Research On The Consistency Of Fractional-Order Multi-Agent System Via Adaptive Control

In recent decades,the consensus problem of fractional-order multi-agents has aroused the attention of numerous scholars at home and abroad.Integer order equations often make the system lose some corresponding information when describing the system,thus affecting the stability of the system.While,the fractional order system can make the system more consistent when describing the material with memory and viscosity.Consistency problem is one of the most basic problems in multi-agent system collaborative control research,and can be applied to many fields.This paper focuses on the consistency of fractional multi-agent intelligence systems.The main contributions are as follows:1)The consistency of two classes of linear and nonlinear fractional-order multi-agent systems with leader is considered.Firstly,under the topology of undirected communication,a control protocol based on the state information of neighboring agents is designed.Secondly,by using Kronecker product of matrices and Lyapunov stability theorem of fractional order systems,sufficient conditions for uniformity of two kinds of multi-agent systems in the form of linear matrix inequality(LMI)are obtained.Finally,a simulation example is given to illustrate the effectiveness and practicability of the obtained results.2)The consistency of adaptive control for two classes of linear and nonlinear fractional-order multi-agent systems with leader followers is studied.Firstly,an adaptive control protocol based on neighboring agents and leader state information is designed under undirected communication topology.Secondly,based on graph theory knowledge,Lyapunov stability theorem for fractional-order systems,Barbalat lemma,Kronecker product and Schur complement lemma,sufficient conditions for uniformity of linear and nonlinear fractional-order multi-agent systems in view of LMI form are obtained.Finally,two simulation examples are given to verify the validity and correctness of the two theoretical results.3)The adaptive control consistency problem of two kinds of double-integrator linear and nonlinear fractional multi-agent systems is considered.Firstly,the control protocol based on the state information of neighboring agents is designed under the directed communication topology,and the corresponding adaptive update law is devised.Secondly,based on the Lyapunov direct method and graph theory of fractional order systems,sufficient conditions for two classes of double integral fractional order multi-agent systems to reach uniformity are obtained.Finally,the effectiveness of the theoretical results is verified by two simulation examples.