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A stability criterion for discrete-time fractional-order echo state network and its application

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Abstract

In this paper, combining the theory of numerical solution of fractional-order differential equation, a new model of discrete-time fractional-order echo state network (DFO-ESN) is proposed. In order to ensure that the DFO-ESN can be used for different learning tasks, the stability of DFO-ESN should be guaranteed. Through using an LMI approach, a sufficient stability criterion for DFO-ESN is given. According to the stability criterion, the selection range of reservoir parameters of DFO-ESN can be expanded, such that we can build the DFO-ESN without considering the initial conditions. For the candidate discrete-time Lyapunov function, it is shown that the reservoir states of DFO-ESN are asymptotically stable when time tends to infinity. Finally, two examples demonstrate the feasibility of stability criterion and the learning performance of DFO-ESN.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61473070 and Grant 61627809 and in part by Fundamental Research Funds for the State Key Laboratory of Synthetical Automation for Process Industries (SAPI) under Grant 2018ZCX22 and Liaoning Revitalization Talents Program under Grant XLYC1802010.

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Xianshuang Yao, Zhanshan Wang & Zhanjun Huang

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  1. Xianshuang Yao
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  2. Zhanshan Wang
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  3. Zhanjun Huang
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Correspondence to Zhanshan Wang.

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The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Yao, X., Wang, Z. & Huang, Z. A stability criterion for discrete-time fractional-order echo state network and its application. Soft Comput 25, 4823–4831 (2021). https://doi.org/10.1007/s00500-020-05489-0

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