Adaptive Control of a Class of Incommensurate Fractional Order Nonlinear Systems With Input Dead-Zone

Changhui Wang,Yongsheng Chai,Mei Liang

doi:10.1109/access.2019.2948657

Changhui Wang, Yongsheng Chai + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2948657

Copy DOI

Abstract

This paper develops a new adaptive control scheme for a class of incommensurate fractional order nonlinear systems with external disturbances and input dead-zone. Based on the backstepping algorithm, the radial basis function neural network (RBF NN) is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the fractional order parameters update laws for RBF NN are proposed as well as the fractional order nonlinear disturbance estimator to estimate the external disturbances. The adaptive RBF NN controller is designed based on the frequency distributed model of fractional integrator for the fractional order systems, and the stability of the closed loop system is proved. Finally, three simulation examples are given to verify the effectiveness and robustness of the proposed method.

Highlights

In the latest two decades, fractional order calculus has attracted more and more attentions and interests in both theory and applications due to its unique properties including hereditary, non-locality and memory [1]–[4]
Many control schemes for the uncertain fractional order system have been considered in above algorithms, the neural networks (NNs) backstepping control method for the incommensurate fractional order systems with external disturbances and input dead-zone is still short of results
Motivated by the aforementioned observations, an adaptive NN control method for a class of incommensurate uncertain fractional order nonlinear systems with external disturbance and input dead-zone is proposed in this study

Summary

INTRODUCTION

In the latest two decades, fractional order calculus has attracted more and more attentions and interests in both theory and applications due to its unique properties including hereditary, non-locality and memory [1]–[4]. Many control schemes for the uncertain fractional order system have been considered in above algorithms, the NN backstepping control method for the incommensurate fractional order systems with external disturbances and input dead-zone is still short of results. Motivated by the aforementioned observations, an adaptive NN control method for a class of incommensurate uncertain fractional order nonlinear systems with external disturbance and input dead-zone is proposed in this study. The contributions are summarized as follows: 1) The state feedback controller is designed in this paper for a class of incommensurate uncertain fractional order nonlinear system with external disturbance and input dead-zone, VOLUME 7, 2019 in which the indirect Lyapunov method with frequency distributed model is used to analyze the stability.

PRELIMINARY

EXAMPLE 1

CONCLUSION