Optimal control analysis on a class of hybrid systems with impulses and switches

Towards a special class of hybrid systems, the hybrid systems with impulses and switches, a global optimal control problem with free system terminal states is proposed in this paper. Based on this problem, the necessary condition is studied, and then the HISS' minimum principle is obtained. In the proof of the above theorem, the general variational methods and matrix cost functional formulations are employed. In the end of the paper, a special linear HISS is illustrated and the optimal control is obtained by calculation.