Title

A LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE HORIZON

Authors

Authors

J. H. Huang; X. Li;J. M. Yong

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Math. Control Relat. Fields

Keywords

Mean-field stochastic differential equation; linear-quadratic optimal; control; MF-stabilizability; Riccati equation; MCKEAN-VLASOV EQUATION; EVOLUTION EQUATION; HILBERT-SPACE; LIMIT; DIFFUSIONS; DYNAMICS; Mathematics, Applied; Mathematics

Abstract

A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by the discussion of the well-posedness of the LQ problem. The optimal control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.

Journal Title

Mathematical Control and Related Fields

Volume

5

Issue/Number

1

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

97

Last Page

139

WOS Identifier

WOS:000349328900005

ISSN

2156-8472

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