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FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law

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  • Ávalos-Ruiz, L.F.
  • Zúñiga-Aguilar, C.J.
  • Gómez-Aguilar, J.F.
  • Escobar-Jiménez, R.F.
  • Romero-Ugalde, H.M.

Abstract

This paper presents the simulation and control implementation on a Field Programmable Gate Array (FPGA) for a class of variable-order fractional chaotic systems by using sliding mode control strategy. Four different fractional variable-order chaotic systems via Atangana–Baleanu–Caputo fractional-order derivative were considered; Dadras, Aizawa, Thomas and 4 Wings attractors. A methodology has been developed to construct variable-order fractional chaotic systems using LabVIEW® software for its implementation in the National Instruments myRio-1900 (Xilinx FPGA Z-7010)® device. The variable-order fractional differential equations and the control law were solved using the variable-order Adams algorithm. Finally, simulation results show that FPGA provides high-speed realizations with the desired accuracy and demonstrate the effectiveness of the proposed sliding mode control.

Suggested Citation

  • Ávalos-Ruiz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2018. "FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 177-189.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:177-189
    DOI: 10.1016/j.chaos.2018.08.021
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    Cited by:

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    2. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    3. Balamurali Ramakrishnan & Victor Kamdoum Tamba & Hayder Natiq & Alex Stephane Kemnang Tsafack & Anitha Karthikeyan, 2022. "Dynamical analysis of autonomous Josephson junction jerk oscillator with cosine interference term embedded in FPGA and investigation of its collective behavior in a network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-12, September.
    4. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Minati, Ludovico & Frasca, Mattia & Valdes-Sosa, Pedro A. & Barbot, Jean-Pierre & Letellier, Christophe, 2023. "Flatness-based real-time control of experimental analog chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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