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On Verification of Uncertain Systems

Reachability analysis is an important tool in verification and synthesis of control systems. It refers to the problem of computing bounds on the set of states that can be reached by a dynamical system. Reachability analysis has received a lot of attention in recent work on hybrid and switched dynamical systems where the aim has been to extend existing verification procedures for discrete systems to systems that involve continuous dynamics. The reachability tools that have been proposed so far only use coarse uncertainty descriptions such as differential inclusions, set disturbances, and ellipsoidal approximations. In this lecture we consider reachability analysis of systems where the disturbances and the model discrepancies are characterized by integral quadratic constraints defined in the time domain. This gives improved approximation properties for many types of unmodeled dynamics. Two specific problems of reachability analysis can be identified 1. Reach set computation, which is the problem of computing bounds on the reach set for trajectories of finite time extent. 2. Transition analysis, which is the problem of estimating the mapping from one switching surface to another switching surface. We will illustrate how our results can be used to verify the existence of periodic solutions in piecewise linear systems that are perturbed by a general class of Lipschitz continuous nonlinearities.

Type of Seminar:
Public Seminar
Dr. Ulf Jonsson, Assoc. Prof.
Optimization and Systems Theory Royal Institute of Technology 100 44 Stockholm, SWEDEN
Jan 09, 2003   14:00

ETH Zentrum, Physikstrasse 3, 8600 Zurich, Building ETL , Room K25
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Ulf Jonsson was born in Barsebäck Sweden. He received the Ph.D. degree in Automatic Control at the Lund Institute of Technology in 1996. He has been a postdoctoral fellow at California Institute of Technology and at Massachusetts Institute of Technology. He is now associate professor at the Division of Optimization and Systems Theory, at the Royal Institute of Technology. His current research interests include design and analysis of nonlinear and uncertain control systems, periodic system theory, robust control along trajectories, and convex optimization applications in systems theory.