AMOS is proud to announce the visit of Professor Andrew R. Teel, University of California at Santa Barbara in fall 2013.

Course Outline

1. Examples of hybrid systems
   Hybrid automata, mechanical systems with impacts, hybrid control systems; Text Chapter 1
2. The solution concept
   Data, hybrid time domains, basic properties of solutions; Text Chapter 2.
3. Asymptotic stability
   Definitions, Lyapunov functions, equivalent characterizations, the invariance principle;
   Text,Chapters 3, 7 & 8. Matrosov functions; Supplemental papers
4. Well-posed hybrid systems
   Basic assumptions, material from set-valued analysis, robustness; Text, chapters 4-6.
5. Consequences of robustness
   Linearizations; Text, Chapter 9. Simulation theory, averaging, singular perturbations; Supplemental papers.

Prerequisites

Exposure to stability theory for nonlinear systems,
E.g., Nonlinear Systems, 3rd ed., Hassan Khalil, Prentice-Hall

Course summary

Based on the book "Hybrid Dynamical Systems", by R. Goebel, R.G. Sanfelice, and A.R. Teel, Princeton University Press, 2012.The course covers modeling and stability theory for hybrid dynamical systems. The stability analysis tools are applied to prove closed-loop stability for control systems that employ hybrid feedback algorithms. The goal is to equip the student with state-of-the-art analysis and synthesis techniques for hybrid feedback systems. In order to follow the material in the course, it is helpful to have taken courses on linear systems (from a state-space point of view) and nonlinear systems (from a book like Hassan Khalil's "Nonlinear Systems"), and to be comfortable with the mathematics used in those courses.

The course starts with examples of hybrid systems. Next we rigorously define the solution concept, with a focus on hybrid time domains. Zeno solutions are discussed, as well as solutions that satisfy dwell-time or average dwell-time constraints. Then we begin to study asymptotic stability, including asymptotic stability of closed sets, which is a generalization that is important for hybrid systems. Lyapunov-based methods are emphasized. Subsequently, we address basic regularity conditions on the data of a hybrid system. These conditions generalize continuity of the right-hand side of a differential equation. They guarantee that the hybrid system is "well posed", in the sense that small perturbations to the data do not change the nature of the possible solutions. Set-valued analysis techniques are introduced to characterize this well-posedness property. Next we revisit asymptotic stability for well-posed hybrid systems and give several equivalent characterizations, including converse Lyapunov theorems. Subsequently, we develop stability analysis tools based on the invariance principle for hybrid systems. Time permitting, we also discuss averaging theory, singular perturbation theory, and input-to-state stability for hybrid systems. If there is time and interest, stochastic hybrid systems will also be discussed.

About the lecturer

Andrew R. Teel received his A.B. degree in Engineering Sciences from Dartmouth College in Hanover, New Hampshire, in 1987, and his M.S. and Ph.D. degrees in Electrical Engineering from the University of California, Berkeley, in 1989 and 1992, respectively. After receiving his Ph.D., he was a postdoctoral fellow at the Ecole des Mines de Paris in Fontainebleau, France. In 1992 he joined the faculty of the Electrical Engineering Department at the University of Minnesota, where he was an assistant professor until 1997. Subsequently, he joined the faculty of the Electrical and Computer Engineering Department at the University of California, Santa Barbara, where he is currently a professor. His research interests are in nonlinear and hybrid dynamical systems, with a focus on stability analysis and control design. He has received NSF Research Initiation and CAREER Awards, the 1998 IEEE Leon K. Kirchmayer Prize Paper Award, the 1998 George S. Axelby Outstanding Paper Award, and was the recipient of the first SIAM Control and Systems Theory Prize in 1998. He was the recipient of the 1999 Donald P. Eckman Award and the 2001 O. Hugo Schuck Best Paper Award, both given by the American Automatic Control Council, and also received the 2010 IEE Control Systems Magazine Outstanding Paper Award. He is an area editor for Automatica, and a Fellow of the IEEE and of IFAC.