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A projection recurrent neural network based sliding mode control to stabilize unknown fractional-order chaotic systems

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Abstract

In this paper, a new approach based on Projection Recurrent Neural Network (PRNN) and Discrete-time Sliding Mode Control (DTSMC) has been proposed to stabilize Fractional-order Chaotic Systems with uncertain fractional-order. The main idea is to describe the FOLS as a linear regression where the unknown parameters vector includes the terms dependent on the fractional order. Constrained Quadratic Programming (CQP) has been introduced to minimize the difference between the FOLS and its regression description, in which the fractional orders are considered as optimization variables. According to the optimality conditions for the CQP, the PRNN as a numerical optimizer has been extended. The exponential reaching laws are used to obtain the control signals of DTSMC. The estimated fractional order is simultaneously applied to the controller. The asymptotic stability of the optimizer, as well as the robustness of the proposed algorithm against the uncertainty in the fractional order, have been evaluated.

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  1. Department of Electrical Engineering, Imam Khomeini International University, Qazvin, Iran

    Abbas Kariminia & Hassan Zarabadipour

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  1. Abbas Kariminia
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Kariminia, A., Zarabadipour, H. A projection recurrent neural network based sliding mode control to stabilize unknown fractional-order chaotic systems. Int. J. Dynam. Control 11, 1736–1750 (2023). https://doi.org/10.1007/s40435-022-01072-7

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