Optimal distributed control with application to asymmetric vehicle platoons

This paper considers a distributed system of identical agents with arbitrary LTI models. A method for distributed state-feedback design is provided. The proposed solution consists of two steps: first a single-agent controller is derived and then, based on the network topology, the gain of this controller is adjusted. LQ optimality of this controller is proved provided that the Laplacian has only real eigenvalues and is non-defective. The result is subsequently used to design a controller for asymmetric vehicle platoon. We show that the same controller with a fixed gain is the optimal controller for any number of vehicles in the platoon. However, the performance of the optimal controller is still subject to inherent limitations given by the network topology. In some cases, even exponential scaling in the number of vehicles must occur for any controller.