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Russia Chelyabinsk; Yekaterinburg
Year
2020
Volume
30
Issue
3
Pages
429-443
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Section Mathematics
Title On one control problem with disturbance and vectograms depending linearly on given sets
Author(-s) Ukhobotov V.I.ab, Ushakov V.N.b
Affiliations Chelyabinsk State Universitya, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesb
Abstract A control problem with a given end time is considered, in which the control vectograms and disturbance depend linearly on the given convex compact sets. A multivalued mapping of the phase space of the control problem to the linear normed space $E$ is given. The goal of constructing a control is that at the end of the control process the fixed vector of the space $E$ belongs to the image of the multivalued mapping for any admissible realization of the disturbance. A stable bridge is defined in terms of multivalued functions. The presented procedure constructs, according to a given multivalued function which is a stable bridge, a control that solves the problem. Explicit formulas are obtained that determine a stable bridge in the considered control problem. Conditions are found under which the constructed stable bridge is maximal. Some problems of group pursuit can be reduced to the considered control problem with disturbance. The article provides such an example.
Keywords control problem, disturbance, stable bridge
UDC 517.977
MSC 49N70, 49N75, 91A23, 91A24
DOI 10.35634/vm200306
Received 24 July 2020
Language Russian
Citation Ukhobotov V.I., Ushakov V.N. On one control problem with disturbance and vectograms depending linearly on given sets, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 3, pp. 429-443.
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