A Linear-Quadratic Optimal Control Problem For Mean-Field Stochastic Differential Equations In Infinite Horizon

Keywords

Linear-quadratic optimal control; Mean-field stochastic differential equation; MF-stabilizability; Riccati equation

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.

Publication Date

1-1-2015

Publication Title

Mathematical Control and Related Fields

Volume

5

Issue

1

Number of Pages

97-139

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3934/mcrf.2015.5.97

Socpus ID

84921765673 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84921765673

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