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 control literature. This advanced graduate-level course will introduce the students to analysis and design of switched and hybrid systems. The selection of specific topics is heavily influenced by the research of the instructor and his collaborators, drawn from his 2003 research monograph and more recent research articles.
Announcements:
Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
illinois.edu
Office hours: TBD
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 (university login required). 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 required homework or exams.
Date |
Topic | Slides |
Reading
| Tue Jan 17 | Introduction to switched and hybrid systems | intro.ppsx | Section 1.1
| Thu Jan 19 | Solutions of switched and hybrid systems | none
| Section
1.2
| Tue Jan 24 | Stability: definitions and
background results | none
| Appendix A
| Thu Jan 26 | Uniform stability
and common Lyapunov
functions | GUAS.ppsx | Sections
2.1.1-2.1.3
| Tue Jan 31 | Uniform stability of switched linear systems | none | Sections 2.1.4, 2.1.5
| Thu Feb 2 | Commutation relations and | stability of switched systems LA.ppsx | Section 2.2, Appendix B
| Tue Feb 7 | Paper
1,
paper 2, paper 3
| Thu Feb 9 | Systems with special
structure | structure.ppsx | Section 2.3
| Tue Feb 14 | Common weak Lyapunov functions;
observability | observability.ppsx | Download paper
| Thu Feb 16 | Multiple Lyapunov functions and
dwell-time switching | constrained.ppsx | Sections
3.1, 3.2
| Tue Feb 21 | Guest lecture by Prof. Rafal Goebel, Loyola University Chicago |
| Thu Feb 23 | Average dwell time; multiple weak Lyapunov
functions; state-dependent switching | constrained.ppsx | Sections
3.2-3.4, paper
| Tue Feb 28 | Input-to-state stability of
switched systems | ISS-invertibility.ppsx |
Paper 1, paper 2
| Thu Mar 2 | Invertibility of
switched systems | Download paper
| Tue Mar 7 | Introduction to hybrid control; | hybrid control of nonholonomic systems parking.ppsx | Chapter 4
| Thu Mar 9
| Tue Mar 14 | No class: Spring break | |
Thu Mar 16 | No class: Spring break | | |
Tue Mar 21 | Control with limited
information | limited-info.ppsx | Section 5.3
| Thu Mar 23 (Zoom) | Paper 1, paper
2, paper 3
| Tue Mar 28 | No class: DL out of town | |
Thu Mar 30 | No class: DL out of town | | |
Thu Apr 4 | Switching adaptive
control | supervisory.ppsx | Chapter
6
| Tue Apr 6
| Tue Apr 11 | Gradient algorithms | gradient.ppsx | Paper 1, paper 2
| Thu Apr 13 | Final project
presentations | |
Tue Apr 18 | Final project
presentations | |
Thu Apr 20 | Limited data-rate control of switched systems | switched-quantized.ppsx | Download paper
| Tue Apr 25 | Final project presentations |
Thu Apr 27 | Final project presentations | |
Tue May 2 | Final project presentations | |
|