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
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. A digital copy is available on SpringerLink, access by logging in to UIUC library account for free download. The textbook material will be supplemented by more recent research articles.
Recorded lectures: Lectures will not be recorded this semester, but recordings from Spring 2023 are available at this Mediaspace channel (audio and video quality is highly variable).
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 20 | Introduction to switched and hybrid systems | intro.ppsx | Section 1.1
| Thu Jan 22 | Solutions of switched and hybrid systems | none
| Section
1.2
| Tue Jan 27 | Stability: definitions and
background results | none
| Appendix A
| Thu Jan 29 | Stability background (end); uniform stability and
common Lyapunov
functions | GUAS.ppsx | Sections
2.1.1-2.1.3
| Tue Feb 3 | Uniform stability of switched linear systems | none | Sections 2.1.4, 2.1.5
| Thu Feb 5 | Commutation relations and
stability of switched systems | LA.ppsx | Paper
| Tue Feb 10 | Commutation relations and
stability of switched systems (continued) | |
| Thu Feb 12 | Guest lecture by Prof. Rafal Goebel, Loyola University Chicago | Paper, book
| Tue Feb 17 | Systems with special
structure | structure.ppsx | Section 2.3
| Thu Feb 19 | Common weak Lyapunov functions;
observability | observability.ppsx | Paper
| Tue Feb 24 | No class: CSL Student Conference | |
| Thu Feb 26 | Multiple Lyapunov functions and
dwell-time switching | constrained.ppsx | Sections
3.1, 3.2.1
| Tue Mar 3 | Average dwell time; multiple weak Lyapunov
functions | constrained.ppsx | Section
3.2.2, paper
| Thu Mar 5 | State-dependent switching | constrained.ppsx | Sections
3.3, 3.4
| Tue Mar 10 | Input-to-state stability of
switched systems | ISS-invertibility.ppsx |
Paper 1, paper 2
| Thu Mar 12 | Invertibility of
switched systems | ISS-invertibility.ppsx | Paper
| Tue Mar 17 | No class: Spring break | |
| Thu Mar 19 | No class: Spring break | |
| Tue Mar 24 | Introduction to hybrid control; obstructions to continuous stabilization | parking.ppsx | Chapter 4
| Thu Mar 26 | Obstructions to continuous stabilization (continued);
nonholonomic
systems |
| Tue Mar 31 | Control with limited
information | limited-info.ppsx | Section 5.3
| Thu Apr 2 | Control with limited
info (continued); small-gain theorems for hybrid systems | | Paper 1, paper 2
| Tue Apr 7 | Switching adaptive
control | supervisory.ppsx | Chapter
6
| Thu Apr 9 | Guest lecture by Dr. Bao Tran on hybrid observers | estimation.ppsx | Thesis (Chapters 8 and 12)
| Tue Apr 14 | Switching adaptive
control (continued) | |
| Thu Apr 16 | Common quadratic Lyapunov functions: computational aspects | gradient.ppsx | Paper 1, paper 2
| Tue Apr 21 | Final project presentations | |
| Thu Apr 23 | Final project presentations | |
| Tue Apr 28 | Final project presentations | |
| Thu Apr 30 | Final project presentations | |
| Tue May 5 | Final project presentations | |
| |