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* Vanessa Jonsson, Nikolai Matni
* Vanessa Jonsson, Nikolai Matni
* Office hours: TBD
* Office hours: TH, 4-5 pm, Ann 213, and upon request
|}
|}


=== Course Description ===
=== Course Description ===
An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems


===Announcements ===
===Announcements ===
* 8 Jan 2014: web page creation, uploaded lecture 1 material  
* 8 Jan 2014: web page creation, uploaded lecture 1 material  
 
=== Tentative Lecture Schedule ===
 
 
=== Lecture Schedule ===


{| class="mw-collapsible " width=100% border=1 cellpadding=5
{| class="mw-collapsible " width=100% border=1 cellpadding=5
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|- valign=top
|- valign=top
| 7 Jan <br>  9 Jan
| 7 Jan <br>  9 Jan
| Linear Differential Equations I
| Robustness, fragility, complexity and control I
* Course overview and administration
* Examples in neuroscience, glycolysis, technology
* Linear differential equations
Inverted pendulum revisited <br>
* Matrix exponential, diagonalization
Discrete time, finite horizon LQR
* Stable and unstable spaces
* Planar systems, behavior of solutions
|  
|  
Perko, 1.1-1.6<br>
* [https://www.cds.caltech.edu/~murray/wiki/images/b/b5/InvertedPendulum_classnote.pdf  notes]<br>
| [[CDS 140a Winter 2014 Homework 1|HW 1]] <br> Due: 15 Jan (Wed)
* [https://www.cds.caltech.edu/~murray/wiki/images/0/04/CDS110bLect1.pdf  slides1],  [https://www.cds.caltech.edu/~murray/wiki/images/a/a6/CDS110bLect1.pptx slides2]
| [https://www.cds.caltech.edu/~murray/wiki/images/0/0f/Cds110bwi14_hw1.pdf hw1]
|- valign=top
|- valign=top
| 14 Jan <br> 16 Jan
| 14 Jan <br> 16 Jan
| Linear Differential Equations II
| Discrete time stochastic LQR <br>
* S + N decomposition, Jordan form
* Finite horizon, infinite horizon
* Stability theory
|
* Linear systems with inputs (nonhomogeneous systems)
* [https://www.cds.caltech.edu/~murray/wiki/images/c/c5/Ln1.pdf lecnotes1 ]
| Perko, 1.7-1.10
* [https://www.cds.caltech.edu/~murray/wiki/images/8/83/Ln2.pdf lecnotes2]
| [[CDS 140a Winter 2014 Homework 2|HW 2]] <br> Due: 22 Jan (Wed)
* [http://lall.stanford.edu/svn/engr207b_2012_to_2013_winter/data/matrix_facts_2011_02_07_01.pdf matrixnotes]
| [https://www.cds.caltech.edu/~murray/wiki/images/d/d9/Cds110bwi14hw2.pdf hw2]
|- valign=top
|- valign=top
| 21 Jan <br> 23 Jan
| 21 Jan <br> 23 Jan
| Nonlinear differential equations
| Continuous time LQR
* Existence and uniqueness
* Pontryagin's maximum principle <br>
* Flow of a differential equation
* Costate equations
* Linearization
SDPs, duality and LQR
| Perko, 2.1-2.6
* Relationship to Riccati solutions
| [[CDS 140a Winter 2014 Homework 3|HW 3]] <br> Due: 29 Jan (Wed)
|  
|  
|- valign=top
|- valign=top
| 28 Jan <br> 30 Jan
