Optimal output consensus control for systems of agents with continuous linear dynamics

In this paper we study the output consensus problem for systems of agents with linear
continuous, time invariant dynamics. We derive control laws with minimal energy that solves
the problem, while using only relative information. Instead of considering a fixed communication
topology for the agents, and derive the optimal control for that topology, we derive the optimal
control law for any communication topology between the agents. We show that the optimal
control uses only relative information but requires the connectivity graph to be complete and
in general requires measurements of the state errors. We identify the cases where the optimal
control is only based on output errors, and show that in the infinite time horizon case, the
optimal controller can always be expressed as a dynamic controller that is only based on the
output errors. Regarding the theoretic contributions of this paper, the control laws are derived
using methods from linear vector space optimization and are given in closed form. To the authors knowledge these methods have not been used within this context before.