Instructor: Mehran Mesbahi

Aeronautics and Astronautics

Gug. 318E

Email: mesbahi@uw.edu

Tel: 206-543-7937

**Syllabus**

**Homework**

HW#1 (Due 1/26/2011): 2.2, 2.3, 2.4, 2.5, 2.10, 2.11

HW#2 (Due 2/2/2011): 2.12, 3.1, 3.2, 3.6

HW#3 (Due 2/16/2011): 4.1, 4.2, 4.4, 4.6, 6.2, 6.6

HW#4 (Due 3/9/2011): 5.4, 6.5, 7.1,7.3, 7.7, 7.8

**Theme:** The course is on linear multivariable control with a particular emphasis on controller synthesis using linear
quadratic (LQ) methods. The LQ methodology is one of the cornerstones of system and control theory from
various point of views, including its historical significance, practical relevance, computational tractability, as well as
its mathematically beauty. In this course we will aim to touch upon some of the facets of LQ methods in order to
gain a better understanding of the theoretical, computational, and practical challenges of dynamic system analysis and
controller synthesis.

**Topics:** The topics to be covered include: relevant material on linear system theory (e.g., controllability, observability),
followed by dynamic programming, Hamilton-Jacobi-Bellman equation, Riccati equation, Lyapunov theory,
computational issues, disturbance rejection, Linear Quadratic Gaussian (LQG) framework, robustness issues, H2 problem,
LQ games, and applications of the theory.

**Midterm**

Midterm will be given out approximately during the second week of February 2011.

**Project**

The project involves three steps:

(1) selection of a paper in your area of interest that uses the LQR/LQG or its extension, (2) emailing me the paper for approval, (3) Writing a report on this paper.

The outline of the report is as follows:

- what is the contribution of the paper? what problem is it trying to address?

- what are the key technical steps in the paper?

- provide a simulation or an example of how this paper's contribution can be applied in practice.

- what is your assessment of the work: it is interesting, important, and relevant?

- include a few references on the works related to the paper.

I prefer that you use Latex; by Word is also fine- in any case, you can use the style files for
both Word or Latex on http://css.paperplaza.net/conferences/support/support.php
2-column format with 10 or 11pt font is okay. I am looking for about 3 (max. 4) pages of report
double column. If you need more room for simulations, that is fine but the text part+references
should not be more than 3-4 pages (double column).

**External links**

S. Boyd: http://www.stanford.edu/class/ee363/