Consensus in topologically interacting swarms under communication constraints and time-delays
The emergence of collective decision in swarming systems underscores the central role played by information transmission. Using network-control- and information-theoretic elements applied to a group of topologically interacting agents seeking consensus under switching topologies, the effects of constraints in the information capacity of the communication channel are investigated. This particular system requires us to contend with constantly reconfigurable and spatially embedded interaction networks. We find a sufficient condition on the information data rate guaranteeing the stability of the consensus process in the noiseless case. This result highlights the profound connection with the topological structure of the underlying interaction network, thus having far-reaching implications in the nascent field of swarm robotics. Furthermore, we analyze the more complex case of combined effect of noise and limited data rate. We find that the consensus process is degraded when decreasing the data rate. Moreover, the relationship between critical noise and data rate is found to be in good agreement with information-theoretic predictions. Lastly, we prove that with not-too-large time-delays, our system of topologically interacting agents is stable, provided the underlying interaction network is strongly connected. Using Lyapunov techniques, the maximum allowed time-delay is determined in terms of linear-matrix inequalities.
KeywordsSwarm Topological interaction Consensus dynamics Communication constraints
This work was supported by a grant from the Singapore National Research Foundation (NRF) under the ASPIRE project, Grant No. NCR-NCR001-040.
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Conflicts of interest
The authors declare that there is no conflict of interest regarding the publication of this article.
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