Convergence rate for consensus with delays |
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Authors: | Angelia Nedi? Asuman Ozdaglar |
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Institution: | 1.Department of Industrial and Enterprise Systems Engineering,University of Illinois,Urbana,Champaign,USA;2.Department of Electrical Engineering and Computer Science,Massachusetts Institute of Technology,Cambridge,USA |
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Abstract: | We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity
in the presence of delays. We consider a widely studied consensus algorithm, in which at each time step, every agent forms
a weighted average of its own value with values received from the neighboring agents. We study an asynchronous operation of
this algorithm using delayed agent values. Our focus is on establishing convergence rate results for this algorithm. In particular,
we first show convergence to consensus under a bounded delay condition and some connectivity and intercommunication conditions
imposed on the multi-agent system. We then provide a bound on the time required to reach the consensus. Our bound is given
as an explicit function of the system parameters including the delay bound and the bound on agents’ intercommunication intervals. |
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