Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/112184
Title: Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies
Authors: Gomoyunov, M. I.
Issue Date: 2021
Publisher: MDPI AG
MDPI AG
Citation: Gomoyunov M. I. Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies / M. I. Gomoyunov // Mathematics. — 2021. — Vol. 9. — Iss. 14. — 1667.
Abstract: The paper deals with a two-person zero-sum differential game for a dynamical system described by differential equations with the Caputo fractional derivatives of an order α ∈ (0, 1) and a Bolza-type cost functional. A relationship between the differential game and the Cauchy problem for the corresponding Hamilton–Jacobi–Bellman–Isaacs equation with fractional coinvariant derivatives of the order α and the natural boundary condition is established. An emphasis is given to construction of optimal positional (feedback) strategies of the players. First, a smooth case is studied when the considered Cauchy problem is assumed to have a sufficiently smooth solution. After that, to cope with a general non-smooth case, a generalized minimax solution of this problem is involved. © 2021 by the author. Licensee MDPI, Basel, Switzerland.
Keywords: DIFFERENTIAL GAMES
FRACTIONAL COINVARIANT DERIVATIVES
FRACTIONAL DIFFERENTIAL EQUATIONS
HAMILTON–JACOBI EQUATIONS
MINIMAX SOLUTION
OPTIMAL STRATEGIES
VALUE FUNCTIONAL
URI: http://hdl.handle.net/10995/112184
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85111316542
PURE ID: 22990710
ISSN: 2227-7390
metadata.dc.description.sponsorship: Funding: This research was funded by the Russian Science Foundation Grant No. 19-71-00073.
RSCF project card: 19-71-00073
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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