Switched/hybrid systems are dynamical systems that combine continuous dynamics and discrete events. Such systems are of theoretical interest and important in many applications, and they have attracted considerable attention in the recent control literature. This advanced graduate-level course will introduce the students to recent research results on analysis and design of switched and hybrid systems.
Announcements:
Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
illinois.edu
Office hours: see me after class
Prerequisites:
The course will build on a standard
first-year graduate course in state-space linear systems, such as
ECE 515.
Some knowledge of nonlinear system analysis techniques
(such as those covered in ECE 517 or ECE 528) is a plus but not a
requirement.
Required text: D. Liberzon, Switching in Systems and Control, Birkhauser, 2003. Available in UofI bookstore, on Amazon.com, and through SpringerLink here. The textbook material will be supplemented by recent research articles.
Final project: This course will involve a final project presentation towards the end of the semester. Details will be explained in class. There will be no exams.
Date |
Topic | Slides |
Reading
| Tue Aug 28 | Introduction to switched and hybrid systems | intro.ppsx | Section 1.1
| Thu Aug 30 | Solutions of switched and hybrid systems | none
| Section
1.2
| Tue Sep 4 | Stability: definitions and
background results | none
| Appendix A
| Thu Sep 6 | Stability under arbitrary switching
and | common Lyapunov functions GUAS.ppsx | Sections
2.1.1-2.1.3
| Tue Sep 11 | none | Sections 2.1.4, 2.1.5
| Thu Sep 13 | Commutation relations and | stability of switched systems LA.ppsx | Section 2.2, Appendix B
| Tue Sep 18 | Paper
1,
paper 2, paper 3
| Thu Sep 20 | Systems with special
structure | structure.ppsx | Section 2.3
| Tue Sep 25 | Common weak Lyapunov functions;
observability | observability.ppsx | Download paper
| Thu Sep 27 | Multiple Lyapunov functions and
dwell-time switching | constrained.ppsx | Sections
3.1, 3.2
| Tue Oct 2 | No class: Allerton conference (tutorial sessions) |
Thu Oct 4 | No class: Allerton conference |
Tue Oct 9 | Average dwell time; multiple weak Lyapunov
functions; | state-dependent switching constrained.ppsx | Sections
3.2-3.4, paper
| Thu Oct 11 | Input-to-state stability of
switched systems | ISS-invertibility.ppsx |
Paper 1, paper 2
| Tue Oct 16 | Invertibility of
switched systems | Download paper
| Thu Oct 18 | Gradient algorithms | gradient.ppsx | Paper 1, paper 2
| Tue Oct 23 | Introduction to hybrid control; | hybrid control of nonholonomic systems parking.ppsx | Chapter 4
| Thu Oct 25
| Tue Oct 30 | Control with limited
information | limited-info.ppsx | Section 5.3
| Thu Nov 1 | Paper 1, paper
2, paper 3
| Tue Nov 6 | Limited data-rate control of switched systems | switched-quantized.ppsx | Download paper
| Thu Nov 8 | Switching adaptive
control | supervisory.ppsx | Chapter
6
| Tue Nov 13
| Thu Nov 15 |
| Tue Nov 20 | No class: Thanksgiving break | |
Thu Nov 22 | No class: Thanksgiving break | | |
Tue Nov 27 | Final project
presentations | |
Thu Nov 29 | Final project presentations | |
Tue Dec 4 | Final project presentations |
Thu Dec 6 | Final project presentations | |
Tue Dec 11 | Final project presentations |
|