The Consensus of Different Fractional-Order Chaotic Multiagent Systems Using Adaptive Protocols

Masoumeh Firouzjahi,Bashir Naderi,Yousef Edrisi Tabriz,Ndolane Sene

doi:10.1155/2022/5129072

Abstract

This paper is concerned with the adaptive consensus problem of incommensurate chaotic fractional order multiagent systems. Firstly, we introduce fractional-order derivative in the sense of Caputo and the classical stability theorem of linear fractional order systems; also, algebraic graph theory and sufficient conditions are presented to ensure the consensus for fractional multiagent systems. Furthermore, adaptive protocols of each agent using local information are designed and a detailed analysis of the leader-following consensus is presented. Finally, some numerical simulation examples are also given to show the effectiveness of the proposed results.

Highlights

Study of multiagent systems over the past decades in various fields such as biology, mechanics, physics, and, more recently, control theories have been found
To achieve the conditions of consensus, graph theory, matrix theory, and the classical stability theorem of fractional-order system have been used, and in terms of classification, there are two general types, consensus with leader and consensus without leader; the latter is more challenging in terms of stability and connected topology than the former
The control signals of the agents are appropriately selected such that their state trajectories follow the leader state, which can be achieved by local information exchanging from the leader and other agents

Summary

Introduction

Study of multiagent systems over the past decades in various fields such as biology, mechanics, physics, and, more recently, control theories have been found (see [1]). Due to the many applications of chaotic systems consensus in data security in fuzzy systems (see [31]), secure communication (see [32]), the effect of market trust on the financial system (see [33]), and the study and treatment of some diseases, such as the study of tumor cell chaos in the tumor immunity fractional model (see [34]) and its application in neural networks to solve fractional differential equations (see [35]), motivated us in this paper to deal with the consensus of the different fractional-order chaotic systems using adaptive control.

Preliminaries

Main Results

Numerical Example

Conclusion