Linear-quadratic mean field control: The invariant subspace method. (September 2019)

• Record Type: Journal Article
• Authors: Chen, Xiang; Huang, Minyi
• Is Part Of: Automatica. Volume 107(2019)
• Page Start: 582
• Page End: 586
• Publication Date: 2019-09
• Subjects: Linear quadratic control -- Social optimization -- Hamiltonian matrix -- Algebraic Riccati equation -- Mean field game; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.04.021
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This note studies linear quadratic (LQ) mean field social optimization problems with non-uniform agents and indefinite state weight, and analyzes the resulting linear system of ordinary differential equations (ODEs) subject to a partial initial condition and a growth condition. We apply a subspace decomposition method for existence analysis and computation. This is accomplished by carefully choosing the unspecified initial condition in the ODE system such that the modes exceeding the admissible growth rate are not activated. We further extend this method to LQ mean field games.