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Keywords = fractional coinvariant derivatives

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16 pages, 328 KiB  
Article
Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies
by Mikhail I. Gomoyunov
Mathematics 2021, 9(14), 1667; https://doi.org/10.3390/math9141667 - 15 Jul 2021
Cited by 8 | Viewed by 2773
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractional Differential Equations and Control Problems)
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