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Improved zeroing neural networks for finite time solving nonlinear equations

  • Emerging Trends of Applied Neural Computation - E_TRAINCO
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Abstract

Nonlinear equation is an important cornerstone of nonlinear science, and many practical problems in scientific and engineering fields can be described by nonlinear equation in mathematics. In this paper, improved zeroing neural network (IZNN) models are presented and investigated for finding the solutions of the time-invariant nonlinear equation (TINE) and time-varying nonlinear equation (TVNE) in predictable and finite time. Compared with the exponential convergence zeroing neural network (ZNN), the convergence time of the IZNN models is finite and able to be estimated; in addition, the IZNN model is more stable and reliable for solving high-order TVNE. Both of the theoretical and numerical simulation results of the ZNN and IZNN for finding the solutions of the TINE and TVNE are presented to demonstrate the superiority and effectiveness of the IZNN model.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for providing valuable comments which helped in improving this manuscript. This work was supported by the National Natural Science Foundation of China [No.61561022,61404049 and U1501253]; Scientific Research Fund of Education Department of Hunan Province [No.17B094].

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Authors and Affiliations

  1. School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China

    Jie Jin, Lv Zhao, Mu Li & Zaifang Xi

  2. College of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, 410114, China

    Fei Yu

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  1. Jie Jin
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  2. Lv Zhao
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  3. Mu Li
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  4. Fei Yu
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Correspondence to Jie Jin.

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Jin, J., Zhao, L., Li, M. et al. Improved zeroing neural networks for finite time solving nonlinear equations. Neural Comput & Applic 32, 4151–4160 (2020). https://doi.org/10.1007/s00521-019-04622-x

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