CSL Decision and Control Group

Title: Lyapunov-like converse results for strong forward invariance.

Abstract: A set is strongly invariant for a dynamical system if all solutions from the set remain in the set. When the dynamics are somewhat irregular, for example given by non-Lipschitz differential equations or a differential "equation" with a multivalued right-hand side, properties of the dynamics on the set are not enough to ensure strong invariance. Well-known conditions for strong invariance involve "subtangential" velocities, which can be expressed in terms of tangent cones to the set. This talk first presents simple sufficient conditions for strong forward invariance of closed or compact sets, given in terms of Lyapunov-like functions, and then focuses on necessary conditions/converse Lyapunov results that construct Lyapunov-like functions for invariant sets. These functions are positive definite with respect to the invariant set, are reasonably smooth, and don't increase too fast along the dynamics. Connections of these functions to usual Lyapunov and barrier functions are explored in the proofs. The results are joint work with A. Teel and R. Sanfelice.

Bio: Rafal Goebel received Ph.D. in mathematics in 2000 from the University of Washington. He held postdoctoral positions at the Departments of Mathematics at University of British Columbia and Simon Fraser University in Vancouver, and at the Electrical and Computer Engineering Department of University of California, Santa Barbara. In 2008, he joined the Department of Mathematics and Statistics at Loyola University Chicago where he is currently a professor. He received the 2009 SIAM Control and Systems Theory Prize, is a co-author of the Hybrid Dynamical Systems: Modeling, Stability, and Robustness book, and the author of the Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control: An Introduction book. His interests include convex, nonsmooth, and set-valued analysis; control, including optimal control; hybrid dynamical systems; mountains; and optimization.

Location & Time: Location TBA, February 11, 3-4PM
Reception in CSL154 at 2:30PM