Docent Seminar, Optimization and Systems Theory
Friday, April 12, 2002, 11.00-12.00, Room 3721, Lindstedtsv. 25

Ulf Jönsson
Optimization and Systems Theory

On reachability analysis 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 been proposed 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. This gives improved approximation of 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.

Two examples will illustrate the motivation for these two problems. Reach set computation will be used to prove that a robot stays within a close neighborhood of its desired path, which is designed based on some nominal dynamics. Transition analysis on the other hand will be used to prove a certain type of robustness for limit cycles in piecewise linear systems.

Our analysis results in a nonconvex optimal control problem, which can be addressed using Lagrange relaxation. We discuss how the dual optimization can be performed and review some special conditions under which there is no duality gap.

Calendar of seminars
Last update: March 27, 2002 by Anders Forsgren,