Performance Driven Reachability Analysis for Optimal Scheduling and Control of Hybrid Systems

In this paper we tackle the optimal control problem for piecewise linear and hybrid systems by using a computational approach based on performance-driven reachability analysis. The idea consists of coupling a reachset exploration algorithm, essentially based on repetitive use of linear programming, to a quadratic programming solver which selectively drives the exploration. In particular, an upper bound on the optimal cost is continually updated during the procedure, and used as a criterion to discern non-optimal evolutions and to prevent their exploration. The result is an efficient strategy of branch-and-bound nature, which is especially attractive for solving long-horizon hybrid optimal control and scheduling problems.