Sufficient optimality conditions for impulsive and switching optimal control problems

In this paper, sufficient optimality conditions are given for a class of impulsive and switching optimal control problems. By parameterizing the length of every subinterval between two jumping instants, we transform the hybrid optimal control problem into an equivalent augmented problem. Sufficient optimality conditions for the hybrid optimal control problem are obtained by using classical sufficient optimality conditions to the augment problem. It is shown that sufficient optimality conditions can be verified by checking the Legendre-Clebsch condition and solving some Riccati matrix equations with certain boundary and jump conditions.