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Uniformly Continuous Generalized Sliding Mode Control

Author

Listed:
  • Aldo Jonathan Muñoz-Vázquez

    (Department of Multidisciplinary Engineering, Texas A&M University, McAllen, TX 78504, USA
    These authors contributed equally to this work.
    Current address: Higher Education Center at McAllen, 6200 Tres Lagos Blv, McAllen, TX 78504, USA.)

  • Guillermo Fernández-Anaya

    (Department of Physics and Mathematics, Universidad Iberoamericana, Mexico City 01219, Mexico
    These authors contributed equally to this work.)

Abstract

This paper explores a general class of singular kernels with the objective of designing new families of uniformly continuous sliding mode controllers. The proposed controller results from filtering a discontinuous switching function by means of a Sonine integral, producing a uniformly continuous control signal, preserving finite-time sliding motion and robustness against continuous but unknown and not necessarily integer-order differentiable disturbances. The principle of dynamic memory resetting is considered to demonstrate finite-time stability. A set of sufficient conditions to design singular kernels, preserving the above characteristics, is presented, and several examples are exposed to propose new families of continuous sliding mode approaches. Simulation results are studied to illustrate the feasibility of some of the proposed schemes.

Suggested Citation

  • Aldo Jonathan Muñoz-Vázquez & Guillermo Fernández-Anaya, 2024. "Uniformly Continuous Generalized Sliding Mode Control," Mathematics, MDPI, vol. 12(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2536-:d:1457996
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    References listed on IDEAS

    as
    1. Yuri Luchko, 2021. "General Fractional Integrals and Derivatives with the Sonine Kernels," Mathematics, MDPI, vol. 9(6), pages 1-17, March.
    2. A.J. Muñoz-Vázquez & V. Parra-Vega & A. Sánchez-Orta, 2017. "A novel continuous fractional sliding mode control," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2901-2908, October.
    Full references (including those not matched with items on IDEAS)

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