Robust Tracking Control of the Euler-Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks.

Yi Wang,Weidong Wu,He Ma,Yu-Ting Bai

doi:10.1155/2021/1277349

Abstract

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

Highlights

Many practical systems can be represented by the El system, such as robotic manipulator [1], hydraulic system [2], and underwater marine system [3]. erefore, due to its wide application, nonlinear Euler–Lagrange systems are a significant class of nonlinear systems
For research position constraint problems, a BLF-based controller is proposed for the marine vessel with uncertainty in [23], which demonstrates the Computational Intelligence and Neuroscience superiority of BLF in the El system design. e BLF technique can dynamically constrain the error within the specified range and guaranteed the performance of tracking control, which enhances the robustness of the control
The design process of the robust tracking control strategy for EL systems based on BLF and self-structuring neural network (SSNN) is introduced. e SSNN is developed to estimate unknown model dynamics. e TABLF is applied to deal with error time-varying constraint problems. e compensator is designed to estimate unknown disturbances and neural network (NN) estimate errors

Summary

Introduction

Many practical systems can be represented by the El system, such as robotic manipulator [1], hydraulic system [2], and underwater marine system [3]. erefore, due to its wide application, nonlinear Euler–Lagrange systems are a significant class of nonlinear systems. In [28,29,30], the adaptive method is combined with NN to design control strategies for a class of uncertain nonlinear systems. E sliding mode control method combines with event-triggered strategy, and a robust trajectory tracking controller is designed for uncertain EL systems [40]. E NN approximate errors and unknown disturbances can compensate by a designed compensator, which ensures tracking stability (2) In order to improve the practicability of the control systems, a self-structure mechanism is developed to adjust NN approximation performance, which can appropriately find optimal NN structures and avoid excessive calculation burden. Rn and Rn×n denote n dimensional column vectors and the n × n real matrices, respectively. ‖ · ‖F and ‖ · ‖ represent the Frobenius norm and the Euclidean norm. diag{·} represents a block-diagonal matrix

Problem Formulation

Main Results

Simulation Results