Optimal control problem for impulsive systems with integral boundary conditions

Abstract

In this paper the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. By the help of the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first variation of the functional is calculated. Various necessary conditions of optimality of the first order are obtained by the help of the variation of the controls.