Optimal impulsive control problems with hysteresis

摘要

This paper deals with an optimal control problem for measure-driven differential equations with hysteresis. The hysteresis is modelled as a scalar rate independent variational inequality. First, we propose a concept of solution to the impulsive control system of our measure-driven differential equations with hysteresis. In general, these solutions belong to the class of functions of bounded variation. Then, we present some approximate results for the impulsive control system with hysteresis. Finally, we establish the existence of a solution to the optimal control problem we consider.