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.

1 Introduction

The control and optimization problems with a large number of agents have attracted lots of authors' interests because they appear in many fields, such as engineering, social, economic, biology and network communication([1] [2] [3]). In these areas, the mean field models which each agent interacts with the average effect of others and the individual has negligible effect on the overall population have attracted extensive attentions([4] [5][6] [7] [8]). Game theoretic solutions, the centralized control solutions and the decentralized control solutions have been developed in many papers([4]℃[16]).