Necessary conditions of optimality for impulsive differential inclusions

In this paper, we address a class of optimal control problems with dynamic constraints are specified by a differential inclusion, the control variables are in the space of positive Borel measures and the state trajectories are considered to be in the space of ℛⁿ -valued functions of bounded variation. A concept of robust solution to a measure differential inclusion is introduced that takes into account the interaction between the control measure and state variables during the jumps. Necessary conditions of optimality are obtained as a limit of the same type of conditions for a sequence of an appropriate class of conventional dynamic optimization problems