Average Consensus of Multi-Agent Systems Under Directed Topologies and Binary-Valued Communications

Abstract

This paper is concerned with the average consensus problem of multi-agent systems with binary-valued communications under directed topologies. The information that each agent communicates with others is binary-valued with a fixed threshold and the control is a quantity of transportation from one agent to another, which causes that a decrease of the transmitter’s state leads to an increase of the same amount of the receiver’s. Due to the limitation of the information obtained, each agent needs to wait for a period of time to collect enough binary-valued information to estimate. Hence, we construct a two-scale control algorithm. At the small-time scale, each agent estimates its neighbors’ states based on the accumulation of binary-valued information for a period of time, during which the control is zero. At the large-time scale, each agent designs the control signal based on the estimation, which results in state updating of the multi-agent system. Then, each agent estimates the new states of its neighbors and the process of alternating estimation and control will be repeated. Finally, we prove that the estimation is convergent and give the mean square convergence rate as the reciprocal of the estimation time. More importantly, the multi-agent system is proved to achieve average consensus and the consensus speed is given. Simulation results are given to validate the algorithm.