Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Jun Liu,Wei Chen,Ping Li,Kaiyu Qin

doi:10.1155/2018/6059574

Abstract

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the double-integrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

Highlights

In the past decade, an increasing number of scholars have been interested in the consensus problems for multiagent systems with potential applications in biology, control engineering, and physics
Suppose that a double-integrator fractional-order multiagent system (FOMAS) is composed of n agents whose network topology G is connected and undirected
Three different time delays are used for simulation: (1) τ = 0.26 s, (2) τ = 0.25 s, and (3) τ = 0.24 s

Summary

Introduction

An increasing number of scholars have been interested in the consensus problems for multiagent systems with potential applications in biology, control engineering, and physics. In [10], the authors discussed the average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, the consensus problem of fractional-order multiagent systems with double integral under fixed topology was studied in [24]. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, the consensus of fractional-order multiagent systems with double integral under switching topology was investigated in [25]. The main contribution of this article lies in the research on the double-integrator fractional-order dynamics which can better reveal the essential characteristic or behavior of an object in the complex environment and the consensus of the double-integrator FOMAS with time delay whose network topology G is, respectively, undirected topology and directed topology.

Preliminaries

Problem Statement

Main Results

Simulation Results

Conclusion