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http://elar.urfu.ru/handle/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://elar.urfu.ru/handle/10995/101730 |
Access: | info:eu-repo/semantics/openAccess |
SCOPUS ID: | 85068863279 |
WOS ID: | 000529559300004 |
PURE ID: | e298a647-d2d7-48ba-bb3f-2575cd6e705d 12907389 |
ISSN: | 21530785 |
DOI: | 10.1007/s13235-019-00320-4 |
Appears in Collections: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
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