On the optimal control of hybrid systems: Optimization of switching times and combinatoric location schedules

A class of the hybrid optimal control problem is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented. These conditions constitute generalizations of the standard Maximum Principle (MP). Based upon these conditions, we propose a class of comparatively simple general Hybrid Maximum Principle (HMP) algorithms for hybrid systems optimization. Furthermore, the HMP algorithms are embedded in the so called HMP[Comb] algorithms class; the latter class extends the HMP class with discrete search algorithms which find locally optimal switching schedules and their associated switching times. The efficacy of the proposed algorithms is illustrated via a computational example.