Research On Finite-time Output Regulation Of Multi-Agent Systems Under Topology Switching

With the wide application of distributed multi-agent systems in the fields of UAV formation control,dynamic robot optimization research,smart grid scheduling,etc.the coordinated output adjustment problem of multi-agent systems has become the core of control engineering,automation,robotics and other fields.Output regulation means that the output of each individual of the multi-agent systems could asymptotically track the reference input or asymptotically reject the disturbance signal,in which the reference input and interference signal are input by an external system.The essence of output regulation is to design a distributed control law,so that the whole closed-loop system can achieve the purpose of asymptotically track the given input from the outside world and the closed-loop system tends to be stable.The distributed output cooperative problem mainly includes three categories: the first is the output consistency problem of multi-agent under the influence of the external environment;the second is the tracking problem;the third is the estimation problem of the target position.However,in the process of realizing output regulation,each agent is inevitably affected by factors such as external environment interference and unstable communication,which will lead the topology of the system to change and will not remain connected at all times.Moreover,in practical engineering applications,there is a high requirement for the convergence performance of the system,especially the length of convergence time.Therefore,in view of the above situation,the cooperative output regulation of heterogeneous linear multi-agent systems is studied from three cases: finite time,topology switching and finite time topology switching.The main contents involved of this thesis include the following aspects:Firstly,a finite-time dynamic distributed observer control protocol is designed to solve the problem that some agents cannot obtain external system signals and need to converge in a finite time.By using matrix theory,graph theory and other methods,the protocol is theoretically analyzed,and it is proved that the designed new observer can obtain information of the external system in finite time.At the same time,the controller based on a finite time observer is designed,and the finite time stability is proved by using Lyapunov method.Subsequently,the effectiveness of the proposed algorithm and protocol is verified by numerical simulation,The results show that the system not only achieves faster convergence speed in a finite time,but also has good transient performance.Secondly,a distributed output feedback switching protocol is proposed for the cooperative output regulation of multi-agent systems with topology switching structure.Considering that the state of the external system is not completely measurable and the system topology changes with time,a controller based on dynamic switching observer is designed by combining graph theory,functional analysis and matrix theory.Through theoretical analysis,the sufficient conditions of the designed observer under topology switching are obtained,which are related to control parameters and communication topology.The stability of the system is analyzed based on Lyapunov stability theory,solving Sylvester equation and other mathematical methods.The simulation results show that the proposed protocol can not only enables the agent to asymptotically track and converge to the external system,but also has good convergence performance under the condition of topological switching.Finally,in order to solve the problem of finite time output regulation of heterogeneous multi-agent systems under topology switching and further improve the convergence speed of the system,a switching control protocol based on distributed finite-time state observer is proposed,which enables heterogeneous multi-agent systems to quickly track and converge to external systems in finite time under the condition of the topology switching,and solves the problem of output regulation.Based on graph theory,Lyapunov stability theory and homogeneity theory and other methods,it is proved that the designed feedback protocol can make the multi-agent systems remain stable in finite time when the communication topology is switched,and the finite-time switching control strategy of multi-agent systems is verified by simulation examples.