Second-Order Sufficient Optimality Conditions for an Optimal Control Problem with Mixed Constraints

In this paper, we study second-order necessary and sufficient optimality conditions for an optimal control problem with state-control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order necessary optimality conditions for an optimal control problem. In some cases, by using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions. Besides, second-order sufficient optimality conditions for an optimal control problem where objective function may only depend on the state, are also discussed. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.