Observer-Type Consensus Protocol for a Class of Fractional-Order Uncertain Multiagent Systems

Hongjie Li

doi:10.1155/2012/672346

Abstract

This paper investigates the consensus problem for a class of fractional-order uncertain multiagent systems with general linear node dynamics. Firstly, an observer-type consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on property of the Kronecker product and stability theory of fractional-order system, some sufficient conditions are presented for robust asymptotical stability of the observer-based fractional-order control systems. Thirdly, robust stabilizing controllers are derived by using linear matrix inequality approach and matrix’s singular value decomposition. Our results are in the form of linear matrix inequalities which can easily be solved by LMI toolbox in MATLAB. Finally, a numerical simulation is performed to show the effectiveness of the theoretical results.

Highlights

The coordination problem of multiagent dynamical systems have attracted an increasing attention in recent years due to its applications in sensor networks, robotic teams, satellites formation 1–3
Different from 26, the observer state is used instead of the agent’s state in consensus protocol, and the dynamic behavior of multiagent is described by fractional-order system; 2 the uncertainty is considered in multiagent systems due to external disturbing factors such as environment temperature, voltage fluctuation, and mutual interfere among components; 3 the feedback gain matrices can be derived by matrix’s singular value decomposition, and the consensus criteria are in the form of linear matrix inequalities which can be solved by applying the LMI toolbox
With the development of fractional calculus, it has been found that many physical systems show fractional dynamical behavior because of special materials and chemical properties, which can be described more accurately using fractional-order calculus than traditional integer-order calculus 27, 28

Summary

Introduction

The coordination problem of multiagent dynamical systems have attracted an increasing attention in recent years due to its applications in sensor networks, robotic teams, satellites formation 1–3. In 10 , the consensus problem of multiagent systems with general form of linear dynamics is investigated under a time-invariant communication topology, an observer-type consensus protocol based on relative output measurements between neighboring agents has been. Different from 26 , the observer state is used instead of the agent’s state in consensus protocol, and the dynamic behavior of multiagent is described by fractional-order system; 2 the uncertainty is considered in multiagent systems due to external disturbing factors such as environment temperature, voltage fluctuation, and mutual interfere among components; 3 the feedback gain matrices can be derived by matrix’s singular value decomposition, and the consensus criteria are in the form of linear matrix inequalities which can be solved by applying the LMI toolbox.

Graph Theory Notions

Caputo Fractional Operator

Problem Formulation

Main Results

A Numerical Example

Conclusions