Convergence rate for consensus with delays

Authors:
Angelia Nedić;Asuman Ozdaglar
Affiliations:
Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, USA;Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, USA
Venue:
Journal of Global Optimization
Year:
2010

Citing 2
Cited 2

Parallel and Distributed Computation: Numerical Methods

Parallel and Distributed Computation: Numerical Methods
Convergence Speed in Distributed Consensus and Averaging

SIAM Journal on Control and Optimization

Delay robustness in consensus problems

Automatica (Journal of IFAC)
Synchronization of multi-agent systems with delayed control input information from neighbors

Automatica (Journal of IFAC)

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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.