Research On Distributed Average Tracking Of Multi-Agent Systems Based On Sampling Data

In recent years,the research of multi-agent systems has attracted the attention of researchers in different fields.Among them,the distributed average tracking(DAT)problem has its own unique challenges as an extension of the consensus problem and coordinated tracking problem.The problem assumes that there is a group of agents,each of which tracks a time-varying reference signal,and that only local communication is used between each agent,and then,a distributed protocol is designed so that all agents will eventually track the average of all reference signals.At present,there have been some research results on the distributed average tracking problem of multi-agent systems,but most of them are based on continuous communication between agents.Meanwhile,with the widespread use of digital sensors and controllers,algorithms are also increasingly dependent on digital platforms.Compared with full-state information transmission,the information at the sampling time can more effectively save network bandwidth and communication costs.Therefore,the distributed average tracking problem of multi-agent systems based on sampled data has certain research significance.In this paper,for three different multi-agent system models,the DAT problem of multiagent systems based on sampled data is studied,and the following research results are obtained:(1)The DAT problem of the first-order multi-agent system based on sampled data is studied.Firstly,using the discrete model method,the first-order system continuous-time model is converted into a discrete-time model with ZOH technique,and a DAT protocol based on sampled data is proposed.At the same time,it is assumed that the network topology graph is undirected and connected,and the derivatives of multiple time-varying reference signals are bounded.Through graph theory and initial conditions,the DAT problem is transformed into a consistency problem.Then the discrete-time Lyapunov method are used to analyze the stability of the system,so the sufficient and necessary conditions for the first-order multi-agent system to achieve asymptotically bounded DAT can be obtained.Finally,the effectiveness of the distributed protocol is verified by numerical simulation.(2)The DAT problem of the general linear multi-agent system based on sampled data is discussed.By using the ZOH technology,the continuous-time model of general linear system can convert into a discrete-time model,and a corresponding DAT protocol based on sampled data is proposed.Assuming that the network topology is undirected and connected,the dynamic equations of multiple time-varying reference signals satisfy the general linear model,while ensuring that the input signals of the reference signals are bounded.Then,using the algebraic graph theory,matrix theory and discrete Lyapunov method,the stability of the error system is analyzed and the sufficient and necessary conditions for the general linear multi-agent system to achieve asymptotic bounded DAT are obtained.Finally,the simulation results further confirmed the validity of the protocol.(3)The DAT problem of the nonlinear multi-agent system that meets the Lipschitz condition is considered.Firstly,the discrete model method is used to obtain the discrete time model of the nonlinear multi-agent system.Assuming that the network topology is undirected and connected,the dynamic equations of multiple time-varying reference signals also satisfy the Lipschitz condition,and the input signals of the reference signals are bounded.Then,by using the algebraic graph theory,matrix theory and discrete Lyapunov method,the stability of the error system is analyzed and the sufficient and necessary conditions for the nonlinear multiagent system to achieve asymptotically bounded DAT can be achieved.Finally,the simulation results using three sets of different parameters confirmed the effectiveness of the distributed protocol,meanwhile,the effects of control gain and sampling period on the final convergence state are discussed.