Consensus for Multiagent Systems with Nonlinear Dynamics and Time Delays Using a Two-Hop Relay Adaptive Method

Qian Cao,Y D Song,Feng Yang,Lei Wang

doi:10.1155/2014/792360

Abstract

This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results.

Highlights

As one of the most typical and important problems of multiagent systems, consensus problem has received increasing attention in various fields, such as economy, electrical engineering, and physics
By applying a frequency domain method, we analyze the maximum time delay which can be tolerant by the system to reach a consensus
The least upper bound of the time delay is smaller than the given result, which means that the proposed adaptive control method may not be feasible even when the necessary condition is satisfied

Summary

Introduction

As one of the most typical and important problems of multiagent systems, consensus problem has received increasing attention in various fields, such as economy, electrical engineering, and physics. Lin et al [8] studied the consensus problem for second-order systems with nonuniform time delays using a frequency domain approach and an upper bound of the maximum of the time-delays was given. This accumulation of time delays may have an influence on the system stability, yet, to our best knowledge, no study has been carried out to address this issue Motivated by this concern, we studied the consensus problem for multiagent systems with both nonlinear dynamics and time delays in this work using adaptive protocols so that the agent states reach a common value and the estimation parameter errors converge to zero as well. By using a frequency domain method, a necessary condition of the maximum tolerated time delay is given for system consensus using the proposed adaptive control method.

Preliminaries and the Model Formation

Main Results

A Simulation Example

Conclusions