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Improved finite-time zeroing neural networks for time-varying complex Sylvester equation solving

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  • Xiao, Lin
  • Yi, Qian
  • Zuo, Qiuyue
  • He, Yongjun

Abstract

There are two equivalent methods for dealing with the nonlinearity of complex-valued problems. The first method is to handle the real part and imaginary part of complex inputs, and the second method is to handle the modulus of complex inputs. Based on these two methods, this paper explores a superior nonlinear activation function and proposes two improved finite-time zeroing neural network (IFTZNN) models for time-varying complex Sylvester equation solving. Regarding the existing neural model activated by the sign-bi-power (SBP) activation function, the convergence upper bounds of the IFTZNN models are much smaller, and thus we can estimate their convergence time more accurately. Furthermore, the detailed theoretical analysis of the IFTZNN models is provided to show their effectiveness. Comparative simulation results also verify the advantages of our proposed IFTZNN models for complex Sylvester equation solving.

Suggested Citation

  • Xiao, Lin & Yi, Qian & Zuo, Qiuyue & He, Yongjun, 2020. "Improved finite-time zeroing neural networks for time-varying complex Sylvester equation solving," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 246-258.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:246-258
    DOI: 10.1016/j.matcom.2020.06.014
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    References listed on IDEAS

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    1. Zhou, Tiejun & Wang, Min & Li, Chen, 2015. "Almost periodic solution for multidirectional associative memory neural network with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 52-60.
    2. Cao, Yang & Samidurai, R. & Sriraman, R., 2019. "Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 57-77.
    3. Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    4. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
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    Cited by:

    1. Zhu, Jingcan & Jin, Jie & Chen, Weijie & Gong, Jianqiang, 2022. "A combined power activation function based convergent factor-variable ZNN model for solving dynamic matrix inversion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 291-307.
    2. Jin, Jie & Chen, Weijie & Qiu, Lixin & Zhu, Jingcan & Liu, Haiyan, 2023. "A noise tolerant parameter-variable zeroing neural network and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 482-498.
    3. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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