Group Consensus Of Networked Euler-Lagrange Systems Under A Directed Graph

Recently,due to the broad applications in sensor networks,multiple robots coopration,cooperative control of multi-agent systems has attracted much attention.The main purpose of the study of multi-agent system is to make each agent cooperate with each other in the system such that complex tasks can be completed.Consensus problem has been the focus of research because of the close relationship with many other cooperative control problems.The group consensus problem studied in this thesis is an extension of the consensus problem.The control objective is to make the state information of agents in same groups approach a common value,while the state information between groups can be different.Most relative existing works focuse on linear system models while many physical systems are nonlinear in practice,and there is a large class of mechanical systems taking the form of nonlinear Euler-Lagrange equation.Therefore,the group consensus of multiple Lagrangian systems has many applications.This dissertation give a deep study on the group consensus for multiple Lagrangian systems.The main contents can be summarized as follows:Group consensus for networked Euler-Lagrange systems is studied under a general nonsymmetric directed graph.The relationships between the interactive agents in the same group are cooperation while the relationships between the interactive agents among difierent group can be either cooperation or competition.To achieve group consensus,we assume that the interaction topology among groups is acyclic and the associated directed graph satisfles the in-degree balance condition.Motivated by the fact that the relative velocity information among neighboring agents is difficult to obtain,we propose a distributed adaptive control algorithm for each agent without relative velocity information to achieve group consensus for networked Euler-Lagrangian systems.Finally,simulation result is presented to demonstrate the efiectiveness of the proposed control algorithms.Many relative research design the control algorithms in the constant gain control value needed to global information,in order to avoid the use of global information system so as to reduce the difficulty and improve the robustness,we design a new fully adaptive distributed control law only with neighbor information,and the adaptive control gains instead of constant gains.In order to explicitly derive the final consensus equilibrium of different groups,we construct the auxiliary state variables,and design a new distributed adaptive controller by introducing a new integral form,and it is proved that the final convergence value is related with interactive topological structure,the initial positions of the agents,and the control gains of the designed control algorithms in theory.Finally,simulation results are presented to show the effectiveness of the proposed control algorithms.