6.245 Fall 2011 Info

6.245 Fall 2011: General Information

Objectives

This is an advanced graduate class presenting major tools of robust control as means of modeling, analysus, and feedback design for nonlinear, distributed, imperfectly known dynamical systems which can be approximated well enough by finite order LTI models.

At the conclusion of the class, the students are expected to have the following skills.

Translate a variety of feedback design settings (nonlinear, uncertain, time-varying) and objectives (closed loop bandwidth, noise rejection, overshoot bounds, etc.) into the standard H2 or H-Infinity optimization problems.
Detect and correct ill-posed optimization settings.
Use Kalman-Yakubovich-Popov lemma to relate frequency and time domain system specifications.
Use semidefinite programming to perform advanced analysis of uncertain and nonlinear models.
Apply Hankel optimal model reduction and balanced truncation to simplify LTI models.
Know basic software tools for optimization of LTI systems.

Prerequisites for this course are

mastery of classical feedback concepts for single-input single output (SISO) systems (6.302 or equivalent),
an appropriate first year graduate control course (either 6.241 or 16.31)

Information resources and literature

There is no required textbook. All necessary information will be supplied in the lecture notes.

The book "Essentials of Robust Control" by Kemin Zhou and John C. Doyle, published by Prentice Hall is a detailed and reasonably modern reference to a major portion of technicalities related to the class material. Anyone who wants to go through the fine details of the famous algorithms for H2 and H-infinity optimization, optimal model order reduction, structured singular values computation etc. will be well advised to buy this book.

Staff

Professor Alexandre Megretski (Lecturer):

Room 32-D730, Ext. 3-9828, email ameg@mit.edu

Lisa Gaumond (Course Secretary):

Room 32-D729, Ext. 4-1543, email lisaqa@mit.edu

Web page

The URL for the 6.245 home page is

http://web.mit.edu/6.245/www/index.html

The home page will link to homework assignments, important announcements, 6.245 questions and answers collection, errata, and other frequently updated information.

Class schedule

Lectures occur on Monday and Wednesday, 1-2.30 pm, Room 36-153.

Homework

As a rule, homework assignments will be posted on the class Web site on Friday evenings, and will be due by the lecture time on Monday the week after the next (i.e. in 10 days). Assignments will contain "theory" tasks (well-posed formal questions covering the mathematical apparatus presented in the class) and/or "practice" tasks (projects in computer-aided analysis or design). The assignments will be collected electronically, either through a Web-based submission procedure, or via Email.

The assignments will be graded and returned as soon as possible. Solutions to the homework will be posted on the Web when the assignment is returned.

Team work on the class assignments is strictly encouraged, as far as generation of ideas is concerned. However, you have to write your own answers, comments, and your own code.

MATLAB

You will have to use some linear algebra/optimization software to solve homework problems. MATLAB, with all needed toolboxes, is available on Athena computers. In addition, some custom-made MATLAB software will be available from the class locker.

Examinations

There will be no quizzes and no final exam.

Make-ups and late submissions

A particular instance of a "theory" task is actually a random sample from a set of similar questions, and does not have a "due" date. Each sample is graded on a pass/fail basis. When a grade is assigned, a similar one can be issued by request, as a "make-up". The final grade on a "theory" task is the percentage of passes among all attempted samples of this task. A "practice" assignment submitted on time is graded in the 0-100 range. A "practice" assignment which is not submitted on time will incur a 20% grade reduction (so that its grade range will be 0 to 80 instead of 0 to 100).

The final grade

The final letter grade in the class will be determined at the end of the semester from the numerical grade N=0.4T+0.6P, where T is the average of the "theory" task grades, and P is the average of the "practice" task grades.

As a rule, a numerical grade above 80 means an "A", 75 to 80 means "A-", 70 to 75 means "B+", etc. For students near the boundaries, other factors may be taken into account to determine the letter grade, such as effort, classroom activity, etc.