Reduced-order Distributed Consensus Controller Design via Edge Dynamics

This paper proposes a novel approach to design reduced-order distributed consensus controllers for multi-agent systems (MASs) with identical linear dynamics of agents. A new model namely edge dynamics representing the differences on agents' states is first presented. Then the distributed consensus controller design is shown to be equivalent to the synthesis of a distributed stabilizing controller for this edge dynamics. Consequently, based on LQR approach, the globally optimal and locally optimal distributed stabilizing controller designs are proposed, of which the locally distributed stabilizing controller for the edge dynamics results in a distributed consensus controller for the MAS with no conservative bound on the coupling strength. This approach is next further developed to obtain reduced-order distributed consensus controllers for linear MASs. Several numerical examples are introduced to illustrate the theoretical results.