The optimal control problem of Markov multi-model hybrid system

The optimal control of Markov multi-model hybrid system was discussed. First, the expect value function of the optimal control was given. With the help of dynamic programming theory, the properties of the expect value function were analyzed. And the conclusion that the expect value function satisfied a HJB-equation was concluded. The optimum solution was constructed with the expect value function. Consequently, the existence of the optimum solution was proofed.