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Home » Issues » Archive of Issues » 2024 - 2 issue » pp. 204-221

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Russia Yekaterinburg
Year
2024
Volume
34
Issue
2
Pages
204-221
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Section Mathematics
Title On solving terminal approach and evasion problems for linear discrete-time systems under state constraints
Author(-s) Kostousova E.K.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract The paper is devoted to elaboration of polyhedral techniques for solving two control problems for linear discrete-time systems with uncertainties under state constraints, namely, the terminal approach problem and the terminal evasion one. Such problems arise in systems with two controls, where the aim of the first is to steer the trajectory onto a given terminal set at a given instant without violating the state constraints, the aim of the other is opposite. It is assumed that the terminal set is a parallelepiped, the controls are bounded by parallelotope-valued constraints, and the state constraints are given in the form of so-called zones. We present techniques for solving both problems basing on polyhedral (parallelotope-valued or parallelepiped-valued) tubes. The techniques for solving the approach problem were proposed by the author earlier, but here additional properties of them are investigated. In particular, for the case without state constraints, guaranteed estimates are found for the trajectory that ensure that it is inside the tube. Convenient sufficient conditions are given to guarantee the obtaining of nondegenerate cross-sections during the calculations. For the evasion problem, a common solution scheme is considered, and then polyhedral techniques are proposed. The whole parametric families of external and internal polyhedral estimates for the solvability tubes for both problems are presented and compared. An illustrative example is given.
Keywords systems with uncertainties, control synthesis, approach problem, evasion problem, polyhedral methods, parallelotopes, parallelepipeds
UDC 517.977
MSC 93C41, 93C55, 93B50, 52B12
DOI 10.35634/vm240203
Received 20 October 2023
Language English
Citation Kostousova E.K. On solving terminal approach and evasion problems for linear discrete-time systems under state constraints, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 2, pp. 204-221.
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