Geodesic
Mean-Field stochastic Linear Quadratic optimal control problems: Open-loop solvabilities
Sun, Jingrui1 
1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, P.R. China.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1099-1127

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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 Riccati equations 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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016023
Classification : 49N10, 49N35, 93E20
Keywords: Mean-field stochastic differential equation, linear quadratic optimal control, Riccati equation, finiteness, open-loop solvability, feedback representation

Sun, Jingrui 1

1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, P.R. China. 
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     title = {Mean-Field stochastic {Linear} {Quadratic} optimal control problems: {Open-loop} solvabilities},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1099--1127},
     publisher = {EDP-Sciences},
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Sun, Jingrui. Mean-Field stochastic Linear Quadratic optimal control problems: Open-loop solvabilities. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1099-1127. doi: 10.1051/cocv/2016023

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