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Real-Time Implementation of a Neural Integrator Backstepping Control via Recurrent Wavelet First Order Neural Network

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Abstract

Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time–frequency plane. The Gaussian, the Mexican hat, and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using continuous wavelet transform. Continuous wavelets are favoured when a high temporal resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of a recurrent high-order neural network model, a novel wavelet neural network structure, here called recurrent wavelet first-order neural network, is proposed in order to achieve a better identification of the behavior of dynamic systems. The effectiveness of our proposal is explored through the design of a centralized neural integrator backstepping control scheme for a two degree-of-freedom robot manipulator evolving in the vertical plane. The performance of the overall neural identification and control scheme is verified through numerical simulation using the mathematical model for a benchmark prototype. Moreover, real-time results validate the effectiveness of our proposal when using a robotic arm, of our own design, powered by industrial servomotors.

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Acknowledgements

This work was supported by CONACYT, México, and by TecNM Projects. Alma Y. Alanis thanks the support of CONACYT-SEP, México, through project CB-256769.

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Authors and Affiliations

  1. División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Blvd. Revolución y Av. INSTITUTO TECNOLÓGICO de La Laguna, Col. Centro, C.P. 27000, Torreón, Coahuila de Zaragoza, México

    Luis A. Vázquez & Francisco Jurado

  2. Centro Universitario de los Lagos, Universidad de Guadalajara, Av. Enrique Díaz de León no. 1144, Col. Paseos de la Montaña C.P., 47460, Lagos de Moreno, Jalisco, México

    Carlos E. Castañeda

  3. Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd. Marcelino García Barragán No. 1421, C.P. 44430, Guadalajara, Jalisco, México

    Alma Y. Alanis

Authors
  1. Luis A. Vázquez
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  2. Francisco Jurado
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  3. Carlos E. Castañeda
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  4. Alma Y. Alanis
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Correspondence to Carlos E. Castañeda.

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Vázquez, L.A., Jurado, F., Castañeda, C.E. et al. Real-Time Implementation of a Neural Integrator Backstepping Control via Recurrent Wavelet First Order Neural Network. Neural Process Lett 49, 1629–1648 (2019). https://doi.org/10.1007/s11063-018-9893-6

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