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
收藏
页码：335 / 362
页数：28
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