Persistence based convergence rate analysis of consensus protocols for dynamic graph networks

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• 作者：Nilanjan Roy Chowdhury^a ; ^{nilanjan@sc.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Srikant Sukumar^a ; ^{srikant@sc.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Niranjan Balachandran^b ; ^{niranj@math.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Consensus ; Time-varying systems ; Cooperative control ; Adaptive control ; Persistence of excitation ; Ramsey theory ; Combinatorics
• 刊名：European Journal of Control
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：29
• 期：Complete
• 页码：33-43
• 全文大小：915 K

文摘

This paper deals with the consensus problem of agents communicating via time-varying communication links in undirected graph networks. The highlight of the current work is to provide practically computable rates of convergence to consensus that hold for a large class of time-varying edge weights. A novel analysis technique based on classical notions of persistence of excitation and uniform complete observability is proposed. The new analysis technique for consensus laws under time-varying graphs provides explicit bounds on rate of convergence to consensus for single integrator dynamics. In the case of double integrators a minor modification to the standard relative state feedback law is shown to guarantee exponential convergence to consensus under similar assumptions as the single integrator case. The consensus problem is re-formulated in the edge agreement framework to which persistence of excitation based results apply. A novel application of results from Ramsey theory allows for proof of consensus and convergence rate estimation under switching graph topology. The current work connects classical results from nonlinear adaptive control and combinatorics to the modern theory of consensus over multi-agent networks.