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Design and analysis of a variable-parameter noise-tolerant ZNN for solving time-variant nonlinear equations and applications

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Abstract

Solvers considering time-varying parameters are more suitable for addressing a variety of time-varying problems, whereas traditional fixed-parameter neural networks are somewhat insufficient for efficiently and quickly solving these problems. Many existing zeroing neural networks ensure rapid convergence using the infinite-valued AFs. For solving time-varying nonlinear equations, this paper proposes a finitely-activated variable parameter noise tolerant zeroing neural network (VPNTZNN), applied to trajectory tracking of redundant robotic arms. The designed variable parameters are error-dependent, enabling adaptive adjustment to optimal values as errors fluctuate, thereby ensuring faster convergence of the proposed VPNTZNN. And the constructed variable parameters and activation functions (AFs) do not escalate infinitely over time. Affected by the above variable parameters, the proposed finitely-activated VPNTZNN achieves rapid finite-time convergence with strong noise suppression. Simulation results validate the effectiveness of our method in solving time-variant nonlinear equations and in trajectory tracking of redundant manipulators. Moreover, this approach employs a finite-valued activation function to design a variable-parameter neural network, thereby avoiding the difficulties of practical implementation.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos 62073291 and 62233016.

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Authors and Affiliations

  1. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

    Yu Zhang, Liming Wang & Guomin Zhong

Authors
  1. Yu Zhang
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  2. Liming Wang
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  3. Guomin Zhong
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Contributions

Yu Zhang: Conceptualization, Methodology, Formal analysis, Software, Writing-original draft, Writing-review & editing. Liming Wang: Data curation, Formal analysis, Investigation, Writing-original draft. Guomin Zhong: Conceptualization, Methodology, Supervision, Formal analysis, Writing-review & editing.

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Correspondence to Guomin Zhong.

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Zhang, Y., Wang, L. & Zhong, G. Design and analysis of a variable-parameter noise-tolerant ZNN for solving time-variant nonlinear equations and applications. Appl Intell 55, 460 (2025). https://doi.org/10.1007/s10489-025-06304-9

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  • DOI: https://doi.org/10.1007/s10489-025-06304-9

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