ECE 586 DL: Hybrid Systems and Control (Spring 2023)

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:

• Recorded videos of the lectures can be accessed at this Mediaspace channel (Illinois login required). Unfortunately, the camera capturing the whiteboard does not always function properly.
• The default lecture format is in-person. However, there may be exceptions when we may need to switch to Zoom. In those cases, an email will be sent to the class. If you are not on the class email list but wish to be notified of such changes, please email the course instructor.

Logistics

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.

Syllabus

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	Average dwell time; multiple weak Lyapunov functions; state-dependent switching	constrained.ppsx	Sections 3.2-3.4, paper
Thu	Input-to-state stability of switched systems	ISS-invertibility.ppsx	Paper 1, paper 2
Tue	Invertibility of switched systems		Download paper
Thu	Gradient algorithms	gradient.ppsx	Paper 1, paper 2
Tue	Introduction to hybrid control; hybrid control of nonholonomic systems	parking.ppsx	Chapter 4
Thu
Tue	No class: Spring break
Thu	No class: Spring break
Tue	Control with limited information	limited-info.ppsx	Section 5.3
Thu			Paper 1, paper 2, paper 3
Tue	Limited data-rate control of switched systems	switched-quantized.ppsx	Download paper
Thu	Switching adaptive control	supervisory.ppsx	Chapter 6
Tue
Thu
Tue
Thu	Final project presentations
Tue	Final project presentations
Thu	Final project presentations
Tue	Final project presentations
Thu	Final project presentations
Tue