ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations
and
Control Processes

Optimal Time Control Problem for Nonlinear Systems with Restrictions

Author(s):

Serikbay Aisagaliev

Professor, Doctorate of Technical Sciences
al-Farabi Kazakh National University,
al-Farabi avenue, 65/66, 050040,
Almaty, Kazakhstan
Phone: 8(727) 2-62-37-48

serikbai.aisagaliev@kaznu.kz

Asem Kabidoldanova

Candidate of Physico-mathematical Sciences
al-Farabi Kazakh National University,
Gagarin avenue, 292/1/38, 050060,
Almaty, Kazakhstan
Phone: 8(727) 2-248-24-29

kabasem@mail.ru

Abstract:

This paper is devoted to constructive method preparation for optimal time control problem of nonlinear with phase, integral restrictions and restrictions on control values.

The analytical-numerical method is offered on the base of imbedding principle. Imbedding principle based on a general solution of the first kind Fredholm integral equation and its analytical expression. Necessary and enough conditions of solution existence for optimal time control problem of nonlinear systems are obtained by the way of boundary value problem imbedding to the special initial optimization problem. The approach permits to apply a numerical methods of initial optimization problems solving. The verifying method of necessary and enough conditions of solution existence is offered. The method of admissible solution construction is developed by the way of minimizing sequences construction for optimal control problem with free endpoint of trajectories and with regularizated functional. Estimation for speed of minimizing sequences convergence is obtained. The method of optimal control and optimal trajectory construction is developed.

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