Study On Consensus Of Networked Multiple Euler-Lagrange Systems

Over the past decades,distributed cooperative control of multi-agent systems has attracted a considerable amount of attention due to the broad applications in many areas such as aerospace,communication and transportation.In practice,Euler-Lagrange equations can be used to represent a large class of mechanical systems.However,there exist inherent nonlinearity,parametric uncertainties and strong coupling in the models.Thus,consensus control of networked Euler-Lagrange systems has emerged a new challenging research area because the results for multi-agent systems modeled by linear dynamics cannot be directly used to deal with the problem discussed in this note,particularly wherein both parametric uncertainties and external disturbance are considered.Therefore,consensus problem of multiple Euler-Lagrange systems is studied in the presence of both model uncertainties and external disturbance.In details,the main issues are summarized in the following three aspects:Firstly,the preliminaries are briefly introduced including the related concepts and properties of Euler-Lagrange system with both unmodeled dynamic and external perturbations,algebraic graph theory and nonlinear theory in order to lay the foundation for the design of the controller in the following chapters.Secondly,a distributed adaptive tracking control algorithm,independent on the accurate model,is proposed in this paper for the consensus issue of multiple Euler-Lagrange systems with one leader.The proposed strategy allows that only a subset of the followers have access to the leader.A distributed observer is produced to estimate the leader's velocity and RBF neural networks algorithm is used to uniformly approximate uncertain external disturbance and model uncertainties.Lyapunov stability theorem is used for convergence analysis.Numerical simulation is conducted to validate the effectiveness of the controller.At last,consensus problem of multiple Euler-Lagrange systems is studied in the presence of both unmodelled dynamic and external disturbances.A distributed control protocol based on the extended state observer(ESO),which is adopted to estimate unmodelled dynamic and external disturbances,is proposed.The algorithm makes up complicated calculation and design process of RBF neural network.It is proved via the passivity theory and Barbalat lemma that all the agents can asymptotically reach consensus.Moreover,the consensus with switching topology is also reachable with the proposed controller.Simulation results show that the states of the manipulators reach consensus with the proposed protocol based on ESO.