Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis

Kharrat, Mohamed; Mercorelli, Paolo

doi:10.3390/math14010030

Open AccessArticle

Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis

by

Mohamed Kharrat

¹

and

Paolo Mercorelli

^2,*

¹

Mathematics Department, College of Science, Jouf University, Sakaka 72388, Saudi Arabia

²

Institute for Production Technology and Systems, Leuphana University of Lueneburg, 21335 Lueneburg, Germany

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(1), 30; https://doi.org/10.3390/math14010030

Submission received: 16 November 2025 / Revised: 13 December 2025 / Accepted: 18 December 2025 / Published: 22 December 2025

(This article belongs to the Special Issue Recent Advances in Adaptive Control Theory and Applications for Nonlinear Systems)

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Abstract

This paper addresses the tracking control problem for pure-feedback stochastic nonlinear systems subject to full state constraints, actuator faults, and backlash-like hysteresis. An adaptive finite-time control strategy is proposed, using radial basis function neural networks to approximate unknown system dynamics. By integrating barrier Lyapunov functions with a backstepping design, the method guarantees semi-global practical finite-time stability of all closed-loop signals. The strategy ensures that all states remain within prescribed limits while achieving accurate tracking of the reference signal in finite time. The effectiveness and superiority of the proposed approach are demonstrated through simulations, including a numerical example and a rigid robot manipulator system, with comparisons to existing methods highlighting its advantages.

Keywords: nonlinear systems; backlash-like hysteresis; actuator faults; full state constraints; finite-time stability

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MDPI and ACS Style

Kharrat, M.; Mercorelli, P. Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis. Mathematics 2026, 14, 30. https://doi.org/10.3390/math14010030

AMA Style

Kharrat M, Mercorelli P. Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis. Mathematics. 2026; 14(1):30. https://doi.org/10.3390/math14010030

Chicago/Turabian Style

Kharrat, Mohamed, and Paolo Mercorelli. 2026. "Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis" Mathematics 14, no. 1: 30. https://doi.org/10.3390/math14010030

APA Style

Kharrat, M., & Mercorelli, P. (2026). Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis. Mathematics, 14(1), 30. https://doi.org/10.3390/math14010030

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Neural Network-Based Adaptive Finite-Time Control for Pure-Feedback Stochastic Nonlinear Systems with Full State Constraints, Actuator Faults, and Backlash-like Hysteresis

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