Optimal coordination of homogeneous agents subject to delayed information exchange

We consider a class of large scale linear-quadratic coordination problems where the information exchange is subject to a time delay. We show that several previously known properties of the optimal solution to the delay-free problem extend to this case. In particular, the optimal control law comprises a diagonal (decentralized) term complemented by a rank-one coordination term, which can be implemented by a simple averaging operation. Moreover, the computational effort required to obtain the controller is independent of the number of agents.