Title

LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS

Authors

Authors

J. M. Yong

Comments

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Abbreviated Journal Title

SIAM J. Control Optim.

Keywords

mean-field stochastic differential equation; linear-quadratic optimal; control; Riccati differential equation; feedback representation; MCKEAN-VLASOV EQUATION; HILBERT-SPACE; EVOLUTION EQUATION; LIMIT; DIFFUSIONS; DYNAMICS; Automation & Control Systems; Mathematics, Applied

Abstract

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which is a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained which are uniquely solvable under certain conditions. Then a feedback representation is obtained for the optimal control.

Journal Title

Siam Journal on Control and Optimization

Volume

51

Issue/Number

4

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

2809

Last Page

2838

WOS Identifier

WOS:000323890100005

ISSN

0363-0129

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