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In a multi-agent system, agents coordinate to achieve global tasks throughlocal communications. Coordination usually requires sufficient informationflow, which is usually depicted by the connectivity of the communicationnetwork. In a networked system, removal of some agents may cause adisconnection. In order to maintain connectivity in agent removal, one candesign a robust network topology that tolerates a finite number of agentlosses, and/or develop a control strategy that recovers connectivity. Thispaper proposes a decentralized control scheme based on a sequence ofreplacements, each of which occurs between an agent and one of its immediateneighbors. The replacements always end with an agent, whose relocation does notcause a disconnection. We show that such an agent can be reached by a localrule utilizing only some local information available in agents' immediateneighborhoods. As such, the proposed message passing strategy guarantees theconnectivity maintenance in arbitrary agent removal. Furthermore, wesignificantly improve the optimality of the proposed scheme by incorporating$\delta$-criticality (i.e. the criticality of an agent in its$\delta$-neighborhood).

A Message Passing Strategy for Decentralized Connectivity Maintenance in Agent Removal