Department of Mathematics - Doctoral School in Mathematics jointly with the Department of Industrial Engineering
Polo F. Ferrari 1, via Sommarive, 5, Povo, Trento, Italy
- Andrew R. Teel (University of California, Santa Barbara, USA)
This short course presents a particular modeling framework for stochastic hybrid dynamical systems.
The framework allows for non-unique solutions and randomness affecting both the continuous-time evolution as well as the jumps of the system. Various examples fitting this framework will be used to illustrate concepts. Stability theory for these systems will be the primary focus of the course.
Different stability notions, including asymptotic stability in probability as well as recurrence, will be considered. Lyapunov function theory for these properties will be developed, as well as invariance-like principles and other relaxations of classical Lyapunov conditions. This theory will require a careful development of the meaning of solution for a stochastic hybrid system. Moreover, in order to motivate the approach taken, some preliminary results pertaining to non-stochastic hybrid systems will be recalled.
Course topics: 1) Brief review of non-stochastic hybrid systems (Formal model, Solution concept, Stability definitions, Lyapunov and Matrosov functions, Invariance principle); 2) Formal models of stochastic hybrid systems; 3) Solution concept for stochastic hybrid systems (Randomness only in the jumps, Randomness also in the flows); 4) Stability definitions (Asymptotic stability in probability, Recurrence); 5) Sufficient conditions for stability (Lyapunov functions, Matrosov functions); 6) Additional results for the case of randomness only in the jumps (A sequential compactness result, An invariance-like principle, Converse Lyapunov theorems, Robustness, Equivalent characterizations of stability).
Timetable. Monday 9 14:00-17:00 room A208, Tuesday 10 9:00-12:00 room A211, Wednesday 11 9:00-12:00 room A212, Thursday 12 9:00 12:00 room A211, Friday 13 9:00-12:00 room A210.
Biosketch: Andrew R. Teel received the M.S. (1989) and Ph.D. (1992) degrees in electrical engineering from the University of California, Berkeley. He was a post-doc fellow at the Ecole des Mines de Paris, France and an Assistant Professor at the Electrical Engineering Department, University of Minnesota. He joined the Electrical and Computer Engineering Department, University of California, Santa Barbara in 1997, 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 received, among many others, the first SIAM Control and Systems Theory Prize in 1998, the 1999 Donald P. Eckman Award and the 2001 O. Hugo Schuck Best Paper Award, both given by the American Automatic Control Council, and the 2010 IEEE Control Systems Magazine Outstanding Paper Award. He is an area editor for Automatica, an IFAC and an IEEE Fellow.
More info: http://r.unitn.it/en/maths/opthysys (Hybrid Systems Optimization unitn project webpage)
Contact: Fabio Bagagiolo fabio.bagagiolo [at] unitn.it, Luca Zaccarian luca.zaccarian [at] unitn.it
Participation to the course is free but the interested participants should contact the organizers by email.