Constrained linear quadratic deterministic mean field control: Decentralized convergence to Nash equilibria in large populations of heterogeneous agents

Authors:

S. Grammatico, F. Parise, J. Lygeros

Conference:

IEEE Conference on Decision and Control

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7402908

Astract:

This paper considers linear quadratic deterministic mean field control problems for large populations of heterogeneous agents subject to convex state and input constraints, coupled via a quadratic cost function which depends on the average population state. We address the problem of steering the optimal-response trajectories of the rational agents to a Nash equilibrium and propose iterative solutions based on specific feedback control mappings, with guaranteed convergence under mild sufficient conditions on the problem data. Contrary to the state of the art, convergence is ensured in the presence of heterogeneous convex constraints and quadratic cost functions for the agents.