Grande Salle de VERIMAG
19 novembre 2009 - 16h00
Reachability Analysis of Nonlinear and Hybrid Systems with Zonotopes
par Matthias Althoff de Technische Universität München
Abstract: The necessity of automatic tools for the verification of dynamic systems is constantly increasing due to the growing complexity of the technical world. A possible answer to this problem is the verification of hybrid systems based on reachability analysis. One of the biggest challenges in reachability analysis is the curse of dimension. As a possible solution to this problem, zonotopes have been suggested as a representation of reachable sets by e.g. W. Kühn and A. Girard. The performance of zonotopes for linear systems is exceptional; however there are still obstacles to overcome when zonotopes are used for nonlinear and hybrid systems which are addressed in this talk.
First, an approach for linear systems with uncertain parameters is introduced, which is an extension to the work of A. Girard. This approach is then extended to nonlinear system based on conservative linearization, i.e. the linearization error is added as an uncertain input. Next, the extension to hybrid systems is presented. A special focus will be the conversion of zonotopes to polytopes and back to zonotopes which is required when the reachable set intersects guard sets.
In the end, a short overview is given on the safety analysis of autonomous cars.
Matthias Althoff received the diploma engineering degree in Mechanical Engineering in 2005 from the Technische Universität München, Germany. Currently he is a PhD student at the Institute of Automatic Control Engineering, Faculty of Electrical Engineering and Information Technology, Technische Universität München, Germany. His research interests include (stochastic) reachability analysis of continuous and hybrid systems, and safety analysis of driving strategies of autonomous cars.
