The minimum principle for deterministic impulsive control systems

We prove the minimum principle for an optimal impulsive control problem. This result is a generalization of the well-known Pontryagin minimum principle, and yields a necessary condition for an optimal impulsive control strategy that minimizes an associated cost. Furthermore, we establish an explicit connection between the value function arising from the dynamic programming principle approach and the costate arising from the minimum principle approach for the impulsive optimal control problem