ON THE FEATURES OF THE NONLINEAR OPTIMIZATION PROBLEM OF OSCILLATION PROCESSES WITH DISTRIBUTED AND BOUNDARY VECTOR CONTROLS

Authors

E.F. Abdyldaeva Kyrgyz-Russian Slavic University named after B.N. Yeltsin
A. Kerimbekov Kyrgyz-Russian Slavic University named after B.N. Yeltsin

Keywords:

nonlinear optimization problem, distributed vector control, boundary vector control, generalized solution, maximum principle, properties of equal ratios, optimal control, optimal process, minimal value of the functional.

Abstract

In this paper the optimal control problem is investigated for elastic oscillations described by Fredholm integro-differential equations where functions of external and boundary influences nonlinearly depend on control parameters. The study was carried out using the concept of a generalized solution of boundary value problem for a controlled process. According to maximum principle for systems with distributed parameters, optimality conditions are established in the form of equalities and inequalities. Optimality conditiond in the form of equality lead to a system of nonlinear integral equations, which have the property of equal relations, and the conditions in the form of inequalitieslead to differential inequalities with regard to functions of external and boundary sources. The property of equal relations is one of the features of the considering nonlinear optimization problem.

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