Finite-Time Tracking Control for a Class of MIMO Nonlinear Systems with Unknown Asymmetric Saturations

Fu Mingyu,Xu Yujie

doi:10.1155/2017/9452171

Abstract

This paper addresses the problem of finite-time tracking control for multiple-input and multiple-output (MIMO) nonlinear systems with asymmetric saturations. A systematic approach is proposed to eliminate the effects of unmeasured external disturbances and unknown asymmetric saturations. In the proposed control strategy, a terminal sliding mode disturbance observer is provided to estimate the augmented disturbance (which contains the unknown asymmetric input saturation and external disturbance). The approximation error of the augmented disturbance can converge to zero in a fixed finite-time interval. Furthermore, a novel finite-time tracking control algorithm is developed to guarantee fast convergence of the tracking error. Compared with the existing results on finite-time tracking control, the chattering problem and the input saturation problem can be solved in a unified framework. Several simulations are given to demonstrate the effectiveness of the proposed approach.

Highlights

The convergence rate is an important issue for dynamical control systems in practice
This paper addresses the problem of finite-time tracking control for multiple-input and multiple-output (MIMO) nonlinear systems with asymmetric saturations
Simulation results are given to validate the effectiveness of the proposed finite time control scheme for a surface vessel under two different situations: without input saturation and with input saturation

Summary

Introduction

The convergence rate is an important issue for dynamical control systems in practice. In [13], a fast terminal dynamics was proposed in the design of the sliding mode control for single-input single-output nonlinear dynamical systems to improve the convergence rate during reaching and sliding phase. Replacing the large gain with output of the disturbance observer will greatly mitigate the twitter, but the convergence of the closed-loop system needs further discussion Another problem in finite-time control is the input saturation, which may bring in chattering and degrade the control performance. Compared with most existing research, our work has two main contributions: (1) the chattering problem and saturation problem are solved in a unified framework; (2) the finite-time convergence of all closed-loop state is guaranteed regardless of external disturbance and unknown asymmetric saturation.

Problem Formulation

Controller Design

Simulation Results

Conclusion