Robust consensus of multi-agent systems with stochastic uncertain channels

Abstract

In this paper, we study the robust consensus problem of a network of general discrete-time linear agents coordinating through unreliable communication channels. Two neighboring agents exchange information via a communication channel, which is modeled in this paper as an ideal transmission system subject to a multiplicative stochastic uncertainty. This uncertain channel model includes the commonly studied logarithmic quantizers and the stochastic packet dropout as special cases. For multi-agent systems with undirected connected graphs and stochastic uncertain communication channels, we derive a sufficient condition to guarantee robust consensus in the mean square sense, which unveils the fundamental limitation posed by the synchronizability factor, the topological entropy of the agents, and the mean square channel capacity. The consensus protocol based on uncertain relative state information is then designed, using the modified algebraic Riccati equation. We also consider the case where the agents are perturbed by uncertainties in the input channels. The relations between the uncertain input and communication channel models are discussed.