Adaptive Vector Nonsingular Terminal Sliding Mode Control for a Class of n-Order Nonlinear Dynamical Systems with Uncertainty

Nannan Shi,Zhuo Zhao,Qiang Meng,Zhikuan Kang

doi:10.1155/2020/7309417

Abstract

This paper proposed an adaptive vector nonsingular terminal sliding mode control (NTSMC) algorithm for the finite-time tracking control of a class of n-order nonlinear dynamical systems with uncertainty. The adaptive vector NTSMC incorporates a vector design idea and novel adaptive updating laws based on the commonly used NTSMC, which consider the common existence of the degree-of-freedom (DOF) directional differences and eliminate the chattering problem. The closed-loop stability of the n-order nonlinear dynamical systems under the adaptive vector NTSMC is demonstrated using Lyapunov direct method. Simulations performed on a two-degree-of-freedom (DOF) manipulator are provided to illustrate the effectiveness and advantages of the proposed adaptive vector NTSMC by comparing with the common NTSMC.

Highlights

Sliding mode control (SMC), which provides invariance to uncertainty, is one of the effective and efficient nonlinear robust control schemes [1, 2]
Motivated by the above discussion, this paper considers the finite-time stabilization for a class of n-order nonlinear dynamical systems with unknown uncertainty upper bound
We considered the finite-time tracking problem of n-link nonlinear dynamical systems with uncertainty. e well-known nonsingular terminal SMC (TSMC) (NTSMC) for the robot manipulator was extended to the general n-link nonlinear dynamical systems, and the corresponding rigorous stability analysis of the NTSMC for the nonlinear systems was established based on the Lyapunov method

Summary

Introduction

Sliding mode control (SMC), which provides invariance to uncertainty, is one of the effective and efficient nonlinear robust control schemes [1, 2]. Few available control schemes without the finite-convergence performance, whose upper bounds of the uncertainty are designed as vector numbers, have been proposed for spacecraft formation flying [29], a class of MIMO nonlinear systems [30]. Motivated by the above discussion, this paper considers the finite-time stabilization for a class of n-order nonlinear dynamical systems with unknown uncertainty upper bound. We aim to design a control scheme to obtain the satisfactory tracking performances of the n-order uncertain nonlinear dynamical systems with uncertainty (described by (1), (4), and (5)) and make the tracking error of the nonlinear systems converge to zero in finite time

Control Development

Adaptive Vector NTSMC for Nonlinear Systems

Conclusions