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Fractional neural observer design for a class of nonlinear fractional chaotic systems

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Abstract

In this paper, a novel observer structure for nonlinear fractional-order systems is presented to estimate the states of fractional-order nonlinear chaotic system with unknown dynamical model. A new fractional error back-propagation learning algorithm is derived to adapt weights of the artificial neural network, by taking advantage of the Lyapunov stability strategy of fractional-order systems which is called Miattag–Leffler stability. The main contribution is the extension of neural observer for fractional dynamics in a way that satisfies Miattag–Leffler conditions. Observer design procedure guarantees the convergence of observer error to the neighborhood of zero. Furthermore, the robustness of the proposed estimator against uncertainties and external disturbances are the main benefits of the proposed method. Simulation results show the effectiveness and capabilities of the proposed observer.

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Authors and Affiliations

  1. Department of Engineering, University of Qom, Qom, Iran

    Amin Sharafian & Reza Ghasemi

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  1. Amin Sharafian
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  2. Reza Ghasemi
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Correspondence to Reza Ghasemi.

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The authors declare that they have no conflict of interest.

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All the authors of the manuscript declared that there is no research involving human participants and/or animal and material that required informed consent.

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Sharafian, A., Ghasemi, R. Fractional neural observer design for a class of nonlinear fractional chaotic systems. Neural Comput & Applic 31, 1201–1213 (2019). https://doi.org/10.1007/s00521-017-3153-y

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