Abstract:
This paper deals with an optimal control problem for a linear discrete system with disturbances. It is required to steer the system robustly to a given terminal set in a finite time while minimizing the guaranteed value of a terminal cost function. A multiply closed control strategy is introduced under the assumption that, at several future time instants, the state of the system is measured exactly and the control input is corrected. An efficient numerical method for constructing a suboptimal multiply closed strategy is proposed. The results of numerical experiments show an improvement in the performance under the optimal control strategy when the number of closing instants increases as well as in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.
Keywords:
linear system, disturbances, robust optimal control, control strategy, algorithm.
Citation:
N. M. Dmitruk, “Multiply Closed Control Strategy in a Linear Terminal Problem of Optimal Guaranteed Control”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 3, 2022, 66–82; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S112–S128
\Bibitem{Dmi22}
\by N.~M.~Dmitruk
\paper Multiply Closed Control Strategy in a Linear Terminal Problem of Optimal Guaranteed Control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2022
\vol 28
\issue 3
\pages 66--82
\mathnet{http://mi.mathnet.ru/timm1928}
\crossref{https://doi.org/10.21538/0134-4889-2022-28-3-66-82}
\elib{https://elibrary.ru/item.asp?id=49352752}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2022
\vol 319
\issue , suppl. 1
\pages S112--S128
\crossref{https://doi.org/10.1134/S0081543822060104}
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Linking options:
https://www.mathnet.ru/eng/timm1928
https://www.mathnet.ru/eng/timm/v28/i3/p66
This publication is cited in the following 6 articles:
N. M. Dmitruk, “Metod postroeniya mnogokratno zamykaemykh strategii v zadache minimizatsii polnogo impulsa upravleniya lineinoi sistemoi s vozmuscheniem”, Tr. IMM UrO RAN, 30, no. 3, 2024, 122–138
V. A. Srochko, A. V. Arguchintsev, “Parametricheskaya regulyarizatsiya funktsionala v lineino-kvadratichnoi zadache optimalnogo upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 32–44
Akmal Mamatov, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 3244, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 2024, 020027
Natalia M. Dmitruk, “Optimal Control Strategies for Constrained Linear Time-Delay Systems with Disturbances”, J Math Sci, 2024
N. M. Dmitruk, “A Method for Constructing Multiply Closed Strategies in the Problem of Minimizing the Total Control Impulse in a Linear System with Disturbance”, Proc. Steklov Inst. Math., 327:S1 (2024), S74
V. A. Srochko, V. G. Antonik, “Reshenie lineino-kvadratichnykh zadach v diskretno-nepreryvnom formate s vneshnimi vozdeistviyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 45 (2023), 24–36
Citation in format AMSBIB
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