On viscosity solutions of path-dependent Hamilton-Jacobi-Bellman-Isaacs equations for fractional-order systems

被引：0

作者：

Gomoyunov, M. I. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, NN Krasovskii Inst Math & Mech, Ural Branch, 16 S Kovalevskaya Str, Ekaterinburg 620108, Russia

[2] Ural Fed Univ, 19 Mira Str, Ekaterinburg 620002, Russia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 399卷

基金：

俄罗斯科学基金会;

关键词：

Differential game; Caputo fractional derivative; Value functional; Path-dependent Hamilton-Jacobi equation; Fractional coinvariant derivatives; Viscosity solution; STOCHASTIC-CONTROL;

D O I：

10.1016/j.jde.2024.04.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order alpha is an element of (0, 1) and a Bolza cost functional. The differential game is associated to the Cauchy problem for the path-dependent Hamilton-Jacobi-Bellman-Isaacs equation with so-called fractional coinvariant derivatives of order alpha and the corresponding right-end boundary condition. A notion of a viscosity solution of the Cauchy problem is introduced, and the value functional of the differential game is characterized as a unique viscosity solution of this problem. (c) 2024 Elsevier Inc. All rights reserved.

引用

页码：335 / 362

页数：28

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