Difference between revisions of "Cds110b WI14"
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* 8 Jan 2014: web page creation, uploaded lecture 1 material  * 8 Jan 2014: web page creation, uploaded lecture 1 material  
+  
+  
+  
+  === Lecture Schedule ===  
+  
+  { class="mwcollapsible " width=100% border=1 cellpadding=5  
+    
+   '''Date'''  
+   '''Topic'''  
+   '''Reading'''  
+   '''Homework'''  
+   valign=top  
+   valign=top  
+   7 Jan <br> 9 Jan  
+   Linear Differential Equations I  
+  * Course overview and administration  
+  * Linear differential equations  
+  * Matrix exponential, diagonalization  
+  * Stable and unstable spaces  
+  * Planar systems, behavior of solutions  
+    
+  Perko, 1.11.6<br>  
+   [[CDS 140a Winter 2014 Homework 1HW 1]] <br> Due: 15 Jan (Wed)  
+   valign=top  
+   14 Jan <br> 16 Jan  
+   Linear Differential Equations II  
+  * S + N decomposition, Jordan form  
+  * Stability theory  
+  * Linear systems with inputs (nonhomogeneous systems)  
+   Perko, 1.71.10  
+   [[CDS 140a Winter 2014 Homework 2HW 2]] <br> Due: 22 Jan (Wed)  
+   valign=top  
+   21 Jan <br> 23 Jan  
+   Nonlinear differential equations  
+  * Existence and uniqueness  
+  * Flow of a differential equation  
+  * Linearization  
+   Perko, 2.12.6  
+   [[CDS 140a Winter 2014 Homework 3HW 3]] <br> Due: 29 Jan (Wed)  
+   valign=top  
+   28 Jan <br> 30 Jan  
+   Behavior of differential equations  
+  * Stable and unstable manifolds  
+  * Stability of equilibrium points  
+   Perko, 2.72.10  
+  <!  
+  * [[Media:cds140awi11Week4Notes.pdfSome notes]]  
+  * [[Media:cds140awi11InvManRemark.pdfRemark on invariant manifolds]]  
+  >  
+    [[CDS 140a Winter 2014 Homework 4HW 4]] <br> Due: 5 Feb (Wed)  
+   valign=top  
+   4 Feb <br> 6 Feb  
+   Nonhyperbolic differential equations  
+  * Lyapunov functions  
+  * Center manifold theorem  
+   Perko, 2.112.13  
+  <!  
+  * [[Media:cds140awi11Week5Notes.pdfNotes on Lyapunov]]  
+  * [[Media:cds140awi11Week5NotesCMT.pdfNotes on Center Manifold]]  
+  * [[Media:cds140awi11CMTLimitCycleExample.pdfAn Example (Center Manifold / Limit Cycle)]]  
+  >  
+   [[CDS 140a Winter 2014 Homework 5HW 5]] <br> Due: 12 Feb (Wed)  
+   valign=top  
+   11 Feb <br> 13 Feb  
+   Hamiltonian systems  
+  * Gradient and Hamiltonian systems  
+  * Energy based stability methods  
+  * Applications  
+   Perko 2.14 + notes  
+  <!  
+  * [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6Hamiltonian.pdf Scanned lecture notes]  
+  * [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]  
+  * [[Media:cds140awi11Week6NotesHamGrad.pdfGradient and Hamiltonian Systems]]  
+  * [[Media:cds140awi11Week6NotesLagHamSum.pdfLagrangian, Summary]]  
+  >  
+   [[CDS 140a Winter 2014 Homework 6HW 6]] <br> Due: 19 Feb (Wed)  
+   valign=top  
+   18 Feb* <br> 20 Feb* <br> 25 Feb  
+   Limit cycles  
+  * Limit sets and attractors  
+  * Periodic orbits and limit cycles  
+  * Poincare' map  
+  * Bendixson criterion for limit cycles in the plane  
+   Perko, 3.13.5, 3.7, 3.9  
+  <!  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L71_orbits15Feb11.pdf Lecture notes on orbits and attractors]  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L72_limitcycles17Feb11.pdf Lecture notes on limit cycles]  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L73_bfs_oscillators.pdf BFS notes on oscillators]  
+  >  
+   [[CDS 140a Winter 2014 Homework 7HW 7]] <br> Due: 5 Mar (Wed)  
+   valign=top  
+   valign=top  
+   27 Feb <br> 4 Mar <br> 6 Mar  
+   Bifurcations  
+  * Structural stability  
+  * Bifurcation of equilibrium points  
+  * Hopf bifurcation  
+   Perko 4.14.4 + notes  
+  <!  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_parmsens24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_bfs_sensitivity.pdf BFS notes on parameter sensitivity]  
+  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L82_bifurcations01Mar11.pdf Lecture notes on bifurcations]  
+  >  
+   [[CDS 140a Winter 2014 Homework 8HW 8]] <br> Due: 12 Mar (Wed)  
+   valign=top  
+   11 Mar* <br>  
+   Course review  
+   <! Reading >  
+   Final exam <br> Due: 19 Mar (Wed)  
+  }  
+  
+  
+  
=== Course Text and References ===  === Course Text and References === 
Revision as of 22:18, 8 January 2014
CDS 110b: Introduction to Control Theory  
Instructors

Teaching Assistants

Course Description
Announcements
 8 Jan 2014: web page creation, uploaded lecture 1 material
Lecture Schedule
Date  Topic  Reading  Homework 
7 Jan 9 Jan 
Linear Differential Equations I

Perko, 1.11.6 
HW 1 Due: 15 Jan (Wed) 
14 Jan 16 Jan 
Linear Differential Equations II

Perko, 1.71.10  HW 2 Due: 22 Jan (Wed) 
21 Jan 23 Jan 
Nonlinear differential equations

Perko, 2.12.6  HW 3 Due: 29 Jan (Wed) 
28 Jan 30 Jan 
Behavior of differential equations

Perko, 2.72.10  HW 4 Due: 5 Feb (Wed) 
4 Feb 6 Feb 
Nonhyperbolic differential equations

Perko, 2.112.13  HW 5 Due: 12 Feb (Wed) 
11 Feb 13 Feb 
Hamiltonian systems

Perko 2.14 + notes  HW 6 Due: 19 Feb (Wed) 
18 Feb* 20 Feb* 25 Feb 
Limit cycles

Perko, 3.13.5, 3.7, 3.9  HW 7 Due: 5 Mar (Wed) 
27 Feb 4 Mar 6 Mar 
Bifurcations

Perko 4.14.4 + notes  HW 8 Due: 12 Mar (Wed) 
11 Mar* 
Course review  Final exam Due: 19 Mar (Wed) 
Course Text and References
The main course text is
 J. Doyle, B. Francis, A. Tannenbaum, Feedback Control Theory, Macmillan, 1992.
 R. M. Murray, OptimizationBased Control, Preprint, 2008.
You may find the following texts useful as well:
 K. J. Åström and R. M. Murray, ', Princeton University Press, 2008.
 B. Friedland, Control System Design: An Introduction to StateSpace Methods, Dover, 2004.
 F. L. Lewis and V. L. Syrmos, Optimal Control, Second Edition, WileyIEEE, 1995. (Google Books)
 A. D. Lewis, A Mathematical Approach to Classical Control, 2003.