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<p>This paper develops two adaptive zeroing neural network models for efficiently solving time-varying generalized Sylvester equations, key problems in control theory and signal processing. Each model combines (i) a novel dynamic adaptive coefficient that balances speed and robustness online and (ii) variable-exponent activation functions that reshape nonlinearity based on real-time errors. We prove global asymptotic stability and fixed-time convergence under bounded noise, with convergence time independent of initial conditions. Numerical experiments confirm these properties, and applications in robotic trajectory tracking and image denoising demonstrate their potential to improve real-time performance in dynamic systems.</p>

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Efficient zeroing neural networks with dynamic adaptive coefficient and variable-exponent activation for time-varying generalized Sylvester equations

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Jiangchuan Zhao,
  • Yanjun Zhang

摘要

This paper develops two adaptive zeroing neural network models for efficiently solving time-varying generalized Sylvester equations, key problems in control theory and signal processing. Each model combines (i) a novel dynamic adaptive coefficient that balances speed and robustness online and (ii) variable-exponent activation functions that reshape nonlinearity based on real-time errors. We prove global asymptotic stability and fixed-time convergence under bounded noise, with convergence time independent of initial conditions. Numerical experiments confirm these properties, and applications in robotic trajectory tracking and image denoising demonstrate their potential to improve real-time performance in dynamic systems.