EE695R: Introduction to Robust Control
Fall Semester 2003
Announcements:
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New!
Final projects
presentation schedule has been posted.
(Date posted: Mon Dec 8 07:00:52 EST 2003)
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New!
Homework 6 solutions have been posted.
(Date posted: Mon Dec 8 07:00:52 EST 2003)
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Homework 5 solutions and Homework 6 have been posted.
(Date posted: Wed Nov 12 17:05:11 EST 2003)
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Midterm solutions have been posted.
(Date posted: Mon Nov 3 16:47:59 EST 2003)
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Homework 4 solutions and Homework 5 have been posted.
(Date posted: Thu Oct 23 17:41:33 EST 2003)
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The due date for Homework 4 has been postponed to October 23.
(Date posted: Wed Oct 8 15:07:41 EST 2003)
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The due date for Homework 4 has been postponed to October 16.
(Date posted: Wed Oct 8 07:48:32 EST 2003)
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New lecture notes have been posted.
(Date posted: Tue Sep 30 15:54:40 EST 2003)
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Homework 4 has been posted.
(Date posted: Tue Sep 30 15:54:40 EST 2003)
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Homework 3 solution has been posted.
(Date posted: Tue Sep 30 15:54:40 EST 2003)
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Homework 3 has been posted.
(Date posted: Tue Sep 16 14:24:03 EST 2003)
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Homework 2 solution has been posted.
(Date posted: Tue Sep 16 14:24:03 EST 2003)
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Homework 1 solution has been posted.
(Date posted: Mon Sep 15 08:20:08 EST 2003)
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Homework 2 has been posted.
(Date posted: Wed Sep 3 08:37:53 EST 2003)
- Classes cancelled on September 9 and September 11 (make-up
classes to be determined)
- The class will meet on August 28 (thursday). Please disregard
the announcement I made in class regarding class cancellation.
- If you would like to by the LMI book from SIAM, let me know by
September 2. I will collect the orders and place them as a SIAM member.
When and where
EE 115, TTh 12:00-1:15.
Teaching staff
- Professor:
Venkataramanan Balakrishnan
- Office: MSEE 252
- Tel: (765) 494-0728
- Email:
- Office hours: By appointment.
Textbook and optional references
There is no textbook. Complete lecture notes will be made
available on the web.
Here are some reference texts. A substantial portion of the course
will follow the first text, so I recommend getting it.
If you are considering buying this text, note that SIAM members
get a signficant discount. You may want to pool together book orders
and get a SIAM member to order them for you.
- Linear Matrix Inequalities in System and Control
Theory, S. Boyd, L. El Ghaoui, E. Feron, and
V. Balakrishnan. Vol. 15 in SIAM Studies in
Applied Mathematics, 1994.
- Robust and Optimal Control, K. Zhou, J.C. Doyle and K. Glover,
Prentice-Hall, 1996.
- New Tools for Robustness of Linear
Systems, B.R. Barmish, MacMillan, 1994.
- Linear Robust Control, M. Green and D.J.N. Limebeer, Prentice
Hall, 1995.
Course requirements/exams
- Occasional homework assignments,
which may involve some simple Matlab programming
- One take-home midterm exam
- A final project
You are allowed, even encouraged, to
work on the homework in small groups, but you must write up
your own homework to hand in.
Grading
- homework 20%
- midterm 30%
- final project 50%
Prerequisites
EE602, or consent
of instructor. Topics required: finite-dimensional linear algebra, exposure
to control and system theory, and basic concepts from
functional analysis.
One of the most useful qualities of a properly designed feedback
control system is robustness, i.e., the ability of the closed-loop
system to continue performing satisfactorily despite large variations
in the (open-loop) plant dynamics. This course will provide an
introduction to the analysis and design of robust feedback control
systems. Topics covered: modeling and paradigms for robust control;
robust stability and measures of robust performance; analysis of
robust stability and performance; design for robust stability and
performance.
Course outline
Robust control -- motivation and overview
Why robust control?
Examples of important robust control problems
Paradigms for robust control
Sources of uncertainties
Parametric families of polynomials or matrices
Multi-model and polytopic systems
Systems with feedback perturbations: Linear
fractional transformations; structured perturbations
Measures of robustness
Robust stability; quadratic stability; stability margins;
invariant ellipsoids; decay rate
Reachable sets with input constraints
Output energy and peak
H-2 and H-infinity performance
Computation of robustness measures
Complexity issues
Exact methods for parametric families:
Kharitonov and Edge theorems
Polytopic systems: LMI methods
Systems with feedback uncertainties: Small-gain
and passivity methods
Systems with structured uncertainties: mu,
Km and LMI analysis
Robust synthesis
Polytopic systems: LMI methods
Systems with feedback uncertainties
Systems with structured uncertainties
Gain-scheduled control