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Russia Yekaterinburg
Section Mathematics
Title On the solution of control problems with fixed terminal time
Author(-s) Ushakov V.N.a, Ershov A.A.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
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
DOI 10.20537/vm160409
Received 17 October 2016
Language Russian
Citation Ushakov V.N., Ershov A.A. On the solution of control problems with fixed terminal time, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 543-564.
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