Abstract

Reachability analysis is critical for obtaining formal safety and performance guarantees for nonlinear and hybrid dynamical systems. However existing computational tools do not scale to models with more than a few state variables. In this talk we present a scalable procedure to compute tight over-approximations of reachable sets.  We first sample a number of trajectories of the system and next establish a tight bound on the divergence between the samples and neighboring trajectories using the concept of matrix measures from contraction theory. The divergence bounds also account for the accumulation of numerical simulation errors along simulation traces, which means that the proposed method provides a guaranteed over-approximation of the reachable set.  We demonstrate that the proposed technique scales well to systems with a large number of states.

Biography

Murat Arcak is a professor at U.C. Berkeley in the Electrical Engineering and Computer Sciences Department.  He received the B.S. degree in Electrical Engineering from the Bogazici University, Istanbul, Turkey (1996) and the M.S. and Ph.D. degrees from the University of California, Santa Barbara (1997 and 2000). His research is in dynamical systems and control theory with applications to synthetic biology, multi-agent systems, and transportation. Prior to joining Berkeley in 2008, he was a faculty member at the Rensselaer Polytechnic Institute. He received a CAREER Award from the National Science Foundation in 2003, the Donald P. Eckman Award from the American Automatic Control Council in 2006, the Control and Systems Theory Prize from the Society for Industrial and Applied Mathematics (SIAM) in 2007, and the Antonio Ruberti Young Researcher Prize from the IEEE Control Systems Society in 2014. He is a member of SIAM and a fellow of IEEE.