LQR control in mean field of discrete-time delayed system

This paper studies the decentralized optimal control of discrete-time system with input delay. We consider LQR problems which have a large number of agents with the identical decoupling dynamical equations and the coupling cost function through the mean field. Using the optimal control and state aggregation methods of the discrete delayed system, we get the decentralized and centralized optimal controllers. And then we prove that the optimal controllers and cost function of the centralized and decentralized solutions are equivalent for the scaler models.