−  * Rec: FBS2e Sec 8.18.3  +  * Rec: FBS2e Sec 8.18.3; FBS2s Ch 5 
* Adv: Sontag Sec 6.1‑6.3, 7.1  * Adv: Sontag Sec 6.1‑6.3, 7.1  
 {{cds131 fa19 pdfhw5fa19.pdfHW #5}} <br>   {{cds131 fa19 pdfhw5fa19.pdfHW #5}} <br>  
Out: 30 Oct <br>  Out: 30 Oct <br>  
Due: 6 Nov <br>  Due: 6 Nov <br>  
−  +  {{cds131 fa19 pdfcaltech/hw5fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 6'''<br> <! Ayush >   '''Week 6'''<br> <! Ayush >  
4 Nov <br> 6 Nov <br> 8 Nov*  4 Nov <br> 6 Nov <br> 8 Nov*  
−   Frequency domain  +   Frequency domain analysis 
−  *  +  * Internal stability 
−  *  +  * Tracking, disturbance rejection 
−  *  +  * I/O performance 
    
−  * Opt  +  * Opt: FBS2e Sec 9.1, 9.2 and 9.5, Sec 10.110.2, Sec 12.112.2 
−  +  * Rec: DFT Ch 3  
−  * Adv: Lewis Ch  +  * Adv: Lewis Ch 58 
<! * Adv: [[http:web.mit.edu/6.242/www/images/lec5_6242_2004.pdfNotes on balanced truncation (Megretski, 2004)]] >  <! * Adv: [[http:web.mit.edu/6.242/www/images/lec5_6242_2004.pdfNotes on balanced truncation (Megretski, 2004)]] >  
 {{cds131 fa19 pdfhw6fa19.pdfHW #6}} <br>   {{cds131 fa19 pdfhw6fa19.pdfHW #6}} <br>  
Out: 6 Nov <br>  Out: 6 Nov <br>  
Due: 13 Nov <br>  Due: 13 Nov <br>  
−  +  {{cds131 fa19 pdfcaltech/hw6fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 7'''<br> <! Jessie >   '''Week 7'''<br> <! Jessie >  
11 Nov <br> 13 Nov <br> 15 Nov*  11 Nov <br> 13 Nov <br> 15 Nov*  
−    +  
−  *  +   Uncertainty and robustness 
−  +  * Types of uncertainty: parametric, operator, disturbances/noise  
−  *  +  * Robust stability and robust performance 
    
−  * Opt: FBS2e Sec 10.  +  * Opt: FBS2e Sec 10.3, Sec 13.113.3 
−  * Rec: DFT Ch  +  * Rec: DFT Ch 4 
−  +  
 {{cds131 fa19 pdfhw7fa19.pdfHW #7}} <br>   {{cds131 fa19 pdfhw7fa19.pdfHW #7}} <br>  
Out: 13 Nov <br>  Out: 13 Nov <br>  
Due: 20 Nov <br>  Due: 20 Nov <br>  
−  +  {{cds131 fa19 pdfcaltech/hw7fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 8'''<br> <! Ayush >   '''Week 8'''<br> <! Ayush >  
18 Nov <br> 20 Nov* <br> 22 Nov  18 Nov <br> 20 Nov* <br> 22 Nov  
−    +   Stabilization 
−  *  +  * Coprime factorization 
−  *  +  * Youla parameterization 
−  +  * Strong stabilization  
−  *  +  * Simultaneous stabilization, robust stabilization (gap metric) [if time] 
−  * Rec: DFT Ch  +   
+  * Rec: DFT Ch 5  
 {{cds131 fa19 pdfhw8fa19.pdfHW #8}} <br>   {{cds131 fa19 pdfhw8fa19.pdfHW #8}} <br>  
Out: 20 Nov <br>  Out: 20 Nov <br>  
Due: 27 Nov <br>  Due: 27 Nov <br>  
−  +  {{cds131 fa19 pdfcaltech/hw8fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 9'''<br> <! Jessie >   '''Week 9'''<br> <! Jessie >  
−  25 Nov <br> 27 Nov  +  25 Nov <br> <s>27 Nov</s> <br> <s>29 Nov</s> <br> 2 Dec <br> 4 Dec* 
 Fundamental limits   Fundamental limits  
* Algebraic limits  * Algebraic limits  
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* Maximum modulus principle  * Maximum modulus principle  
    
−  * Opt: FBS2e Sec 14.  +  * Opt: FBS2e Sec 14.1, 14.2. 14.4 
* Rec: DFT Ch 6  * Rec: DFT Ch 6  
* Adv: Lewis, Ch 9  * Adv: Lewis, Ch 9  
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Out: 27 Nov <br>  Out: 27 Nov <br>  
Due: 6 Dec (Fri) <br>  Due: 6 Dec (Fri) <br>  
−  +  Office hours: <br>  
+  * 3 Dec (Tue), 4p5p  
+  * 5 Dec (Thu), 4p5p, '''314 ANB'''  
+  {{cds131 fa19 pdfcaltech/hw9fa19_solns.pdfSolns}} (Caltech only)  
 valign=top   valign=top  
 '''Week 10'''<br> <! Ayush >   '''Week 10'''<br> <! Ayush >  
−  +  6 Dec  
 Review for final   Review for final  
−  
    
