The mean‐field linear quadratic optimal control problem for stochastic systems controlled by impulses

In the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state...

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Bibliographic Details
Published inAsian journal of control Vol. 26; no. 2; pp. 575 - 583
Main Authors Dragan, Vasile, Aberkane, Samir
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.03.2024
Asian Control Association (ACA) and Chinese Automatic Control Society (CACS)
Subjects
Automatic
Differential equations
Engineering Sciences
Mathematical analysis
Optimal control
Stochastic systems
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ISSN1561-8625
1934-6093
DOI10.1002/asjc.3214

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Summary:In the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state variables, we introduce an adequately defined system of two coupled matrix Lyapunov‐type differential equations with jumps. Such equations are central for the definition of the optimal feedback gains corresponding to the closed‐loop representation of the optimal LQ control.
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content type line 14
ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.3214