This article is cited in 18 papers

Optimal control of impulsive systems with nonlocal boundary conditions

Ya. A. Sharifov<sup>ab

a</sup> Baku State University, Baku, Republic of Azerbaijan
^b Institute of Cybernetics, National Academy of Sciences, Republic of Azerbaijan, Baku, Republic of Azerbaijan

Abstract: In this paper we study an optimal control problem, where states of a control system are described by impulsive differential equations with nonlocal boundary conditions. With the help of the contraction principle we prove the existence and uniqueness of a solution to the corresponding boundary value problem with fixed admissible controls. We calculate the first and second variations of the functional. Using the variation of controls, we establish various necessary optimality conditions of the second order.

Keywords: nonlocal boundary conditions, optimal control, impulsive systems, existence and uniqueness of solutions.

UDC: 517.977

Received: 11.01.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 65–72

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