Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101587
Title: Extremal shift to accompanying points in a positional differential game for a fractional-order system
Экстремальный сдвиг на сопутствующие точки в позиционной дифференциальной игре для системы дробного порядка
Authors: Gomoyunov, M. I.
Issue Date: 2019
Publisher: Krasovskii Institute of Mathematics and Mechanics
Citation: Gomoyunov M. I. Extremal shift to accompanying points in a positional differential game for a fractional-order system / M. I. Gomoyunov. — DOI 10.21538/0134-4889-2019-25-1-11-34 // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2019. — Vol. 25. — Iss. 1. — P. 11-34.
Abstract: A two-person zero-sum differential game is considered. The motion of the dynamical system is described by an ordinary differential equation with a Caputo fractional derivative of order α ∈ (0, 1). The performance index consists of two terms: the first depends on the motion of the system realized by the terminal time and the second includes an integral estimate of the realizations of the players’ controls. The positional approach is applied to formalize the game in the “strategies — counter-strategies” and “counter-strategies — strategies” classes as well in the “strategies — strategies” class under the additional saddle point condition in the small game. In each case, the existence of the value and of the saddle point of the game is proved. The proofs are based on an appropriate modification of the method of extremal shift to accompanying points, which takes into account the specific properties of fractional-order systems. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Keywords: CAPUTO DERIVATIVE
COUNTER-STRATEGY
DIFFERENTIAL GAME
EXTREMAL SHIFT
FRACTIONAL-ORDER DIFFERENTIAL EQUATION
GAME VALUE
POSITIONAL STRATEGY
URI: http://hdl.handle.net/10995/101587
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85078269582
PURE ID: 9205451
ISSN: 1344889
DOI: 10.21538/0134-4889-2019-25-1-11-34
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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