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A flexible-predefined-time convergence and noise-suppression ZNN for solving time-variant Sylvester equation and its application to robotic arm

Author

Listed:
  • Zheng, Boyu
  • Han, Zhiyong
  • Li, Chunquan
  • Zhang, Zhijun
  • Yu, Junzhi
  • Liu, Peter X.

Abstract

Although the zeroing neural network (ZNN) has strong competitiveness in solving the time-varying Sylvester equation (TVSE), its convergence and robustness as two key indicators still need to be further improved. To address these problems, we propose a flexible-predefined-time convergence and noise-suppression ZNN (FPCNS-ZNN). Different from most existing ZNN variants, the proposed FPCNS-ZNN provides the following three new improvements: (1) In FPCNS-ZNN, a new specially designed time-variant-gain (SD-TVG) is proposed to better improve the convergence speed at each stage of iterative computation. (2) In FPCNS-ZNN, a new flexible nonlinear activation function (FN-AF) is proposed to flexibly control the convergence speed and predefine convergence time with certain robustness. (3) SD-TVG and FN-AF are dexterously combined to construct the new FPCNS-ZNN, which can obtain faster convergence speed and stronger robustness. Through detailed theoretical analysis and mathematical derivation, the proposed FPCNS-ZNN model has been confirmed to have promising stability, flexible-predefined-time, and strong robustness. It should be noted that the predefined-time upper bound of the proposed FPCNS-ZNN is accurately calculated by dexterously using the Beta function. Computer simulations and comparative experiments indicate that the proposed FPCNS-ZNN has faster convergence speed and stronger robustness compared with three state-of-the-art ZNN variants. Finally, the proposed FPCNS-ZNN is used to solve the motion planning problem of the robotic arm, and the experiment results illustrate the utility of the model.

Suggested Citation

  • Zheng, Boyu & Han, Zhiyong & Li, Chunquan & Zhang, Zhijun & Yu, Junzhi & Liu, Peter X., 2024. "A flexible-predefined-time convergence and noise-suppression ZNN for solving time-variant Sylvester equation and its application to robotic arm," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923011876
    DOI: 10.1016/j.chaos.2023.114285
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    References listed on IDEAS

    as
    1. Wang, Guancheng & Li, Qinrou & Liu, Shaoqing & Xiao, Hua & Zhang, Bob, 2022. "New zeroing neural network with finite-time convergence for dynamic complex-value linear equation and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Xiao, Lin & Li, Linju & Cao, Penglin & He, Yongjun, 2023. "A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. 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.
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