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Sliding mode control: A survey with applications in math

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  • Pisano, Alessandro
  • Usai, Elio

Abstract

The paper presents a brief survey on Variable Structure Control Systems with Sliding Modes. Starting from a general case of sliding modes in dynamical systems with discontinuous right-hand side, classic approaches to sliding mode control systems are considered and some basic results about the control of uncertain systems are given. Then, Higher-Order Sliding Modes are presented as a tool to remove discontinuity from the control action, to deal with higher relative degree systems and to improve the accuracy of the real sliding mode behavior when the discrete time implementation is considered.

Suggested Citation

  • Pisano, Alessandro & Usai, Elio, 2011. "Sliding mode control: A survey with applications in math," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 954-979.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:5:p:954-979
    DOI: 10.1016/j.matcom.2010.10.003
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    Cited by:

    1. Mobayen, Saleh & Majd, Vahid Johari & Sojoodi, Mahdi, 2012. "An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 1-10.
    2. Hollweg, Guilherme Vieira & Evald, Paulo Jefferson Dias de Oliveira & Milbradt, Deise Maria Cirolini & Tambara, Rodrigo Varella & Gründling, Hilton Abílio, 2022. "Design of continuous-time model reference adaptive and super-twisting sliding mode controller," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 215-238.
    3. Pierluigi Colli & Gianni Gilardi & Jürgen Sprekels, 2016. "Constrained Evolution for a Quasilinear Parabolic Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 713-734, September.
    4. Zhang, Ziyu & Yang, Xinsong & Lam, Hak-Keung & Xiang, Zhengrong, 2024. "Event-triggered control for switched systems with sensor faults via adaptive fuzzy observer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 244-259.
    5. Mohamed, Guermouche & Sofiane, Ahmed Ali & Nicolas, Langlois, 2018. "Adaptive super twisting extended state observer based sliding mode control for diesel engine air path subject to matched and unmatched disturbance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 111-130.
    6. Fu, Dongyang & Si, Yang & Wang, Difeng & Xiong, Yizhen, 2024. "An accelerated neural dynamics model for solving dynamic nonlinear optimization problem and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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