Reachability Analysis of Nonlinear and Hybrid Systems using Zonotopes PDF slides
Matthias Althoff, ECE

05/07/2010, 2pm, GHC-6115


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 stochastic reachability analysis with a special focus on the safety analysis of autonomous cars.


Matthias Althoff is currently a postdoctoral researcher in the group of Prof. Bruce Krogh, department of Electrical and Computer Engineering at Carnegie Mellon University. He is shortly defending his Ph.D. degree at the Technische Universität München, Germany, and he received the diploma engineering degree in Mechanical Engineering in 2005 from the same university. His research interests include (stochastic) reachability analysis of continuous and hybrid systems, and safety analysis of autonomous cars.


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nsfSupported by an Expeditions in Computing award from the National Science Foundation