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 have 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: Thursdays 3:30-4:30pm.
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 or on Amazon.com. Also available as PDF download from SpringerLink (subscription access from UIUC). The textbook material will be supplemented by recent research articles.
Final project: This course will involve a final research project, on a topic of your choosing, with an oral and/or written presentation towards the end of the semester. There will be no exams.
Date |
Topic | Slides |
Reading | Notes
| Tue Aug 27 | Introduction to switched and hybrid systems | intro.ppsx | Section 1.1 |
Thu Aug 29 | | no class (DL out of town)
| Tue Sep 3 | no class (DL out of town)
| Thu Sep 5 | no class (DL out of town)
| Tue Sep 10 | Solutions of switched and hybrid systems |
none | Section
1.2
| |
Thu Sep 12 | Stability: definitions and
background results |
none | Appendix A
| |
Tue Sep 17 | Stability under arbitrary switching
and | common Lyapunov functions GUAS.ppsx | Sections
2.1.1-2.1.3 | |
Thu Sep 19 | none | Sections 2.1.4, 2.1.5 |
Tue Sep 24 | Commutation relations and | stability of switched systems LA.ppsx | Section 2.2, Appendix B |
| Thu Sep 26 | Paper
1,
paper 2 |
| Tue Oct 1 | Systems with special
structure | structure.ppsx | Section 2.3 |
| Thu Oct 3 | | | | no class: Allerton conference
| Tue Oct 8 | Common weak Lyapunov functions;
observability | observability.ppsx | Download paper |
| Thu Oct 10 | Multiple Lyapunov functions and
dwell-time switching | constrained.ppsx | Sections
3.1, 3.2, paper
| |
Tue Oct 15 | Average dwell time; multiple weak Lyapunov
functions |
Thu Oct 17 | State-dependent switching | Sections
3.3, 3.4 | |
Tue Oct 22 | Input-to-state stability of
switched systems | ISS-invertibility.ppsx |
Paper 1, paper 2 |
Thu Oct 24 | Invertibility of
switched systems | Download paper | |
Tue Oct 29 | Gradient algorithms;
introduction to hybrid control | gradient.ppsx | Paper 1, paper 2 |
| Thu Oct 31 | Hybrid control of
nonholonomic
systems | parking.ppsx | Chapter 4 |
| Tue Nov 5 | Control with limited
information | limited-info.ppsx | Section 5.3
|
| Thu Nov 7 | Paper 1, paper
2 | will finish at 3:00pm
| Tue Nov 12 | Switching adaptive
control | supervisory.ppsx | Chapter
6 |
| Thu Nov 14 |
| Tue Nov 19 | Final project
presentations | | |
| Thu Nov 21 | Final project presentations | | |
| Tue Nov 26 | | | | no class: break
| Thu Nov 28 | | | | no class: break
| Tue Dec 3 | Final project presentations | | |
| Thu Dec 5 | Final project presentations | | |
| Tue Dec 10 | Final project presentations | | |
| |