NDLI: Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies

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Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies

Content Provider	MDPI
Author	Gomoyunov, Mikhail
Copyright Year	2021
Description	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 $α\in(0,1)$ 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.
Starting Page	1667
e-ISSN	22277390
DOI	10.3390/math9141667
Journal	Mathematics
Issue Number	14
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-07-15
Access Restriction	Open
Subject Keyword	Mathematics Industrial Engineering Fractional Differential Equations Differential Games Hamilton–jacobi Equations Fractional Coinvariant Derivatives Minimax Solution Value Functional Optimal Strategies
Content Type	Text
Resource Type	Article

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