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Predefined-time convergence in fractional-order systems

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  • Muñoz-Vázquez, Aldo Jonathan
  • Sánchez-Torres, Juan Diego
  • Defoort, Michael
  • Boulaaras, Salah

Abstract

The contribution of this paper is the design of a novel controller that enforces predefined-time convergence in fractional-order systems, which are defined by means of the Caputo derivative, whose order lays between zero and one. The controller is based on a dynamic extension, which induces an integer-order reaching phase, such that, the solution of the closed-loop system turns out to converge to the origin before a predefined fixed-time. The resulting controller is continuous and still able to face a large class of continuous but not necessarily differentiable disturbances. It is worth to remark that, the proposed controller does not include any term that depends on the initial conditions of the system, and that it is well-defined for any time. Numerical tests show the reliability of the proposed scheme.

Suggested Citation

  • Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Defoort, Michael & Boulaaras, Salah, 2021. "Predefined-time convergence in fractional-order systems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309620
    DOI: 10.1016/j.chaos.2020.110571
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    References listed on IDEAS

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    Cited by:

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    2. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Martínez-Fuentes, Oscar & Díaz-Muñoz, Jonathan Daniel & Muñoz-Vázquez, Aldo Jonathan & Tlelo-Cuautle, Esteban & Fernández-Anaya, Guillermo & Cruz-Vega, Israel, 2024. "Family of controllers for predefined-time synchronization of Lorenz-type systems and the Raspberry Pi-based implementation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. ZOUARI, Farouk & IBEAS, Asier & BOULKROUNE, Abdesselem & CAO, Jinde & AREFI, Mohammad Mehdi, 2021. "Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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