ECE 497 DL
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,
to Hybrid Dynamical Systems, Springer, 2000.
Note: not available in the bookstore. A copy has been placed on reserve
in the library.
Assignments and grading policy: Your grades will be based on homework
and final projects. There will be no exams in this course.
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
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
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
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.
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
See my home page for
papers on supervisory control.
MATLAB files for the nonholonomic robot simulation:
Parking movies: Andy,
1. Definition of a hybrid system
2. Solutions to hybrid systems
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