Barrier Function-Based Asymptotic Tracking Control of Uncertain Nonlinear Systems With Multiple States Constraints

Zhenle Dong,Jianyong Yao,Jianwei Ma

doi:10.1109/access.2020.2966563

Abstract

This technical note focus on the tracking control problem of uncertain nonlinear systems with multiple states constraints. Based on the Barrier Lyapunov function and backstepping technology, a new continuous smooth control solution can be ultimately synthesized to realize asymptotic tracking control in presence of multiple states constraints and modeling uncertainties. Firstly, the modeling uncertainties are divided into periodic and un-periodic components and Fourier expansion technology is employed to translate the periodic disturbance into the form which can be easily compensated. Then the Barrier Lyapunov function are flexibly utilized to design the virtual control law of every step and the final controller, which can guarantee the specified states within certain bounds regardless of the amplitude of system output. Meanwhile, a novel nonlinear control technology is introduced to each design step to realize the final asymptotic tracking control despite the matched and mismatched uncertainties. By analyzing the choice of the control parameters, the backstepping cross-term is skillfully dealt with and the stability of the whole system is proved rigorously. Finally, the simulation results on a three-order nonlinear hydraulic system demonstrate the satisfactory performance of the proposed control method.

Highlights

Nonlinear adaptive robust controller uses a nonlinear dissipative robust component whose feedback gains needs to be greater than the total uncertainties [12], [20]
APPLICATION EXAMPLE we demonstrate the proposed controller on a three-order electro-hydraulic system widely used in industry [16], [18], [20], [32], [34], [35] and can be described as: x1 = x2 x2 = x3 − bx2 + d x3 = gu − f1 − f2 where x1, x2, x3 represents the system states, parameter b is the constant but unknown viscous friction coefficient, g, f1, f2 represents function which depends on the system states and other system parameters
A novel control technique is proposed for a class of common uncertain nonlinear system, the main contribution is that it can handle the multiple states constraints and modeling uncertainties at the same time, while guarantee the asymptotic tracking with a continuous control input

Summary

INTRODUCTION

Improving tracking accuracy and robustness is the eternal pursuit of various nonlinear system and so developing high performance motion controller has always been attractive for many industrial applications. Popular control methods are sliding mode control (SMC)[1], fuzzy control [2], [3], neural network control [4]–[11], nonlinear adaptive robust control [12], [13], RISE (the robust integral of the sign of the error) control [14], observer-based control [15], [16], repetitive control [17] All these techniques have achieved widespread use and it is worth noting that the essence of them lies in the treatment of modeling uncertainties. Multiple system states are likely to tolerate certain amplitude constraint due to the physical/performance limits, or the smallest amplitude abrupt change is prefer in some serious wording conditions such as large initial condition offsets, heavy external disturbances and so on To handle this tough issue, many techniques have been developed. A novel asymptotic controller integrating barrier function-based backstepping design [25] and nonlinear control technique proposed in [29] is presented.

PROBLEM FORMULATION AND DYNAMIC MODELS

MAIN RESULTS

PROOF OF A

PROOF OF B

APPLICATION EXAMPLE

CONCLUSION