Optimal Distributed Controller Design with Communication Delays: Application to Vehicle Formations

This paper develops a controller synthesis algorithm for distributed LQG control problems under output feedback. We consider a system consisting of three interconnected linear subsystems with a delayed information sharing structure. While the state-feedback case of this problem has previously been solved, the extension to output-feedback is nontrivial, as the classical separation principle fails. To find the optimal solution, the controller is decomposed into two independent components. One is delayed centralized LQR, and the other is the sum of correction terms based on additional local information. Explicit discrete-time equations are derived whose solutions are the gains of the optimal controller.