Abstract:
A control system with a phase constraint is considered in a finite-dimensional Euclidean space. The problem of making this system approach the target set at a fixed time instant is studied. A method for constructing an approximate solution to the approach problem is given, which involves the concept of the solvability set of an approach problem.
Bibliography: 24 titles.
This work was supported by the Presidium of the Russian Academy of Sciences (Fundamental Scientific Research Program no. 01 “The newest methods of mathematical modelling in the investigation of nonlinear dynamical systems”).
Citation:
A. A. Ershov, A. V. Ushakov, V. N. Ushakov, “An approach problem for a control system and a compact set in the phase space in the presence of phase constraints”, Sb. Math., 210:8 (2019), 1092–1128
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\pages 1092--1128
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Linking options:
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https://doi.org/10.1070/SM9141
https://www.mathnet.ru/eng/sm/v210/i8/p29
This publication is cited in the following 8 articles:
Khalik G. Guseinov, Anar Huseyin, Nesir Huseyin, Vladimir N. Ushakov, “Approximation of the set of integrable trajectories of the control system with limited control resources”, International Journal of Control, 2025, 1
Yan Cui, Yang Yu, Yanshan Liu, Xinran Hao, Hongwei Gao, “An Approach Problem for Control Systems Based on Runge–Kutta Methods”, Comput. Math. and Math. Phys., 64:9 (2024), 1991
N. Huseyin, A. Huseyin, Kh. G. Guseinov, “On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions”, Tr. IMM UrO RAN, 28, no. 3, 2022, 274–284
A. Huseyin, N. Huseyin, Kh. G. Guseinov, “Approximations of the Images and Integral Funnels of the $L_p$ Balls under a Urysohn-Type Integral Operator”, Funct. Anal. Appl., 56:4 (2022), 269–281
A. A. Ershov, “Linear parameter interpolation of a program control in the approach problem”, J. Math. Sci., 260:6 (2022), 725–737
P. D. Lebedev, A. L. Kazakov, “Iteratsionnye algoritmy postroeniya nailuchshikh pokrytii vypuklykh mnogogrannikov naborami razlichnykh sharov”, Tr. IMM UrO RAN, 27, no. 1, 2021, 116–129
Vladimir Ushakov, Aleksandr Ershov, Lecture Notes in Control and Information Sciences - Proceedings, Stability, Control and Differential Games, 2020, 225
Citation in format AMSBIB
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