Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems

被引：0
|
作者：
Anton Plaksin
机构：
[1] N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences,
[2] Ural Federal University,undefined
来源：
Applied Mathematics & Optimization | 2023年 / 88卷
关键词：
Neutral-type systems; Hamilton–Jacobi equations; Coinvariant derivatives; Viscosity solutions; Minimax solutions; Optimal control problems; 49L20; 49L25; 34K40;
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摘要：
The paper deals with path-dependent Hamilton–Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale’s form. A viscosity (generalized) solution of a Cauchy problem for such equations is considered. The existence, uniqueness, and consistency of the viscosity solution are proved. Equivalent definitions of the viscosity solution, including the definitions of minimax and Dini solutions, are obtained. Application of the results to an optimal control problem for neutral-type systems in Hale’s form are given.
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