Abstract:
The paper considers the problem of approximate construction of reachability sets for a linear control system, when the control action is constrained simultaneously by geometric and several integral constraints. A variant of the transition from a continuous to a discrete system is proposed by uniformly dividing the time interval and replacing the controls at the step of dividing them with their mean values. The convergence of the reachability set of the approximating system to the reachability set of the original system in the Hausdorff metric is proved as the discretization step tends to zero, and an estimate is obtained for the rate of convergence. An algorithm for constructing the boundary of reachable sets based on solving a family of conic programming problems is proposed. Numerical simulation has been carried out.
The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075–02–2022–874).
Citation:
I. V. Zykov, “Approximate calculation of reachable sets for linear control systems with different control constraints”, Izv. IMI UdGU, 60 (2022), 16–33
\Bibitem{Zyk22}
\by I.~V.~Zykov
\paper Approximate calculation of reachable sets for linear control systems with different control constraints
\jour Izv. IMI UdGU
\yr 2022
\vol 60
\pages 16--33
\mathnet{http://mi.mathnet.ru/iimi433}
\crossref{https://doi.org/10.35634/2226-3594-2022-60-02}
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https://www.mathnet.ru/eng/iimi433
https://www.mathnet.ru/eng/iimi/v60/p16
This publication is cited in the following 3 articles:
D.N. Ibragimov, S.S. Samonov, “On the conditions of limited sets of reachability and controllability for linear systems with discrete time and total first-order constraints on scalar control”, Modelling and Data Analysis, 15:1 (2025), 51
V. P. Maksimov, “K voprosu o tochnosti vychisleniya dostizhimykh znachenii tselevykh funktsionalov dlya sistem upravleniya s nepreryvnym i diskretnym vremenem”, Tr. IMM UrO RAN, 30, no. 3, 2024, 207–216
V. P. Maksimov, “On the Error of Calculating the Reachable Values of Objective Functionals for Control Systems with Continuous and Discrete Times”, Proc. Steklov Inst. Math., 327:S1 (2024), S198
Citation in format AMSBIB
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