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.
- nonholonomic mobile robots,
- $ H_\infty $-based tracking control,
- fractional order controllers,
- neural networks
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

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.

References

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