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ECE 586 DL: Hybrid Systems and Control (Fall 2009)

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.

Logistics

Instructor: Daniel Liberzon. Office: 144 CSL. Email: liberzon at uiuc.edu
Schedule: Tue Thu 2-3:20, 57 Everitt Lab.
Office hours: Thu 3:40-5.
Prerequisite: 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.
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 presentation towards the end of the semester. There will be no exams.

Syllabus

A tentative course syllabus is given below. Powerpoint slides for each lecture will usually be added on the day of the lecture. To view them, it is best to save them first and then open with Powerpoint. All section and page numbers in the "reading" column refer to the textbook unless otherwise noted.

Date	Topic	Slides	Reading	Notes
Tue Aug 25				no class (DL out of town)
Thu Aug 27				no class (DL out of town)
Tue Sep 1	Hybrid and switched systems and their solutions	intro.pps	Section 1.1
Thu Sep 3	Hybrid and switched systems and their solutions	none	Section 1.2
Tue Sep 8	Stability: definitions and background results	none	Appendix A
Thu Sep 10	Stability: definitions and background results	none	Appendix A
Tue Sep 15	Stability under arbitrary switching and common Lyapunov functions	GUAS.pps	Sections 2.1.1-2.1.3
Thu Sep 17		none	Sections 2.1.4, 2.1.5
Tue Sep 22	Commutation relations and stability of switched systems	LA.pps	Section 2.2, Appendix B
Thu Sep 24	Commutation relations and stability of switched systems	LA.pps	Paper 1, paper 2
Tue Sep 29	Systems with special structure	structure.pps	Section 2.3
Thu Oct 1				no class: Allerton conference
Tue Oct 6	Common weak Lyapunov functions; observability	observability.pps	Download paper
Thu Oct 8	Multiple Lyapunov functions and dwell-time switching	constrained.pps	Sections 3.1, 3.2, paper
Tue Oct 13	Average dwell time; multiple weak Lyapunov functions		Sections 3.1, 3.2, paper	will finish at 2:50pm (CSL seminar)
Thu Oct 15	State-dependent switching		Sections 3.3, 3.4
Tue Oct 20	Input-to-state stability of switched systems	ISS-invertibility.pps	Download paper	will finish at 2:50pm (ME seminar)
Thu Oct 22	Invertibility of switched systems	ISS-invertibility.pps	Download paper
Tue Oct 27	Gradient algorithms; introduction to hybrid control	gradient.pps	Paper 1, paper 2
Thu Oct 29	Hybrid control of nonholonomic systems	parking.pps	Chapter 4
Tue Nov 3	Control with limited information	limited-info.pps	Section 5.3
Thu Nov 5	Control with limited information	limited-info.pps	Paper 1, paper 2
Tue Nov 10	Switching adaptive control	supervisory.pps	Chapter 6
Thu Nov 12	Switching adaptive control	supervisory.pps	Chapter 6
Tue Nov 17	Final project presentations
Thu Nov 19	Final project presentations
Tue Nov 24				no class: break
Thu Nov 26				no class: break
Tue Dec 1	Final project presentations
Thu Dec 3	Final project presentations
Tue Dec 8	Final project presentations