On fast queue consensus of discrete-time second-order multi-agent networks over directed topologies

Abstract

Queue consensus, which aims to drive a set of agents to form a prescribed queue while moving with a common reference velocity, has attracted much attention due to its wide applications. This paper investigates the problem of fast queue consensus for a class of directed multi-agent networks with discrete-time second-order agent dynamics. First, a discrete-time consensus-based control protocol is constructed, and the necessary and sufficient condition to achieve queue consensus is presented. Then, the explicit formulas for the control parameters to achieve the fastest convergence are derived. It is found that the convergence rate of the reference velocity dominates the convergence performance of the overall network. To further accelerate the convergence rate, the agents' node memory is introduced to redesign the update rule of the reference velocity. Furthermore, the analytic formulas of the improved optimal convergence rate and control parameters are established. Finally, numerical examples are given to validate the effectiveness of the proposed theoretical results.