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This article is cited in 7 scientific papers (total in 7 papers)
Linear Systems
Minimax control of deviations for the outputs of a linear discrete time-varying system
D. V. Balandina, R. S. Biryukovb, M. M. Koganb a Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, Russia
b Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, Russia
Abstract:
It is demonstrated how to design optimal digital controllers on a finite horizon for the linear time-varying objects with uncertain initial conditions and external disturbances. The square of an optimality criterion, called the maximum output deviation, represents the exact guaranteed maximum value of the squared Euclidean norm of the system output normalized by the sum of the squared Euclidean norms of disturbances and a quadratic form of the initial state of a system. The maximum output deviations and the worst-case disturbances and/or initial conditions causing them, as well as the minimax controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) are calculated as solutions to a semidefinite programming problem. The necessary and sufficient conditions for the finite-time stability and boundedness of a system are established; they can be used for controller design.
Keywords:
linear discrete time-varying system, maximum deviation of output, optimal control, multiobjective problem, optimal vibrational protection.
Citation:
D. V. Balandin, R. S. Biryukov, M. M. Kogan, “Minimax control of deviations for the outputs of a linear discrete time-varying system”, Avtomat. i Telemekh., 2019, no. 12, 3–23; Autom. Remote Control, 80:12 (2019), 2091–2107
Linking options:
https://www.mathnet.ru/eng/at15191 https://www.mathnet.ru/eng/at/y2019/i12/p3
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Abstract page: | 277 | Full-text PDF : | 38 | References: | 34 | First page: | 26 |
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