Optimal impulsive control problems with state and mixed constraints

The optimal control of a complex process described by a system of measure differential equations under a constraint imposed on the total impulse of control was studied. The system is considered with state constraints in natural and fast time and with mixed constraints relating a control measure and a phase trajectory. Based on a discontinuous change of time, a method is developed for transforming the problem into an equivalent one with bounded controls. By using Theorem, necessary optimality conditions in the class of admissible processes of problem (P) can be obtained by converting the corresponding optimality conditions in problem (RP). The appearance of the unknown function of bounded variation as a Lagrange multiplier and an increase in the dimension of the adjoint variables are associated with the mixed constraints.