Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102691
Title: Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables
Асимптотическое разложение решения одной сингулярно возмущенной задачи оптимального управления с интегральным выпуклым критерием качества, терминальная часть которого аддитивно зависит от медленных и быстрых переменных
Authors: Danilin, A. R.
Shaburov, A. A.
Issue Date: 2020
Publisher: Udmurt State University
Citation: Danilin A. R. Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables / A. R. Danilin, A. A. Shaburov. — DOI 10.35634/2226-3594-2020-55-03 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2020. — Vol. 55. — P. 33-41.
Abstract: The paper deals with the problem of optimal control with a Boltz–type quality index over a finite time interval for a linear steady–state control system in the class of piecewise continuous controls with smooth control constraints. In particular, we study the problem of controlling the motion of a system of small mass points under the action of a bounded force. The terminal part of the convex integral quality index additively depends on slow and fast variables, and the integral term is a strictly convex function of control variable. If the system is completely controllable, then the Pontryagin maximum principle is a necessary and sufficient condition for optimality. The main difference between this study and previous works is that the equation contains the zero matrix of fast variables and, thus, the results of A. B. Vasilieva on the asymptotic of the fundamental matrix of a control system are not valid. However, the linear steady–state system satisfies the condition of complete controllability. The article shows that problems of optimal control with a convex integral quality index are more regular than time–optimal problems. © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved.
Keywords: ASYMPTOTIC EXPANSION
OPTIMAL CONTROL
SINGULARLY PERTURBED PROBLEMS
SMALL PARAMETER
URI: http://hdl.handle.net/10995/102691
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85093877425
PURE ID: 13199973
ISSN: 22263594
DOI: 10.35634/2226-3594-2020-55-03
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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