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

Mikhail I. Gomoyunov
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Mikhail I. Gomoyunov: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya Str., 16, 620108 Ekaterinburg, Russia

Mathematics, 2021, vol. 9, issue 14, 1-16

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 ? ? ( 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 ? 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.

Keywords: fractional differential equations; differential games; Hamilton–Jacobi equations; fractional coinvariant derivatives; minimax solution; value functional; optimal strategies (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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