Abstract
This paper investigates the consensus of second-order multi-agent systems under switched topologies. Previous studies indicate that a consensus cannot be reached if the topology is fixed and has no spanning tree, but it is possible to reach a consensus for the multi-agent systems under switched topologies even if every topology has no spanning tree. However, in this paper, we show that some second-order multi-agent systems cannot reach a consensus even if the union of the directed interaction graphs has a spanning tree, and even if the union has a spanning tree frequently enough. It is often complex to judge whether the second-order multi-agent systems can reach a consensus or not under switched topologies if every topology has no spanning tree. This paper proposes a sequence-based topology-dependent method to determine whether a consensus can be reached in this circumstance. Our results are supported by examples and counterexamples.
Highlights
As a beneficial action to a group, cooperation widely exists in the nature [1]
The motivation of this paper is to provide a rule to judge whether a consensus can be reached for the second-order multi-agent systems if every topology has no spanning tree, because many multi-agent systems can reach a consensus under jointly connected topologies, while others cannot achieve with the same protocol
Based on the above motivation, we propose a sequencebased topology-dependent method to study the consensus of second-order multi-agent systems when every topology has no spanning tree
Summary
As a beneficial action to a group, cooperation widely exists in the nature [1]. The main target of cooperation is to reach a global goal with limited exchange of information among adjacent agents following a local control protocol [2]. A few works designed control protocols for the consensus of second-order multi-agent systems when all topologies have no spanning tree under some special conditions in [31]–[39]. They mainly considered the condition that a consensus can be determinately reached when the topologies have jointly connected topologies. Based on the above motivation, we propose a sequencebased topology-dependent method to study the consensus of second-order multi-agent systems when every topology has no spanning tree. That is, having jointly connected topologies or maintaining a spanning tree frequently enough is not a sufficient condition to ensure the second-order multi-agent systems to reach a consensus.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
