A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. (English) Zbl 1326.49051
Summary: 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 the semi-definite programming method.
MSC:
| 49N10 | Linear-quadratic optimal control problems |
| 49J55 | Existence of optimal solutions to problems involving randomness |
| 49K45 | Optimality conditions for problems involving randomness |
| 49K40 | Sensitivity, stability, well-posedness |
| 49N35 | Optimal feedback synthesis |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E20 | Optimal stochastic control |
| 93D15 | Stabilization of systems by feedback |
| 90C22 | Semidefinite programming |
Keywords:
linear-quadratic optimal control problem; mean-field stochastic differential equations; MF-stabilizability; well-posedness; algebraic Riccati equations; semi-definite programmingSoftware:
SDPT3References:
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