| 28 Jan <br> 30 Jan
| Behavior of differential equations
| State estimation <br>
* Stable and unstable manifolds 
Kalman Filters
* Stability of equilibrium points
|
| Perko, 2.7-2.10
| [https://www.cds.caltech.edu/~murray/wiki/images/4/47/Cds110bwi14_hw3.pdf hw3]
<!--
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
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| | [[CDS 140a Winter 2014 Homework 4|HW 4]] <br> Due: 5 Feb (Wed)
|- valign=top
|- valign=top
| 4 Feb <br> 6 Feb
| 4 Feb <br> 6 Feb
| Non-hyperbolic differential equations
| Discrete time output feedback LQG
* Lyapunov functions
* Connections with H2 optimal control
* Center manifold theorem
|  
| Perko, 2.11-2.13
|
<!--
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
* [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]]
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| [[CDS 140a Winter 2014 Homework 5|HW 5]] <br> Due: 12 Feb (Wed)
|- valign=top
|- valign=top
| 11 Feb <br> 13 Feb
| 11 Feb <br> 13 Feb
| Hamiltonian systems
| Modeling, Robustness/efficiency tradeoffs <br>
* Gradient and Hamiltonian systems
* Heart rate variability
* Energy based stability methods
|  
* Applications
* [https://www.cds.caltech.edu/~murray/wiki/images/c/cb/2HRVdetails.pdf lecslides]
| Perko 2.14 + notes
*[https://www.cds.caltech.edu/~murray/wiki/images/4/4b/Main_text.pdf HRVpreprint ] [https://www.cds.caltech.edu/~murray/wiki/images/b/b4/SI.PDF HRVSI]
<!--
|  
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6-Hamiltonian.pdf Scanned lecture notes]
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
-->
| [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: 19 Feb (Wed)
|- valign=top
|- valign=top
| 18&nbsp;Feb* <br> 20 Feb* <br> 25 Feb
| 18 Feb <br> 20 Feb <br>
| Limit cycles
|
* Limit sets and attractors
|  
* Periodic orbits and limit cycles
|  
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.1-3.5, 3.7, 3.9
<!--
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-2_limitcycles-17Feb11.pdf Lecture notes on limit cycles]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators]
-->
| [[CDS 140a Winter 2014 Homework 7|HW 7]] <br> Due: 5 Mar (Wed)
|- valign=top
|- valign=top
|- valign=top
|- valign=top
| 27 Feb <br> 4 Mar <br> 6 Mar
| 25 Feb <br> 27 Feb <br>
| Bifurcations
|  
* Structural stability
|
* Bifurcation of equilibrium points
|- valign=top
* Hopf bifurcation
| 4 Mar <br> 6 Mar <br>
| Perko 4.1-4.4 + notes
|
<!--
|
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]
|  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations]
-->
| [[CDS 140a Winter 2014 Homework 8|HW 8]] <br> Due: 12 Mar (Wed)
|- valign=top
|- valign=top
| 11 Mar* <br>  
| 11 Mar <br>  
| Course review
|
| <!-- Reading -->
|  
| Final exam  <br> Due: 19 Mar (Wed)
|  
|}
|}


