Collaboration Control of Fractional-Order Multiagent Systems with Sampling Delay

Hong-Yong Yang,Jian-Zhong Gu,Lei Guo,Banghai Xu

doi:10.1155/2013/854960

Abstract

Because of the complexity of the practical environments, many distributed multiagent systems cannot be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. In this paper, collaboration control problems of continuous-time networked fractional-order multiagent systems via sampled control and sampling delay are investigated. Firstly, the sampled-data control of multiagent systems with fractional-order derivative operator is analyzed in a directed weighted network ignoring sampling delay. Then, the collaborative control of fractional-order multiagent systems with sampled data and sampling delay is studied in a directed and symmetrical network. Many sufficient conditions for reaching consensus with sampled data and sampling delay are obtained. Some numerical simulations are presented to illustrate the utility of our theoretical results.

Highlights

In recent years, consensus problems in distributed networked multiagent systems have attracted increasing attention of more and more researches including control theory, mathematics, biology, physics, computer science, and robotics
We investigate the consensus of fractionalorder multiagent systems (FOMAS) with sampled-data control
Suppose that the order of the fractional multiagent dynamics is α = 0.8 and the system control gain is γ = 1; we can obtain the relationship between the sampling period and the upper bound of sampling delays (Figure 2) from the conditions in Theorem 7

Summary

Introduction

Consensus problems in distributed networked multiagent systems have attracted increasing attention of more and more researches including control theory, mathematics, biology, physics, computer science, and robotics. To the best of our knowledge, there are few researches done on the coordination control of fractional-order multiagent systems via sampled data. We investigate the consensus of fractionalorder multiagent systems (FOMAS) with sampled-data control. The main innovation of this paper lies in the study on the distributed coordination of FOMAS with sampled data and sampling delay.

Fractional Calculus

Problem Statement

Sampled Control of FOMAS

Consensus of FOMAS with Sampled Data and Sampling Delay

Simulations

Conclusions