H2 optimal Cooperation of Homogeneous Agents Subject to Delyed Information Exchange*

We consider a class of large-scale H2 coordination problems where subsystems are coupled through a penalty on their average behavior and the information exchange between agents is subject to a time delay. We derive explicit analytic expressions for the optimal control law and show that it is scalable both in terms of implementation and the computational effort required to obtain it. Specifically, the only centralized information processing required to implement the controller is averaging of local agent information, and the computational effort required to obtain it scales linearly with the number of agents. These results are a highly non-trivial extension to two previously studied special cases, where the information exchange is either delay-free or the coordination constraints are hard.