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Intelligent robust control of inverted pendulum using hierarchical sliding mode and ELM-based estimator.

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Title: Intelligent robust control of inverted pendulum using hierarchical sliding mode and ELM-based estimator.
Authors: FARAJ, Iman1 imanattwan@alsafwa.edu.iq, KHAWWAF, Jasim2
Source: Archive of Mechanical Engineering. 2026, Vol. 73 Issue 1, p19-41. 23p.
Subjects: Inverted pendulum (Control theory), Sliding mode control, Robust control, Damping (Mechanics), Extreme learning machines, Control theory (Engineering), Lyapunov stability
Abstract: The Inverted Pendulum Cart (IPC) system is a significant challenge in control theory, is used as a benchmark for evaluating advanced actuator control techniques, and has critical applications in robotics and autonomous systems. This paper proposes a new control strategy based on a Hierarchical Non-Singular Fast Terminal Sliding Mode (HNFTSM) controller technique enhanced by an Extreme Learning Machine (ELM) neural network to achieve system stability. HNFTSM provides finite time convergence and resistance to disturbances and uncertainty, while the ELM contributes to estimating these disturbances to improve performance. The stability of this strategy is proven using the Lyapunov stability theory, which ensures that all system states reach the desired equilibrium in finite time. Furthermore, the proposed hierarchical control scheme guarantees finite-time convergence of all closed loop IPC states under bounded uncertainties. A comprehensive comparative analysis is conducted against other advanced control techniques, including HSMC, HNTSM, ELM-HNTSM, and conventional NFTSM controllers. Simulation results show that the proposed approach outperforms other methods in tracking accuracy, convergence speed, singularity avoidance, and chattering reduction, which enhances the effectiveness of system control and makes it promising for practical applications. [ABSTRACT FROM AUTHOR]
Copyright of Archive of Mechanical Engineering is the property of Polish Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Intelligent robust control of inverted pendulum using hierarchical sliding mode and ELM-based estimator.
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  Data: <searchLink fieldCode="JN" term="%22Archive+of+Mechanical+Engineering%22">Archive of Mechanical Engineering</searchLink>. 2026, Vol. 73 Issue 1, p19-41. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Inverted+pendulum+%28Control+theory%29%22">Inverted pendulum (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Sliding+mode+control%22">Sliding mode control</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink><br /><searchLink fieldCode="DE" term="%22Damping+%28Mechanics%29%22">Damping (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Extreme+learning+machines%22">Extreme learning machines</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink>
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  Data: The Inverted Pendulum Cart (IPC) system is a significant challenge in control theory, is used as a benchmark for evaluating advanced actuator control techniques, and has critical applications in robotics and autonomous systems. This paper proposes a new control strategy based on a Hierarchical Non-Singular Fast Terminal Sliding Mode (HNFTSM) controller technique enhanced by an Extreme Learning Machine (ELM) neural network to achieve system stability. HNFTSM provides finite time convergence and resistance to disturbances and uncertainty, while the ELM contributes to estimating these disturbances to improve performance. The stability of this strategy is proven using the Lyapunov stability theory, which ensures that all system states reach the desired equilibrium in finite time. Furthermore, the proposed hierarchical control scheme guarantees finite-time convergence of all closed loop IPC states under bounded uncertainties. A comprehensive comparative analysis is conducted against other advanced control techniques, including HSMC, HNTSM, ELM-HNTSM, and conventional NFTSM controllers. Simulation results show that the proposed approach outperforms other methods in tracking accuracy, convergence speed, singularity avoidance, and chattering reduction, which enhances the effectiveness of system control and makes it promising for practical applications. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Archive of Mechanical Engineering is the property of Polish Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.24425/ame.2025.157604
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      – Code: eng
        Text: English
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        PageCount: 23
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      – SubjectFull: Inverted pendulum (Control theory)
        Type: general
      – SubjectFull: Sliding mode control
        Type: general
      – SubjectFull: Robust control
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      – SubjectFull: Damping (Mechanics)
        Type: general
      – SubjectFull: Extreme learning machines
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      – SubjectFull: Control theory (Engineering)
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      – SubjectFull: Lyapunov stability
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            – D: 01
              M: 01
              Text: 2026
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              Y: 2026
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