Level Set Methods for Computation in Hybrid Systems

Abstract. Reachability analysis is frequently used to study the safety of control systems. We present an implementation of an exact reachability operator for nonlinear hybrid systems. After a brief review of a previously presented algorithm for determining reachable sets and synthesizing control laws--upon whose theory the new implementation rests--an equivalent formulation is developed of the key equations governing the continuous state reachability. The new formulation is implemented using level set methods, and its effectiveness is shown by the numerical solution of three examples. 1 Introduction The reachability operator, a function or algorithm that can determine the evolution of sets of trajectories, is key in the synthesis and verification of controllers for continuous, discrete or hybrid systems. Regardless of whether reachability appears implicitly, such as in the generation of invariant sets, or explicitly, no technique for determining safe control systems can avoid its use. It is natural that methods for its accurate, automatic computation are attracting considerable attention