Optimal control for switched systems with impulsive effects

In this paper, we studies the optimal control problem for controlled switched systems with impulsive effects. By establishing the dynamic programming principle for this kind of system, we derive the necessary conditions for optimality of an associated hybrid performance functional. Next, we provide the sufficient conditions for optimality. Specializing the obtained results to the case of linear controlled switched systems with impulsive effects, we derive the corresponding sufficient conditions. Finally, one example is given to illustrate the results.