This article is cited in 23 papers

MATHEMATICS

On the solution of control problems with fixed terminal time

V. N. Ushakov, A. A. Ershov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia

Abstract: We consider the nonlinear controlled system in a finite-dimensional Euclidean space in a finite time interval. We study the problem of a system approaching a given compact set in finite time. Approximate solution of the approaching problem is discussed. The approach used to construct an approximate solution is based on constructions based on the notion of a set of solvability of the approaching problem. The concept of correcting control with and without additional operating influences is introduced. We propose a scheme of approximate backward construction of the solvability set, as well as the scheme of control software, which allows finding approximately a solution to the approaching problem. In it, the operating influence breaks down into “main” and “correcting”. An estimate of the deviation of the operated system from the target set at the final moment is constructed and it is shown that the use of additional correcting control in the control process can essentially improve the result of control.

Keywords: control problem, approaching problem, correcting control, controlled system, integral funnel, set of solvability.

UDC: 517.977.58

MSC: 49M25

Received: 17.10.2016

DOI: 10.20537/vm160409

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