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

    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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