Study on the minimum principle of hybrid impulsive and switching systems with Ekeland´s variational principle

The global optimal control problem with free system terminal states is proposed for the hybrid impulsive and switching systems (HISS). Towards the problem mentioned above, the necessary condition of the above problem, the HISS´ minimum principle, is given. In the process of proving the above theorem, the Ekeland´s variational principle and the matrix cost functional formulation are utilized. Based on the main result, a special linear HISS is illustrated and the optimal control algorithm is presented.