Abstract
Consideration was given to the difference approximation of the control system obeying a differential inclusion with retarded argument. Approximation of an ensemble of the trajectories of a differential inclusion by a sequence of ensembles of the trajectories of the corresponding difference (discrete) inclusions was investigated. Estimates enabling one to judge whether the approximating sequences converge were obtained. The possibility of applying the results obtained to one minimax problem of optimal control of the system under consideration was demonstrated.
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Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Uncertainty), Moscow: Nauka, 1977.
Chernous’ko, F.L. and Melikyan, A.A., Igrovye zadachi upravleniya i poiska (Game Problems of Control and Search), Moscow: Nauka, 1978.
Kein, V.N., Optimizatsiya sistem upravleniya po minimaksnomu kriteriyu (Minimax Criterion-based Optimization of the Control Systems), Moscow: Nauka, 1985.
Mordukhovich, B.Sh., Metody approksimatsii v zadachakh optimizatsii i upravleniya (Methods of Approximation in the Problems of Optimization and Control), Moscow: Nauka, 1988.
Otakulov, S., On Approximation of a Minimax Problem for Controllable Differential Inclusions, Dokl. Akad. Nauk Resp. Uzbek., 1993, no. 6, pp. 7–10.
Otakulov, S., On the Minimization Problem of Reachable Set Estimation of Control System, in Proc. IFAK Workshop on Generalized Solutions in Control Problems (GSCP-2004), Pereslavl-Zalessky, Russia, 2004, pp. 212–217.
Duda, E.V. and Minchenko, L.I., On the Optimal Trajectories of Differential Inclusions with Delay, Diff. Uravn., 1997, vol. 33, no. 8, pp. 1023–1029.
Minchenko, L.I. and Sirotko, S.I., On the Necessary Optimality Conditions for Discrete Inclusions with Delay, Vest. Akad. Nauk BSSR, 2000, no. 4, pp. 13–19.
Otakulov, S. and Kholiyarova, F.Kh., On the Theory of Controllable Differential Inclusions with Retarded Argument, Dokl. Akad. Nauk Resp. Uzbek., 2005, no. 3, pp. 14–17.
Otakulov, S. and Kholiyarova, F.Kh., The Problem of Speed for One Class of Differential Inclusions with delay, Vestn. Tashkent. Gos. Tekh. Univ., 2004, no. 3, pp. 19–26.
Otakulov, S., Azizov, I., and Kholiyarova, F.Kh., On Properties of Ensemble of Trajectories of the Controllable Discrete Inclusion with Delays, in Proc. Int. Conf. “Stability of Control Processes,” St. Petersburg, Russia, 2005, vol. 1, pp. 311–319.
Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods of Solution of Extremal Problems), Moscow: Nauka, 1981.
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Original Russian Text © S. Otakulov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 4, pp. 157–167.
This work was supported by the Foundation for Basic Research TSNIT RUz, project no. 1F.1.1.16.
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Otakulov, S. On the difference approximation of the delay control system. Autom Remote Control 69, 690–699 (2008). https://doi.org/10.1134/S0005117908040152
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DOI: https://doi.org/10.1134/S0005117908040152