Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/76272
Title: Mean-field stochastic linear quadratic optimal control problems : open-loop solvabilities
Authors: Sun, JR 
Keywords: Mean-field stochastic differential equation
Linear quadratic optimal control
Riccati equation
Finiteness
Open-loop solvability
Feedback representation
Issue Date: 2017
Publisher: EDP Sciences
Source: ESAIM. Control, optimisation and calculus of variations, 2017, v. 23, no. 3, p. 1099-1127 How to cite?
Journal: ESAIM. Control, optimisation and calculus of variations 
Abstract: This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Then, it is proved that the uniform convexity of the cost functional is equivalent to the solvability of two coupled differential Riccatie quations and the unique open-loop optimal control admits a state feedback representation in the case that the cost functional is uniformly convex. Finally, some examples are presented to illustrate the theory developed.
URI: http://hdl.handle.net/10397/76272
ISSN: 1292-8119
EISSN: 1262-3377
DOI: 10.1051/cocv/2016023
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