Performance-Guaranteed Switching Adaptive Control for Nonlinear Systems With Multiple Unknown Control Directions

Yang Liu,Chaoyang Dong,Wenqiang Zhang,Zhijie Zhou

doi:10.1109/access.2020.2974754

Yang Liu, Chaoyang Dong + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.2974754

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Abstract

In this paper, an adaptive control strategy with novel performance-guaranteed switching mechanism is proposed for a class of nonlinear parametric strict-feedback systems with unknown parameters and multiple unknown control directions. Firstly, adaptive controller is designed by combining tuning function design and barrier Lyapunov function (BLF) techniques, to handle parameter uncertainties and avoid over-parametrization phenomenon. The unknown control directions are estimated online with the proposed novel switching criterion composed of a BLF-type monitoring function and a threshold function. It is shown that the correct directions can be identified rapidly with only finite times of switching and mis-switching problem is avoided. At switching moments, a novel reset mechanism is triggered to adjust the value of integrator to avoid failure of BLF method. Consequently, tracking error of reference signal converges to zero asymptotically and all closed-loop signals are proved to be bounded. In addition, the tracking errors can be restricted into prescribed intervals without information of control directions. Numerical results demonstrate the effectiveness and performance of the proposed method.

Highlights

Recent years have seen intensively studies on control problems of uncertain nonlinear systems [1] due to practical application demands [2], [3] and theoretical challenges [4]–[6]
Liu et al.: Performance-Guaranteed Switching Adaptive Control for Nonlinear Systems With Multiple Unknown Control Directions approximate the correct directions based on a switching logic and once reached, stability is achieved
In this paper, we propose a performance-guaranteed switching adaptive controller for parametric strict feedback (PSF) nonlinear systems in the presence of multiple unknown control directions

Summary

INTRODUCTION

Recent years have seen intensively studies on control problems of uncertain nonlinear systems [1] due to practical application demands [2], [3] and theoretical challenges [4]–[6]. Y. Liu et al.: Performance-Guaranteed Switching Adaptive Control for Nonlinear Systems With Multiple Unknown Control Directions approximate the correct directions based on a switching logic and once reached, stability is achieved. Reference [32] utilized the upper limit of an integral-type Lyapunov function to construct the switching logic, based on which the finite-time stabilization of a class of uncertain nonlinear systems was realized. According to the previous discussions, a naturally challenging topic is to design a performance-guaranteed switching controller for uncertain nonlinear systems with multiple unknown control directions. We will address this problem by resorting to BLF method and designing a novel BLFtype switching logic, which has not been studied yet. For any x ∈ Rn, x denotes its Euclidean norm. diag (·) refers to a diagonal matrix

PROBLEM FORMULATION

SWITCHING MECHANISM DESIGN

MAIN RESULTS

SIMULATION STUDIES

CONCLUSION