=== Course Text and References ===
=== Course Text and References ===
Line 146: Line 111:
* 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])
* 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])
* A. D. Lewis, ''[http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control]'', 2003.
* A. D. Lewis, ''[http://penelope.mast.queensu.ca/math332/notes.shtml A Mathematical Approach to Classical Control]'', 2003.
=== Selected Papers ===
1. M Chiang, SH Low, AR Calderbank, JC. Doyle (2007) Layering As Optimization Decomposition, PROCEEDINGS OF THE IEEE, Volume: 95  Issue: 1  Jan 2007 [https://www.cds.caltech.edu/~murray/wiki/images/6/6d/01IEEEProcNetsLayeringAsOptDecomp.pdf link]
2. Martins NC, Dahleh MA, Doyle JC (2007) Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information,  IEEE Trans Auto Control, Feb 2007 [https://www.cds.caltech.edu/~murray/wiki/images/d/df/02-2007-FundamentalLimits.pdf link]
3. Bowman, Balch, Artaxo, Bond, Carlson, Cochrane, D’Antonio, DeFries, Doyle, et al. Fire in the Earth System, Science, Vol. 324 no. 5926 pp. 481-484 24 April 2009 [https://www.cds.caltech.edu/~murray/wiki/images/b/b9/03ScienceFire.pdf link]
4. Willinger W, Alderson D, and Doyle JC (2009) Mathematics and the internet: A source of enormous confusion and great potential. Notices Amer Math Soc 56:586-599. [https://www.cds.caltech.edu/~murray/wiki/images/b/b3/04AMSNoticesInternet.pdf link]
5. Alderson DL, Doyle JC (2010) Contrasting views of complexity and their implications for network-centric infrastructures. IEEE Trans Systems Man Cybernetics—Part A: Syst Humans 40:839-852.  [https://www.cds.caltech.edu/~murray/wiki/images/3/31/05AldersonDoyle-tsmca-July2010.pdf link]
6. Gayme DF, McKeon BJ, Papachristodoulou P, Bamieh B, Doyle JC (2010) A streamwise constant model of turbulence in plane Couette flow, J Fluid Mech, vol 665, pp 99-119 [https://www.cds.caltech.edu/~murray/wiki/images/3/37/06GaymeJFM2010.pdf link]
7. H. Sandberg, J. C. Delvenne, J. C. Doyle. (2011) On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements, IEEE Trans Auto Control, Feb 2011
8. J Lavaei, A Babakhani, A Hajimiri, and JC Doyle (2011), Solving Large-Scale Hybrid Circuit-Antenna Problems, IEEE Transactions on Circuits and Systems I, vol. 58, no. 2, pp. 374-387, Feb. 2011. [https://www.cds.caltech.edu/~murray/wiki/images/0/04/08LavaeiCircuits.pdf link]
9. Chandra F, Buzi G, Doyle JC (2011) Glycolytic oscillations and limits on robust efficiency. Science, Vol 333, pp 187-192. [https://www.cds.caltech.edu/~murray/wiki/images/6/68/09ScienceGlycolyticOscOnlineFinal.pdf link]
10. JC Doyle, ME Csete (2011) Architecture, Constraints, and Behavior, P Natl Acad Sci USA, vol. 108, Sup 3 15624-15630 [https://www.cds.caltech.edu/~murray/wiki/images/4/47/10PNASOnlineFinalSackler2011.pdf link]
11. Gayme DF, McKeon BJ, Bamieh B, Papachristodoulou P, Doyle JC (2011) Amplification and Nonlinear Mechanisms in Plane Couette Flow, Physics of Fluids, V23, Issue 6, 065108 [https://www.cds.caltech.edu/~murray/wiki/images/4/47/11PhysOfFluidsForcedSolutions2011.pdf link]
12. Page, M. T., D. Alderson, and J. Doyle (2011), The magnitude distribution of earthquakes near Southern California faults, J. Geophys. Res., 116, B12309, doi:10.1029/2010JB007933.
13. Namas R, Zamora R, An, G, Doyle, J et al, (2012) Sepsis: Something old, something new, and a systems view, Journal Of Critical Care  Volume: 27  Issue: 3  [https://www.cds.caltech.edu/~murray/wiki/images/a/a6/13SepsisJCritCareNihms300207.pdf link]
14. Chen, L; Ho, T; Chiang, M, Low S; Doyle J,(2012) Congestion Control for Multicast Flows With Network Coding, IEEE Trans On Information Theory  Volume: 58  Issue: 9  Pages: 5908-5921 
[https://www.cds.caltech.edu/~murray/wiki/images/5/55/14ChenEtAlMulticastIEEETIT2012.pdf  link ]

