Reduced-order Distributed Consensus Controller Design via Edge Dynamics

TL;DR

This paper introduces a new method for designing reduced-order distributed consensus controllers for multi-agent systems using edge dynamics, achieving optimal stabilization without conservative coupling bounds.

Contribution

It presents a novel edge dynamics model and develops reduced-order controllers via LQR, improving efficiency and removing conservative bounds in multi-agent consensus control.

Findings

Edge dynamics effectively represent agent state differences.

Optimal controllers are derived using LQR for stability.

Reduced-order controllers achieve consensus without conservative bounds.

Abstract

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.