ECE 497 DL
Home
Page
ECE 497 DL: Hybrid Systems and Control
ECE Dept, UIUC, Spring 2001
Instructor: Daniel Liberzon
Office: 144 C&SRL
Email: liberzon at uiuc.edu
Phone: (217) 244-6750
Schedule: Tue Thu 11:30-12:50, 57 Everitt Lab.
Office hours: Tu 2:30-4, Wed 11:30-1.
Prerequisite: ECE 415 (Linear Systems) or consent of instructor.
Textbook: A. van der Schaft and H. Schumacher,
An Introduction
to Hybrid Dynamical Systems, Springer, 2000.
Note: not available in the bookstore. A copy has been placed on reserve
in the library.
Supplementary reading:
-
D. Liberzon and A. S. Morse,
Basic problems in stability and design
of switched systems, IEEE Control Systems Magazine, vol. 19, no. 5,
pp. 59-70, Oct. 1999. This is a
survey paper on switched systems.
Available in postscript format here.
-
H. K. Khalil, Nonlinear Systems, 2nd edition, Prentice Hall, 1996.
This is the textbook for ECE 428 with a very good treatment of Lyapunov
stability.
-
A. A. Agrachev and D. Liberzon,
Lie algebraic stability criteria for
switched systems, SIAM Journal on Control and Optimization, to appear.
Features an appendix on Lie algebras. Available in postscript format
here.
-
J. Hespanha and A. S. Morse,
Stabilization of Nonholonomic Integrators
via Logic-Based Switching, Automatica (Special Issue on Hybrid Systems),
35(3):385-393, Mar 1999. This paper discusses an advanced technique
for hybrid stabilization of the nonholonomic integrator. Available
in postscript format here.
-
I. Kolmanovsky, N. H. McClamroch,
Developments in nonholonomic control
problems, IEEE Control Systems Magazine, vol. 15, 1995, pp. 20-36.
This is a survey paper on nonholonomic systems.
-
R. W. Brockett and D. Liberzon, Quantized feedback stabilization of
linear systems, IEEE Transactions on Automatic Control, vol. 45, July
2000, pp. 1279-1289. This is a paper on quantized linear systems.
Available in pdf format here.
-
D. Liberzon, A hybrid control framework for systems with quantization,
submitted to 40th CDC. Contains more general results and extensions to
nonlinear systems. Available in postscript format here.
-
E. D. Sontag, On the input-to-state stability property, European
Journal of Control, vol. 1, 1995, pp. 24-36. This is a survey on input-to-state
stability (ISS). Available in postscript format here.
-
J. P. Hespanha, D. Liberzon, and A. S. Morse, Logic-based switching
control of a nonholonomic system with parametric modeling uncertainty,
Systems and Control Letters (special issue on hybrid systems), vol. 38,
no. 3, pp. 167-177, Nov 1999. This is a paper on
supervisory control
which treats a nonholonomic system with uncertainty; see also the
paper's appendix. Available in postscript format here.
-
J. P. Hespanha, D. Liberzon, and
A. S. Morse, Supervision of integral-input-to-state stabilizing controllers,
Automatica, to appear. Discusses controller design in the supervisory
framework. Available in postscript format here.
-
J.
P. Hespanha, D. Liberzon, and A. S. Morse, Hysteresis-based supervisory
control of uncertain linear systems, submitted to Automatica, Jan 2001.
Discusses hysteresis switching logics. Available in postscript format
here.
-
See my home page for
other
papers on supervisory control.
Assignments and grading policy: Your grades will be based on homework
and final projects. There will be no exams in this course.
MATLAB files for the nonholonomic robot simulation:
sfrobota.m,
robotmpg.m,
mpgwrite.zip
Parking movies: Andy,
Rong,
Hui-Hung (1,
2,
3,
4,
5),
Sean
Final Projects
Course outline:
I. Introduction
-
1. Definition of a hybrid system
-
2. Solutions to hybrid systems
-
3. Examples
II. Stability analysis of hybrid systems
-
1. Common Lyapunov functions
-
2. Algebraic stability criteria
-
3. Systems with special structure
-
4. Slow switching
-
5. Multiple Lyapunov functions
III. Hybrid control design
-
1. Convex combinations and Lyapunov functions
-
2. Stabilization of linear systems by hybrid output feedback
-
3. Stabilization of mechanical systems
-
4. Control with limited information
-
5. Switching logics and supervisory control