9 research outputs found
Decentralized Control for Discrete-time Mean-Field Systems with Multiple Controllers of Delayed Information
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