Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/27693
Title: Discrete time mean-field stochastic linear-quadratic optimal control problems
Authors: Elliott, R
Li, X 
Ni, YH
Keywords: Mean-field theory
Riccati difference equation
Stochastic linear-quadratic optimal control problem
Issue Date: 2013
Publisher: Pergamon-Elsevier Science Ltd
Source: Automatica, 2013, v. 49, no. 11, p. 3222-3233 How to cite?
Journal: Automatica 
Abstract: This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.
URI: http://hdl.handle.net/10397/27693
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2013.08.017
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