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: Thursdays immediately after clas.
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 25 | Introduction to switched and hybrid systems | intro.ppsx | Section 1.1
| Thu Aug 27 | Solutions of switched and hybrid systems |
none | Section
1.2
| Tue Sep 1 | Stability: definitions and
background results |
none | Appendix A
| Thu Sep 3 | Stability under arbitrary switching
and | common Lyapunov functions GUAS.ppsx | Sections
2.1.1-2.1.3
| Tue Sep 8 | none | Sections 2.1.4, 2.1.5
| Thu Sep 10 | Commutation relations and | stability of switched systems LA.ppsx | Section 2.2, Appendix B
| Tue Sep 15 | Paper
1,
paper 2
| Thu Sep 17 | Systems with special
structure | structure.ppsx | Section 2.3
| Tue Sep 22 | Common weak Lyapunov functions;
observability | observability.ppsx | Download paper
| Thu Sep 24 | Multiple Lyapunov functions and
dwell-time switching | constrained.ppsx | Sections
3.1, 3.2, paper
| Tue Sep 29 | Average dwell time; multiple weak Lyapunov
functions
| Thu Oct 1 | No class: Allerton conference |
Tue Oct 6 | State-dependent switching | constrained.ppsx | Sections
3.3, 3.4
| Thu Oct 8 | Input-to-state stability of
switched systems | ISS-invertibility.ppsx |
Paper 1, paper 2
| Tue Oct 13 | Invertibility of
switched systems | Download paper
| Thu Oct 15 | Gradient algorithms | gradient.ppsx | Paper 1, paper 2
| Tue Oct 20 | Introduction to hybrid control; | hybrid control of nonholonomic systems parking.ppsx | Chapter 4
| Thu Oct 22
| Tue Oct 27 | Control with limited
information | limited-info.ppsx | Section 5.3
| Thu Oct 29 | Paper 1, paper
2
| Tue Nov 3 | Limited data-rate control of switched systems; | multi-agent coordination with quantized sensing switched-quantized.ppsx | Download paper
| Thu Nov 5 | polygons.pdf | Paper 1, paper
2
| Tue Nov 10 | Switching adaptive
control | supervisory.ppsx | Chapter
6
| Thu Nov 12
| Tue Nov 17 | Final project
presentations | |
Thu Nov 19 | Final project presentations | |
Tue Nov 24 | No class: Thanksgiving break | |
Thu Nov 26 | No class: Thanksgiving break | | |
Tue Dec 1 | Final project presentations |
Thu Dec 3 | Final project presentations | |
Tue Dec 8 | Final project presentations |
|