HJB equation for optimal control system with random impulses

被引：26

作者：

Guo, Yu ^{[1
]}

Shu, Xiao-Bao ^{[1
]}

Xu, Fei ^{[2
]}

Yang, Cheng ^{[1
]}

机构：

[1] Hunan Univ, Sch Math, Changsha, Hunan, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON, Canada

来源：

OPTIMIZATION | 2024年 / 73卷 / 04期

关键词：

HJB equation; random impulse; viscosity solution; optimal control; POSITIVE SOLUTIONS; EXISTENCE;

D O I：

10.1080/02331934.2022.2154607

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper studies the optimal control problem of random impulsive differential equations. Based on the influence of random impulse generation, we define a more reasonable performance index by setting the random function and obtain the HJB equation of random impulse. Using the basic analysis method and stochastic process theory, we prove that the value function satisfies the random impulse HJB equation, and the value function is the viscosity solution of the random impulse HJB. As an application, we present an example of optimal feedback control.

引用

页码：1303 / 1327

页数：25

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