Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method
Optimization and Control
2018-11-02 v2
Abstract
This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation (ODE) system and apply a subspace decomposition method to find the solution. This approach is effective for both the existence analysis and numerical computations. We further extend the decomposition method to LQ mean field games.
Cite
@article{arxiv.1801.02306,
title = {Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method},
author = {Xiang Chen and Minyi Huang},
journal= {arXiv preprint arXiv:1801.02306},
year = {2018}
}
Comments
Proc. IEEE CDC, Dec 2018