#### Title

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

#### 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

#### ISSN

2156-8472

#### Recommended Citation

"A LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE HORIZON" (2015). *Faculty Bibliography 2010s*. 6583.

http://stars.library.ucf.edu/facultybib2010/6583

## Comments

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