Optimal Memory Scheme for Accelerated Consensus Over Multi-Agent Networks

Consensus overmulti-agent networks can be accelerated by utilizing agent’s memory to the control protocol. In this paper, a general protocol with memory information from the node and its neighbors is designed. We aim to provide an optimal memory scheme to accelerate consensus. The contributions of this paper include: (i) For the one-tap memory scheme, we prove that the memory information of neighbors is unnecessary for the optimal convergence. (ii) It is proved that in the worst-case scenario, one-tap node memory is sufficient to achieve the optimal convergence rate, that is, adding more taps of past information from neighbors can not improve the rate further. (iii) It is found that the convergence rate with two-tap memory can be further improved on star networks. Numerical examples are presented to illustrate the validity and correctness of the obtained results.