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Fractional order neural networks for system identification

Author

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  • Zuñiga Aguilar, C.J.
  • Gómez-Aguilar, J.F.
  • Alvarado-Martínez, V.M.
  • Romero-Ugalde, H.M.

Abstract

Neural networks and fractional order calculus have shown to be powerful tools for system identification. In this paper we combine both approaches to propose a fractional order neural network (FONN) for system identification. The learning algorithm was generalized considering the Grünwald-Letnikov fractional derivative. This new black box modeling approach is validated by the identification of three different systems (two benchmark systems and a real system). Comparisons vs others approaches showed that the proposed FONN model reached better accuracy with less number of parameters.

Suggested Citation

  • Zuñiga Aguilar, C.J. & Gómez-Aguilar, J.F. & Alvarado-Martínez, V.M. & Romero-Ugalde, H.M., 2020. "Fractional order neural networks for system identification," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s096007791930390x
    DOI: 10.1016/j.chaos.2019.109444
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    1. Pan, Shing-Tai & Lai, Chih-Chin, 2008. "Identification of chaotic systems by neural network with hybrid learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 233-244.
    2. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    3. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    4. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
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    3. Qiu, Hongling & Cao, Jinde & Liu, Heng, 2023. "Passivity of fractional-order coupled neural networks with interval uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 845-860.
    4. Rui Luo & Zhinan Peng & Jiangping Hu, 2023. "On Model Identification Based Optimal Control and It’s Applications to Multi-Agent Learning and Control," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
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    6. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    7. Hashemi, M.S. & Inc, Mustafa & Yusuf, Abdullahi, 2020. "On three-dimensional variable order time fractional chaotic system with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    8. Jayaraman Venkatesh & Alexander N. Pchelintsev & Anitha Karthikeyan & Fatemeh Parastesh & Sajad Jafari, 2023. "A Fractional-Order Memristive Two-Neuron-Based Hopfield Neuron Network: Dynamical Analysis and Application for Image Encryption," Mathematics, MDPI, vol. 11(21), pages 1-17, October.
    9. M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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