Mean-Field Stochastic Linear-Quadratic Optimal Control Problems: Weak Closed-Loop Solvability
Optimization and Control
2019-09-27 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1907.01740,
title = {Mean-Field Stochastic Linear-Quadratic Optimal Control Problems: Weak Closed-Loop Solvability},
author = {Jingrui Sun and Hanxiao Wang},
journal= {arXiv preprint arXiv:1907.01740},
year = {2019}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1806.05215, arXiv:1904.01442