Decentralized Control for Discrete-time Mean-Field Systems with Multiple Controllers of Delayed Information

TL;DR

This paper develops a novel decentralized control strategy for discrete-time mean-field systems with multiple controllers under asymmetric information, utilizing stochastic difference equations and Riccati-type equations.

Contribution

It introduces the first necessary and sufficient conditions for asymmetric information LQ control in multi-controller mean-field systems, using a new orthogonal decomposition approach.

Findings

Derived solvability conditions via MF-FBSDEs.

Proposed optimal control based on non-symmetric Riccati equations.

Extended control theory to systems with multiple controllers and delayed information.

Abstract

In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete-time mean field system. Different from previous works, multiple controllers with different information sets are involved in the mean field system dynamics. The coupling of different controllers makes it quite difficult in finding the optimal control strategy. Fortunately, by applying the Pontryagin's maximum principle, the corresponding decentralized control problem of the finite horizon is investigated. The contributions of this paper can be concluded as: For the first time, based on the solution of a group of mean-field forward and backward stochastic difference equations (MF-FBSDEs), the necessary and sufficient solvability conditions are derived for the asymmetric information LQ control for the mean field system with multiple controllers. Furthermore, by the use of an innovative orthogonal decomposition approach, the optimal decentralized control strategy is derived, which is based on the solution to a non-symmetric Riccati-type equation.