Research On The Consistency Problem Of Multiple Euler-Lagrange Systems On Symbolic Network

The multiple Euler-Lagrange(EL)system,regarded as a classic and universal nonlinear system in applications of multi-agent systems(MASs),has become a hot research topic for multi-agent systems in recent years.And multiple Euler-Lagrange systems have widespread practical applications,such as industrial production,automation technology,robot,or other fields.Due to its strong coupling,uncertain dynamic parameters,non-linearity,etc.,there exists certain difficulties for the research of multiple Euler-Lagrange systems.The consensus problem is in the heart of the control field,and the research on multi-agent system has ended,most is to solve the coordinated optimization and distributed control,cluster behavior of multi-agent system.Topology usually represents interaction between the agent.With the in-depth study of the consensus issues,it is no longer limited to focusing on the cooperation network,which brings different opportunities and challenges to the control field.In a long period of research in the past,the edge weights of the communication topology network are all described by non-negative real numbers.In fact,the topological network edge weights of multi-agent systems may also be described by negative numbers.Now,consensus issues on the signed network has become a hot issue in the the control field.This article studies the consensus problem of multiple Euler-Lagrange systems on the signed network,the main research contents summarized are as follows:(1)The consensus problem is studied subject to the multiple Euler-Lagrange system over the fixed signed network under the "Leading-Following" framework.The system model has the uncertainty of parameter,and the consensus control protocol is designed.Through the Lyapunov stability principle and Barbalat’s lemma,a dynamic leader and static leader are given,respectively,and the "Leader-Following" consistency problem of multiple Euler-Lagrange system on the symbol network is solved.(2)The consensus problem is studied subject to the multiple Euler-Lagrange system over the fixed signed network under the "Leading-Following" framework,where each follower dynamic model contains disturbance generated by an external system,and it is assumed that the follower cannot obtain the leader’s state information exactly.Design a distributed observer for each follower by using the state information of neighbor nodes.Through the analysis of Lyapunov stability principle and Barbalat’s lemma,it is proved that the control protocol can achieve the consensus of multiple Euler-Lagrange systems on the fixed signed network.(3)The consensus problem is studied subject to the multiple Euler-Lagrange system over the switching signed network under the "Leading-Following" framework,where each follower dynamics model contains disturbance generated by external systems.And considering the switching communication topology,and the assumption is given that the switched signed network is jointly connected and the union graph contains a directed spanning tree.The desired trajectory of leader is generated by an external system,and each follower cannot obtain information of the leader and disturbance information.In order to solve this problem,a type of observer is built,then a distributed control protocol is proposed.Consensus goal can be achieved by using the Lyapunov stability principle and the generalized Barbalat’s lemma for analysis.