Cooperative Linear-Quadratic Mean Field Control and Hamiltonian Matrix Analysis
Xiang Chen · 2017
In this thesis, we present a new methodology to investigate the existence and uniqueness of the solution of the Social Certainty Equivalence (SCE) equation system related to social optima in mean field linear-quadratic-Gaussian (LQG) control problems.The methodology involves Hamiltonian matrices and continuous-time algebraic Riccati equations (CARE), and it avoids the restrictive contractive assumption typically used in a fixed point approach.For computing the stabilizing solution of CARE, we also develop a computational method related to generalized eigenvectors and Schur vectors.We further extend our method to solve a linear-quadratic mean field game.