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Peer-reviewedCC BY 4.0Axioms

New Tools for Finite-Time Fuzzy Control of Fractional-Order Systems: Stability Lemmas, Composite Disturbance Observers, and Singularity-Free Designs

  • Abdesselem Boulkroune1
  • Naamane Bounar1
  • Farouk Zouari2
  • Asier Ibeas3
  1. 1LAJ, Department of Automatic Control, Faculty of Science and Technology, University of Jijel, Jijel 18000, Algeria
  2. 2Laboratoire de Recherche en Automatique (LARA), Ecole Nationale d’Ingénieurs de Tunis (ENIT), Université de Tunis El Manar, Tunis 1002, Tunisia
  3. 3Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
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Abstract

This article presents a series of command-filter-based, finite-time adaptive fuzzy tracking control schemes for fractional-order nonlinear systems (FONSs) subject to input saturation and composite disturbances. A unified design framework is proposed to tackle these issues, combining adaptive fuzzy systems for online uncertainty estimation with novel fractional-order adaptive disturbance observers for robust perturbation approximation. Within this framework, several practical finite-time control schemes are developed, each offering a distinct approach to key design challenges, including finite-time fractional-order filter design, compensation strategies for filter errors, and measures to avoid singularity issues in virtual control law differentiation. The work also includes a review and theoretical comparison with existing methods. The practical finite-time stability of each closed-loop scheme is established via Lyapunov theory, supported by new technical lemmas introduced herein. Finally, numerical simulations are provided to illustrate the effectiveness and relative merits of the proposed control strategies.

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Cite

BibTeXRIS
BibTeX
@article{boulkroune2026tools,
  title = {{New Tools for Finite-Time Fuzzy Control of Fractional-Order Systems: Stability Lemmas, Composite Disturbance Observers, and Singularity-Free Designs}},
  author = {Abdesselem Boulkroune and Naamane Bounar and Farouk Zouari and Asier Ibeas},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100732},
  url = {https://www.mdpi.com/2075-1680/15/10/732},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - New Tools for Finite-Time Fuzzy Control of Fractional-Order Systems: Stability Lemmas, Composite Disturbance Observers, and Singularity-Free Designs
AU  - Abdesselem Boulkroune
AU  - Naamane Bounar
AU  - Farouk Zouari
AU  - Asier Ibeas
PY  - 2026
DA  - 2026/10/01
JO  - Axioms
DO  - 10.3390/axioms15100732
UR  - https://www.mdpi.com/2075-1680/15/10/732
AB  - This article presents a series of command-filter-based, finite-time adaptive fuzzy tracking control schemes for fractional-order nonlinear systems (FONSs) subject to input saturation and composite disturbances. A unified design framework is proposed to tackle these issues, combining adaptive fuzzy systems for online uncertainty estimation with novel fractional-order adaptive disturbance observers for robust perturbation approximation. Within this framework, several practical finite-time control schemes are developed, each offering a distinct approach to key design challenges, including finite-time fractional-order filter design, compensation strategies for filter errors, and measures to avoid singularity issues in virtual control law differentiation. The work also includes a review and theoretical comparison with existing methods. The practical finite-time stability of each closed-loop scheme is established via Lyapunov theory, supported by new technical lemmas introduced herein. Finally, numerical simulations are provided to illustrate the effectiveness and relative merits of the proposed control strategies.
SN  - 2075-1680
ER  -