Instructors: Ivan Papusha, Richard M. Murray |
This is the webpage for a new special topics course targeting graduate students and advanced undergraduates in engineering and applied math fields.
Homework 6 is due on Wed, May 13. Make sure your problem catalog has date stamp ≥ 05/06/2015. For part #3(d), it is recommended to use Matlab and CVX. Refer to the SDP mode documentation.
Homework 7 is due on Wed, May 20.
Homework 8 (last one) is due on Wed, May 27.
No class (Memorial day) on Mon, May 25.
There is no midterm or final.
If you wish to take the course for credit, please sign up with Caltech's Access: choose CDS270, section 2.
The course will develop both a theoretical and a practical knowledge of Lyapunov theory and robust control as they pertain to modeling, analyzing, optimizing, and controlling dynamical systems from application areas in electrical systems, circuits, mechanical systems, robotics, and networks. We will highlight computational tools from convex optimization, particularly Linear Matrix Inequalities (LMIs) and semidefinite programming (SDP), as a unifying language in classical and modern control of linear systems. If time allows, we will make the jump to the rich area of nonlinear systems and path planning.
To fully appreciate the course material, students should have some level of mathematical sophistication, including a working knowledge of linear algebra, real analysis, and facility with MATLAB. A background in convex optimization (ACM 113) and/or control theory (CDS 112) will be helpful, but not required.
The final grade is tentatively based on
50% homework
50% attendance/participation
Each homework assignment consists of a combination of theoretical and computational problems, many of which can be freely chosen by the student from an ever-expanding catalog of problems.
HW | Reading | Catalog exercises* | Solution | Due |
1 | BV, Appendix A | #1 | Wed Apr 8 | |
2 | lmibook Ch1–2 | #11 or CYOA | Wed Apr 15 | |
3 | lmibook Ch1–2 | #2 or CYOA | Wed Apr 22 | |
4 | BV, Ch4–5 | #4 or CYOA | Wed Apr 29 | |
5 | Bertsekas, Ch1 | #13 or CYOA | Wed May 6 | |
6 | lmibook Ch4–6 | #3 or CYOA | Wed May 13 | |
7 | lmibook Ch7 | #12 or CYOA | Wed May 20 (drop day) | |
8 | Davis Ch1–3 | #19 or CYOA | Wed May 27 (last day of class) |
*CYOA: Choose your own adventure — do the assigned problem, or any other problem from the catalog that you haven't done.
All lecture notes will be provided in class and made available online. We will use material and readings adapted from the following texts:
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, SIAM, 1994.
S. Boyd. EE363: Linear Dynamical Systems. course notes.
D. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific, 2005.
S. LaValle. Planning Algorithms. Cambridge University Press, 2006.
S. Boyd, L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
G. E. Dullerud, F. Paganini. A Course in Robust Control Theory: A Convex Approach. Springer, 2000.
T. A. Davis. Direct Methods for Sparse Linear Systems. SIAM, 2006.