HJB equation for optimal control system with random impulses

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...

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Bibliographic Details
Published inOptimization Vol. 73; no. 4; pp. 1303 - 1327
Main Authors Guo, Yu, Shu, Xiao-Bao, Xu, Fei, Yang, Cheng
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis LLC
Subjects
Differential equations
Feedback control
HJB equation
Optimal control
Performance indices
random impulse
Stochastic processes
viscosity solution
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2154607