In this paper, we derive the Pontryagin’s maximum principle for optimal control problems governed by nonlinear impulsive differential equations. Our method is based on Dubovitskii-Milyutin theory, but in doing so, we assumed that the linear variational impulsive differential equation around the optimal solution is exactly controllable, which can be satisfied in many cases. Then, we consider an example as an application of the main result. After that, we study the case when the differential equation is of neutral type. Finally, several possible problems are proposed for future research where the differential equation, the constraints, the time scale, the impulses, etc. are changed.
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