Sharifov Ya. A.
Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions
Ukr. Mat. Zh. - 2012. - 64, № 6. - pp. 836-847
We consider the problem of optimal control in which the state of the controlled system is described by impulsive differential equations under nonlocal boundary conditions, which is a natural generalization of the Cauchy problem. Using the principle of contracting mappings, we prove the existence and uniqueness of a solution of a nonlocal boundary-value problem with pulse action with fixed admissible controls. Under certain conditions for the initial data of the problem, we calculate the gradient of a functional and obtain necessary optimality conditions.