Consensus of discrete-time multi-agent systems over packet dropouts channels

Abstract

In this paper, we investigate the consensus problem for discrete linear multi-agent systems (MASs) with Markovian packet dropouts. Both identical and nonidentical packet dropouts are studied. For the discrete-time MASs under identical packet dropouts, we present the expectation of the total sojourn time of packet dropouts and successful message transmission, the switching number from packet dropouts to successful message transmission, and the awaken number of packet dropouts and successful message transmission. Based on these expectations, a linear consensus controller is designed through analyzing the transient properties of the Markov process such that the MASs can reach consensus almost surely for any initial distribution of packet dropouts. When it comes to the nonidentical packet dropouts where all the packets are independent and stochastic, a Markovian-lossy-channel based switching model (MLCBS model) is proposed. Based on the MLCBS model, we also propose an easy-to-implement linear consensus controller such that the MASs with nonidentical packet dropouts can achieve consensus almost surely. Finally, the theoretical results are illustrated by simulation examples.