A LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE HORIZON
Abbreviated Journal Title
Math. Control Relat. Fields
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
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.
Mathematical Control and Related Fields
"A LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE HORIZON" (2015). Faculty Bibliography 2010s. 6583.