LIDS Technical Report # 2779 1 Constrained Consensus ∗

We study the problem of reaching a consensus in the estimates generated by multiple agents forming a network with time-varying connectivity. Our main focus is on constrained consensus problems where the estimates of different agents are constrained to lie in different constraint sets. We consider a distributed “projected consensus algorithm” in which agents combine their local averaging operation with projection onto their individual constraint sets. This algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents. We establish convergence of the projected consensus algorithm. We also provide convergence rate estimates for the cases when the weights are constant and equal, and when the weights are time-varying but all agents have the same constraint set.

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