Distributed Control of Active–Passive Networked Multiagent Systems

An active–passive networked multiagent system framework is introduced and analyzed, which consists of agents subject to exogenous inputs (active agents) and agents without any inputs (passive agents). Specifically, we propose an integral action-based distributed control approach and establish its transient time and steady-state performance characteristics using results from graph theory, matrix mathematics, Lyapunov stability, and ${\mathcal L}$ stability. Apart from the existing relevant literature, where either none of the agents are subject to exogenous inputs (i.e., average consensus problem) or all agents are subject to these inputs (i.e., dynamic average consensus problem), the key feature of our approach is that the states of all agents converge to the average of the exogenous inputs applied only to the active agents. We further discuss the conditions when the performance of the proposed distributed controller specializes to the performance of standard distributed controllers used for average consensus and dynamic average consensus of leaderless networks, and draw connections between pinning control and containment control of leader–follower networks. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed distributed control approach.