Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111130
Title: Extremal Shift to Accompanying Points in a Positional Differential Game for a Fractional-Order System
Authors: Gomoyunov, M. I.
Issue Date: 2020
Publisher: Pleiades Publishing
Pleiades Publishing Ltd
Citation: Gomoyunov M. I. Extremal Shift to Accompanying Points in a Positional Differential Game for a Fractional-Order System / M. I. Gomoyunov // Proceedings of the Steklov Institute of Mathematics. — 2020. — Vol. 308. — P. 83-105.
Abstract: A two-person zero-sum differential game is considered. The motion of the dynamic system is described by an ordinary differential equation with a Caputo fractional derivative of order α ∈ (0, 1). The quality 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 “strategy–counterstrategy” and “counterstrategy–strategy” classes as well as in the “strategy–strategy” classes 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. © 2020, Pleiades Publishing, Ltd.
Keywords: CAPUTO DERIVATIVE
COUNTERSTRATEGY
DIFFERENTIAL GAME
EXTREMAL SHIFT
FRACTIONAL-ORDER DIFFERENTIAL EQUATION
GAME VALUE
POSITIONAL STRATEGY
URI: http://hdl.handle.net/10995/111130
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85085555126
PURE ID: 12922424
ISSN: 0081-5438
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85085555126.pdf288,57 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.