Latest revision as of 03:04, 22 February 2014

CDS 110b: Introduction to Control Theory

Instructors

  • John Doyle, [email protected]
  • Lectures: Tu/Th, 9-10:30, 105 ANB
  • Office hours: TBD (please e-mail to schedule)

Teaching Assistants

  • Vanessa Jonsson, Nikolai Matni
  • Contact: [email protected]
  • Office hours: TH, 4-5 pm, Ann 213, and upon request

Course Description

An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems

Announcements

  • 8 Jan 2014: web page creation, uploaded lecture 1 material

Tentative Lecture Schedule

Date Topic Reading Homework
7 Jan
9 Jan 		Robustness, fragility, complexity and control I
  • Examples in neuroscience, glycolysis, technology

Inverted pendulum revisited
Discrete time, finite horizon LQR

hw1
14 Jan
16 Jan 		Discrete time stochastic LQR
  • Finite horizon, infinite horizon
 hw2
21 Jan
23 Jan 		Continuous time LQR
  • Pontryagin's maximum principle
  • Costate equations

SDPs, duality and LQR

  • Relationship to Riccati solutions
28 Jan
30 Jan 		State estimation

Kalman Filters

hw3
4 Feb
6 Feb 		Discrete time output feedback LQG
  • Connections with H2 optimal control
11 Feb
13 Feb 		Modeling, Robustness/efficiency tradeoffs
  • Heart rate variability
18 Feb
20 Feb
25 Feb
27 Feb
4 Mar
6 Mar
11 Mar

Course Text and References

The main course text is

You may find the following texts useful as well:

Selected Papers

1. M Chiang, SH Low, AR Calderbank, JC. Doyle (2007) Layering As Optimization Decomposition, PROCEEDINGS OF THE IEEE, Volume: 95 Issue: 1 Jan 2007 link

2. Martins NC, Dahleh MA, Doyle JC (2007) Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information, IEEE Trans Auto Control, Feb 2007 link

3. Bowman, Balch, Artaxo, Bond, Carlson, Cochrane, D’Antonio, DeFries, Doyle, et al. Fire in the Earth System, Science, Vol. 324 no. 5926 pp. 481-484 24 April 2009 link

4. Willinger W, Alderson D, and Doyle JC (2009) Mathematics and the internet: A source of enormous confusion and great potential. Notices Amer Math Soc 56:586-599. link

5. Alderson DL, Doyle JC (2010) Contrasting views of complexity and their implications for network-centric infrastructures. IEEE Trans Systems Man Cybernetics—Part A: Syst Humans 40:839-852. link

6. Gayme DF, McKeon BJ, Papachristodoulou P, Bamieh B, Doyle JC (2010) A streamwise constant model of turbulence in plane Couette flow, J Fluid Mech, vol 665, pp 99-119 link

7. H. Sandberg, J. C. Delvenne, J. C. Doyle. (2011) On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements, IEEE Trans Auto Control, Feb 2011

8. J Lavaei, A Babakhani, A Hajimiri, and JC Doyle (2011), Solving Large-Scale Hybrid Circuit-Antenna Problems, IEEE Transactions on Circuits and Systems I, vol. 58, no. 2, pp. 374-387, Feb. 2011. link

9. Chandra F, Buzi G, Doyle JC (2011) Glycolytic oscillations and limits on robust efficiency. Science, Vol 333, pp 187-192. link

10. JC Doyle, ME Csete (2011) Architecture, Constraints, and Behavior, P Natl Acad Sci USA, vol. 108, Sup 3 15624-15630 link

11. Gayme DF, McKeon BJ, Bamieh B, Papachristodoulou P, Doyle JC (2011) Amplification and Nonlinear Mechanisms in Plane Couette Flow, Physics of Fluids, V23, Issue 6, 065108 link

12. Page, M. T., D. Alderson, and J. Doyle (2011), The magnitude distribution of earthquakes near Southern California faults, J. Geophys. Res., 116, B12309, doi:10.1029/2010JB007933.

13. Namas R, Zamora R, An, G, Doyle, J et al, (2012) Sepsis: Something old, something new, and a systems view, Journal Of Critical Care Volume: 27 Issue: 3 link

14. Chen, L; Ho, T; Chiang, M, Low S; Doyle J,(2012) Congestion Control for Multicast Flows With Network Coding, IEEE Trans On Information Theory Volume: 58 Issue: 9 Pages: 5908-5921 link

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