Limited Time Sliding Mode Coordinated Control Of The Network Euler-Lagrange System

In recent years,with the rapid development of network communication and computer technology,the coordination control problem of Multi-Agent System(MAS)has attracted wide attention from experts and scholars in mathematics,biology,control and AI fields.Because many mechanical systems can be modeled by the Euler-Lagrange equation,therefore the research on the coordinated control of nonlinear network Euler-Lagrange system(NELS)has great significance.This paper studies the finite-time coordinated control of the NELS from the theoretical aspect.The main contents are as follows.The consensus problem for NELS without a leader is studied.First,a sliding mode control algorithm is proposed in the presence of the external disturbances under undirected topology,which enables the MAS to achieve consensus in a finite time.Then,considering the problem of parameter uncertainty,an adaptive sliding mode coordination control algorithm is presented to guarantee the finite-time stability of the closed loop system.The coordination tracking problem for NELS with a leader is developed.First consider the external disturbances and directed topology,gives the sliding coordination control algorithm,the MAS can achieve coordinated tracking in a finite time.Then the NELS coordinated tracking problem with the parameter uncertainty is considered.Under the condition of directed topology,an adaptive coordinated control algorithm is designed to guarantee that tracking errors converge to an arbitrarily small bound around zero in finite time.Finally,the communication delay problem and external disturbances are considered,and a coordinated control algorithm is presented.Based on the algebraic graph theory and the Lyapunov stability theorem,it is proved that the proposed control algorithm can guarantee the finite-time stability of the closed loop system.The numerical simulation system is developed,and the control algorithms presented in this paper are simulated and verified.The simulation results verify the effectiveness and feasibility of the algorithms.