+   Final <br>  
+  Out: 6 Dec <br>  
+  Due: 13 Dec, 2 pm <br>  
+  Office hours:  
+  * 9 Dec (Mon), 4p5p  
+  * 10 Dec (Tue), 4p‑5p  
+  {{cds131 fa19 pdfcaltech/finalfa19_solns.pdfSolns}} (Caltech only)  
}  }  
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The primary course texts are  The primary course texts are  
* [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org ''Feedback Systems: An Introduction for Scientists and Engineers''], Princeton University Press, Second Edition*, 2019.  * [FBS2e] K. J. Astrom and Richard M. Murray, [http://fbsbook.org ''Feedback Systems: An Introduction for Scientists and Engineers''], Princeton University Press, Second Edition*, 2019.  
−  * [FBS2s] Richard M. Murray, ''Feedback Systems:  +  * [FBS2s] Richard M. Murray, ''{{cds131 fa19 pdffbslinsys_31Oct2019.pdfFeedback Systems: Notes on Linear Systems Theory}}'', 2019. (Updated 31 Oct 2019) 
* [DFT] J. Doyle, B. Francis and A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.pdf ''Feedback Control Theory''], Dover, 2009 (originally published by Macmillan, 1992).  * [DFT] J. Doyle, B. Francis and A. Tannenbaum, [http://www.control.utoronto.ca/people/profs/francis/dft.pdf ''Feedback Control Theory''], Dover, 2009 (originally published by Macmillan, 1992).  
* [OBC] R. M. Murray, "OptimizationBased Control", 2010. [http://www.cds.caltech.edu/~murray/amwiki/index.php?title=OBC:Main_Page Online access]  * [OBC] R. M. Murray, "OptimizationBased Control", 2010. [http://www.cds.caltech.edu/~murray/amwiki/index.php?title=OBC:Main_Page Online access]  
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The following additional references may also be useful:  The following additional references may also be useful:  
−  * [Lew03] A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [  +  * [Lew03] A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [https://mast.queensu.ca/~andrew/teaching/pdf/332notes.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.  * J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), ''Schaum's Outline of Feedback and Control Systems'', 2nd Edition, 2013. 
Latest revision as of 07:20, 18 December 2019
Linear Systems Theory  
Instructors

Teaching Assistants

This is the course homepage for CDS 131, Fall 2019. This course is intended for first year graduate students in controls, advanced undergraduates in EE, ChE, and ME who have taken a basic controls course (e.g., CDS 110, ChE 105, EE 113), and motivated graduate students in other disciplines would would like to learn more about linear systems and control. All students taking the course should also have a good understanding of (matrix) differential equations and linear algebra.
Catalog Description
CDS 131. Linear Systems Theory. 9 units (306); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; statespace and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and outputfeedback. Instructor: Murray.
Lecture ScheduleThere will be 23 one hour lectures per week, with the specific days varying from weektoweek. The lecture days for each week will be announced in class and posted here at least 1 week in advance. Reading:

Announcements

Date  Topic  Reading  Homework 
Week 1 30 Sep 
Introduction and review


HW #1 Out: 2 Oct 
Week 2 7 Oct 
Linear I/O systems


HW #2 Out: 9 Oct 
Week 3 14 Oct 
Reachability


HW #3 Out: 16 Oct 
Week 4 21 Oct 
State feedback


HW #4 Out: 23 Oct 
Week 5 28 Oct 
Observability and state estimation


HW #5 Out: 30 Oct 
Week 6 4 Nov 
Frequency domain analysis


HW #6 Out: 6 Nov 
Week 7 11 Nov 
Uncertainty and robustness


HW #7 Out: 13 Nov 
Week 8 18 Nov 
Stabilization


HW #8 Out: 20 Nov 
Week 9 25 Nov 
Fundamental limits


HW #9 Out: 27 Nov
Solns (Caltech only) 
Week 10 6 Dec 
Review for final  Final Out: 6 Dec
Solns (Caltech only) 
Grading
The final grade will be based on homework sets, a midterm exam, and a final exam:
 Homework (70%): Homework sets will be handed out weekly and due on Wednesdays by 2 pm either in class or in the labeled box across from 107 Steele Lab. Each student is allowed up to two extensions of no more than 2 days each over the course of the term. Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean. MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).
 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 (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).
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
 [FBS2e] K. J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, Second Edition*, 2019.
 [FBS2s] Richard M. Murray, Feedback Systems: Notes on Linear Systems Theory, 2019. (Updated 31 Oct 2019)
 [DFT] J. Doyle, B. Francis and A. Tannenbaum, Feedback Control Theory, Dover, 2009 (originally published by Macmillan, 1992).
 [OBC] R. M. Murray, "OptimizationBased Control", 2010. Online access
 [Son98] E. D. Sontag, Mathematical Control Theory, Springer, 1998. Online access
* Please make sure to use the second edition [FBS2e].
The following additional references may also be useful:
 [Lew03] A. D. Lewis, A Mathematical Approach to Classical Control, 2003. Online access.
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.