Enhanced LMI-Based composite nonlinear control for a knee rehabilitation exoskeleton robot considering motion constraints

Sahar Jenhani; Hassène Gritli; Jyotindra Narayan; Sahar Jenhani; Hassène Gritli; Jyotindra Narayan

doi:10.3934/mmc.2026013

Mathematical Modelling and Control

2026, Volume 6, Issue 2: 163-184. doi: 10.3934/mmc.2026013

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Research article

Enhanced LMI-Based composite nonlinear control for a knee rehabilitation exoskeleton robot considering motion constraints

1.
Laboratory of Robotics, Informatics and Complex Systems (RISC Lab - LR16ES07), National Engineering School of Tunis, University of Tunis El Manar, BP. 37, Le Belvédère, 1002, Tunis, Tunisia
2.
Higher Institute of Information and Communication Technologies, University of Carthage, Technopole of Borj Cédria, Route de Soliman, BP 123, Hammam Chatt 1164, Ben Arous, Tunisia
3.
Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna 801106, India

Received: 24 December 2024 Revised: 28 May 2025 Accepted: 06 August 2025 Published: 08 June 2026

This paper proposes a novel robust control strategy for the stabilization of a knee rehabilitation exoskeleton robot. Unlike traditional methods, the designed controller combines a linear state-feedback law with a nonlinear compensation term to effectively address the robot’s nonlinear dynamics under parameter uncertainties, external disturbances, and motion constraints. Two complementary approaches are introduced: one assumes a constant bound on the nonlinearities and another employs a state-dependent linear constraint. For each approach, tailored Linear Matrix Inequality (LMI) conditions are derived using specific technical lemmas, including Young’s inequality, the S-procedure, the Schur complement, and the matrix inversion lemma. The originality of this work lies in the systematic integration of motion constraints and external disturbances into the LMI framework for composite control. Numerical simulations validate the proposed methodology, thereby demonstrating superior robustness and stability performance compared to conventional control strategies.
- knee exoskeleton robot,
- robust position control,
- composite controller,
- motion constraints,
- linear matrix inequality (LMI)
Citation: Sahar Jenhani, Hassène Gritli, Jyotindra Narayan. Enhanced LMI-Based composite nonlinear control for a knee rehabilitation exoskeleton robot considering motion constraints[J]. Mathematical Modelling and Control, 2026, 6(2): 163-184. doi: 10.3934/mmc.2026013

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Abstract

This paper proposes a novel robust control strategy for the stabilization of a knee rehabilitation exoskeleton robot. Unlike traditional methods, the designed controller combines a linear state-feedback law with a nonlinear compensation term to effectively address the robot’s nonlinear dynamics under parameter uncertainties, external disturbances, and motion constraints. Two complementary approaches are introduced: one assumes a constant bound on the nonlinearities and another employs a state-dependent linear constraint. For each approach, tailored Linear Matrix Inequality (LMI) conditions are derived using specific technical lemmas, including Young’s inequality, the S-procedure, the Schur complement, and the matrix inversion lemma. The originality of this work lies in the systematic integration of motion constraints and external disturbances into the LMI framework for composite control. Numerical simulations validate the proposed methodology, thereby demonstrating superior robustness and stability performance compared to conventional control strategies.

References

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