Mean-field stochastic linear-quadratic optimal control problems: weak closed-loop solvability. (English) Zbl 1461.93553
Summary: This paper is concerned with mean-field stochastic linear-quadratic (MF-SLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closed-loop optimal strategy is introduced. It is shown that the open-loop solvability is equivalent to the existence of a weak closed-loop optimal strategy. Moreover, when open-loop optimal controls exist, there is at least one of them admitting a state feedback representation, which is the outcome of a weak closed-loop optimal strategy. Finally, an example is presented to illustrate the procedure for finding weak closed-loop optimal strategies.
MSC:
| 93E20 | Optimal stochastic control |
| 49N10 | Linear-quadratic optimal control problems |
| 49N80 | Mean field games and control |
| 93B52 | Feedback control |
Keywords:
mean-field stochastic differential equation; linear-quadratic optimal control; open-loop solvability; weak closed-loop solvability; state feedbackReferences:
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