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ELM with guaranteed performance for online approximation of dynamical systems

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Abstract

This paper presents an adaptive identification approach based on extreme learning machine (ELM), single hidden layer feedfoward neural networks, high-order neural networks (HONN), and adaptive control theory. Drawing on Lyapunov-like analysis employing Barbalat’s Lemma, the designed identifiers ensure the boundedness of all associated approximation errors and convergence of the residual state error, even in the presence of disturbances and unknown dynamics. Two cases are considered: a standard topology and a modified ELM with high-order regressor. Both with enhanced identification model and learning algorithms. Extensive simulations, to verify the theoretical results, and a comparative study, to show the performance of the proposed schemes, are performed. Simulation results depict that the HONN architecture combined with the ELM technique offers significant advantages over the standard one, insofar as faster training and lower computational burden are considered.

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Authors and Affiliations

  1. Banco Central do Brasil, SBS Quadra 3 Bl. B - Ed. Sede, Braslia, DF, CEP 70074-900, Brazil

    Emerson Grzeidak

  2. Departamento de Engenharia Elétrica, Universidade de Brasília, Braslia, DF, CEP 70910-900, Brazil

    José A. R. Vargas

  3. Departamento de Engenharia Mecânica, Universidade de Brasília, Braslia, DF CEP, 70910-900, Brazil

    Sadek C. A. Alfaro

Authors
  1. Emerson Grzeidak
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  2. José A. R. Vargas
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  3. Sadek C. A. Alfaro
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Correspondence to Emerson Grzeidak.

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Grzeidak, E., Vargas, J.A.R. & Alfaro, S.C.A. ELM with guaranteed performance for online approximation of dynamical systems. Nonlinear Dyn 91, 1587–1603 (2018). https://doi.org/10.1007/s11071-017-3966-3

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  • DOI: https://doi.org/10.1007/s11071-017-3966-3

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