Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101730
Title: Solution to a Zero-Sum Differential Game with Fractional Dynamics via Approximations
Authors: Gomoyunov, M.
Issue Date: 2020
Publisher: Birkhauser
Citation: Gomoyunov M. Solution to a Zero-Sum Differential Game with Fractional Dynamics via Approximations / M. Gomoyunov. — DOI 10.1007/s13235-019-00320-4 // Dynamic Games and Applications. — 2020. — Vol. 10. — Iss. 2. — P. 417-443.
Abstract: The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order α∈ (0 , 1). The goal of the first (second) player is to minimize (maximize) a given quality index. The main contribution of the paper is the proof of the fact that this differential game has the value, i.e., the lower and upper game values coincide. The proof is based on the appropriate approximation of the game by a zero-sum differential game in which the dynamical system is described by a first-order functional differential equation of a retarded type. It is shown that the values of the approximating differential games have a limit, and this limit is the value of the original game. Moreover, the optimal players’ feedback control procedures are proposed that use the optimally controlled approximating system as a guide. An example is considered, and the results of computer simulations are presented. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: APPROXIMATION
CONTROL WITH A GUIDE
DIFFERENTIAL GAME
FRACTIONAL DERIVATIVE
FRACTIONAL DIFFERENTIAL EQUATION
OPTIMAL STRATEGIES
VALUE OF THE GAME
URI: http://hdl.handle.net/10995/101730
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85068863279
PURE ID: 12907389
e298a647-d2d7-48ba-bb3f-2575cd6e705d
ISSN: 21530785
DOI: 10.1007/s13235-019-00320-4
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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