Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions - Sharifov, Ya. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We consider the problem of optimal control in which the state of the controlled system is described by impulsive differentialequations under nonlocal boundary conditions, which is a natural generalization of the Cauchy problem. Using the principleof contracting mappings, we prove the existence and uniqueness of a solution of a nonlocal boundary-value problem withpulse action with fixed admissible controls. Under certain conditions for the initial data of the problem, we calculate thegradient of a functional and obtain necessary optimality conditions.