Consensus Analysis and Convergence Rate Optimization for Open Multiagent Systems

This article investigates the fast consensus problem in open multiagent systems (OMASs), where agents can randomly join or leave the network. Such dynamic behaviors significantly impact system consensus and its convergence rates. To address these challenges, we analyze both the frequency of agent switching and the duration during which the network remains nonconnected. A consensus condition for OMAS with time-varying network topology is derived, and explicit upper bounds on switching frequency and dwell time are established to guarantee consensus. To further achieve fast consensus, a convergence rate optimization scheme is proposed, along with a distributed implementation based on the alternating direction method of multiplier. Extensive simulations demonstrate the effectiveness and superiority of the proposed control strategy compared to existing OMAS consensus approaches.