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Adaptive Fault-Tolerant Control for Pure-Feedback Stochastic Nonlinear Systems with Sensor and Actuator Faults

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Abstract

In this article, for a class of stochastic pure-feedback nonlinear systems with simultaneous actuator and sensor faults, the problem of adaptive fault-tolerant control is examined. The stochastic pure-feedback nonlinear system is first converted into a strict-feedback by applying the mean value theorem and radial basis function neural networks are used to approximate the unknown functions. Only one adaptive parameter needs to be calculated online rather than the actual weight vector elements by determining the greatest value of the norm of the neural network weight vector. With the help of regrouping and parameter separation methods, the unavailability of state variables caused by sensor faults is addressed. The Lyapunov function methods and the backstepping recursive design technique are used to design an adaptive fault-tolerant controller. It is shown that by choosing proper the design parameters, the tracking errors converge to a small region of the origin, and all the signals in the closed-loop system are bounded in probability. The performance of the proposed controller is illustrated using a numerical example and a real-world example of a rigid robot manipulator system.

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Acknowledgements

This work was supported by MATRICS project Grant No. MTR/2021/000478 from the Science and Engineering Research Board (SERB), India.

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra, Jammu and Kashmir, 182320, India

    Arun Bali, Rahul Kumar & Uday Pratap Singh

  2. School of Computing Science and Engineering, VIT Bhopal University, Bhopal-Indore Highway, Kothrikalan, Sehore, Madhya Pradesh, 466114, India

    Siddharth Singh Chouhan

  3. Satish Dhawan Centre for Space Sciences, Central University of Jammu, Bagla, Rahya-Suchani, Samba, Jammu and Kashmir, 181143, India

    Gourav Kumar

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  1. Arun Bali
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Bali, A., Chouhan, S.S., Kumar, G. et al. Adaptive Fault-Tolerant Control for Pure-Feedback Stochastic Nonlinear Systems with Sensor and Actuator Faults. Circuits Syst Signal Process 42, 5838–5867 (2023). https://doi.org/10.1007/s00034-023-02366-7

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