| Zeit: | 3. Juli 2023 |
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Prof. Murat Arcak
The University of California, Berkeley
Berkeley, CA, USA
Monday 2023-07-03 4:00 p.m.
IST Seminar Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
Abstract
The computation of reachable sets is critical for characterizing the behavior of safety-critical systems. Since the reachable set can rarely be computed exactly, several methods have been developed to approximate this set with various set representations. However, these methods are computationally expensive and do not scale well to high dimensional systems. This talk will present a suite of methods with superior scalability properties. After a quick review of some of our earlier techniques using monotonicity and sensitivity concepts, we will discuss more recent results with a data-driven approach. This approach is particularly suitable for high-dimensional and analytically intractable system models. We use a finite ensemble of sample trajectories to compute reachable set estimates, and we provide guarantees of high accuracy in a probabilistic sense with associated sample complexity bounds. We will present two computational methods with this flavor. The first one uses scenario optimization to construct reachable set estimates as approximate solutions to chance-constrained optimization problems. The second method uses a class of polynomials derived from empirical moment matrices, whose sublevel sets act as non-convex estimates of the reachable set.
Biographical Information
Murat Arcak is a professor at U.C. Berkeley in the Electrical Engineering and Computer Sciences Department, with a courtesy appointment in Mechanical Engineering. 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 in multi-agent systems and transportation. 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 ACM and SIAM, and a fellow of IEEE and the International Federation of Automatic Control (IFAC).