Controller Synthesis for Hybrid Systems: the Hamilton-Jacobi Approach

lygeros, sastry©eecs, berkeley, edu We present a procedure for synthesizing controllers for safety specifications for hybrid systems. The pro-cedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the Reach-Avoid set). We present a characterization of the Reach-Avoid set in terms of the solution of a pair of coupled Hamilton-Jacobi par-tial differential equations. We also discuss a compu-tational algorithm for solving such partial differential equations, and present an example derived from air-craft conflict resolution