Position tracking control of nonholonomic mobile robots via $ H_\infty $-based adaptive fractional-order sliding mode controller

Naveen Kumar; Km Shelly Chaudhary; Naveen Kumar; Km Shelly Chaudhary

doi:10.3934/mmc.2025009

Mathematical Modelling and Control

2025, Volume 5, Issue 1: 121-130. doi: 10.3934/mmc.2025009

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Position tracking control of nonholonomic mobile robots via $H_\infty$ -based adaptive fractional-order sliding mode controller

Naveen Kumar ^1,2,
Km Shelly Chaudhary ^{1,3
,
,}

1.
Department of Mathematics, National Institute of Technology Kurukshetra, Kurukshetra 136119, Haryana, India
2.
Department of Mathematics, Mahatma Jyotiba Phule Rohilkhand University Bareilly, Bareilly 243006, Uttar Pradesh, India
3.
Department of Mathematics, Meerut College Meerut, Meerut 250002, Uttar Pradesh, India

Received: 01 May 2024 Revised: 31 October 2024 Accepted: 10 November 2024 Published: 31 March 2025

In this article, the position tracking control problem of a nonholonomic wheeled mobile robot with system uncertainties and external disruptions is examined. In the design control technique, a fractional-order sliding surface is presented for faster response of the dynamical system's states. Based on this sliding surface, a robust $H_\infty$ -based adaptive fractional-order sliding mode controller is developed to effectively handle the system's uncertainty and external disruptions. In the structure of the designed control scheme, the radial basis function neural network is utilized to reproduce the nonlinear function of the dynamical structure. The controller's $H_\infty$ part compensates for the negative effects of the external disturbances and uncertainties robustly. The Lyapunov approach is used to determine the stability of the dynamical system. Furthermore, a numerical simulation analysis is carried out to show the effectiveness of the proposed control technique.

Keywords:

Citation: Naveen Kumar, Km Shelly Chaudhary. Position tracking control of nonholonomic mobile robots via $H_\infty$ -based adaptive fractional-order sliding mode controller[J]. Mathematical Modelling and Control, 2025, 5(1): 121-130. doi: 10.3934/mmc.2025009

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Abstract

A correction on

Monotonicity and inequalities related to complete elliptic integrals of the second kind

by Fei Wang, Bai-Ni Guo and Feng Qi. AIMS Mathematics, 2020, 5(3): 2732–2742.

DOI: 10.3934/math.2020176

In Acknowledgments section, the Grant number of "Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering" is missing. Here we give the complete information of this fund.

The changes have no material impact on the conclusion of this article. The original manuscript will be updated ^[1]. We apologize for any inconvenience caused to our readers by this change.

Acknowledgments

This work was partially supported by the Foundation of the Department of Education of Zhejiang Province (Grant No. Y201635387), the National Natural Science Foundation of China (Grant No. 11171307), the Visiting Scholar Foundation of Zhejiang Higher Education (Grant No. FX2018093), and the Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering (Grant No. A027120206).

The authors thank anonymous referees for their careful corrections to, helpful suggestions to, and valuable comments on the original version of this manuscript.

Conflict of interest

The authors declare that they have no conflict of interest.

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