Anchored consensus in multiagent systems

Consensus algorithms have a degree of freedom that permits the possibility of drift in the presence of noise, even though consensus is maintained. In this paper we introduce the alternative notion of anchored consensus. In this new framework one node acts as an anchor. The remaining nodes adjust their states as they would in a standard consensus algorithm. The anchor node also adjusts its state as before with two notable modifications. First it is fed by an external source a constant, potentially noisy signal. Second it has an additional self-feedback term that assists in the anchoring process. We investigate the behavior of this algorithm and demonstrate that in the noise free case consensus is achieved at an exponential rate. Further near consensus is achieved in the noisy case without the unbounded drift manifest in traditional consensus algorithms.