Research On Formation And Containment Control Of A Class Of Fractional-order Linear Multi-agent Systems

In recent years,the cooperative control of multi-agent system is widely used in military,aerospace and other fields,which attracts more and more scholars' attention.Its main research fields include containment control,consensus control,trajectory tracking control and formation control.Compared with the integral-order system,the fractionalorder system performs better in the study of some physical problems and engineering applications.Therefore,unlike the existing integer-order multi-agent systems,this paper considers the multi-agent system with fractional-order linear dynamics,and study the time-varying formation control and containment control of multi-agent systems.The results are as follows:1.The time-varying formation control problem of fractional-order linear multiagent system based on fixed and switched directed communication topology is solved.First of all,compared with the fractional-order system whose order ? is ? ?(0,1],the fractional-order considered in this paper satisfies ? ?(0,n],which is an extension of the existing research.Secondly,due to the fact that the state of agents are very difficult to obtain in the actual operation,the distributed observer-based control protocol is designed in this paper.In order to realize the time-varying formation control,the real state input controller which can not be obtained is replaced by the estimated state information.In addition,considering the complexity of communication between agents in the real situation,this paper applies switching communication topology to describe the information transfer mode of multi-agent systems,which is more practical.Then,by a series of linear transformations,the time-varying formation control problem of the original system is transformed into the asymptotic stability problem of the new system.By using Laplace transformation,the fractional-order linear systems asymptotic stability theorem and other tools,a reasonable controller is designed,and the sufficient conditions for realizing the time-varying formation control are obtained.Finally,the simulation experiment is designed to prove the rationality of the theory.2.The containment control and robust containment control of fractional-order heterogeneous linear multi-agent systems are studied,in which the follower systems have heterogeneous linear dynamics,the leader systems are homogeneous linear systems and have measurable linear control inputs.First of all,different from the existing results,this paper considers the containment control problem whose leader systems have bounded linear inputs.Secondly,the order ? of fractional-order system satisfies? ?(0,n],which extends the fractional-order linear system of ? ?(0,1] considered in most papers and generalizes the results.After that,this paper uses the communication information between agents,uses observation technology to estimate the control input of leader systems,and designs the corresponding control protocol to solve the problem that the real state is difficult to obtain.In addition,in practical application,the controller must pass through the actuator before inputting the system.Because of the performance deterioration of the actuator itself or the influence of the control input on the actuator,the actuator faults are easy to occur.Therefore,this paper proposes to study the containment control of fractional-order heterogeneous linear systems with actuator faults.Based on the asymptotic stability theorem of fractional-order linear systems and Laplace transform,sufficient conditions for the containment control of fractional-order heterogeneous linear systems and the robust containment control with actuator faults are given.Finally,this paper presents a series of simulation experiments to verify the feasibility of the containment control.