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<p>As the optimization demands of dynamic systems grow increasingly complex, traditional static optimization methods face significant challenges in addressing time-varying parameters, nonlinear constraints, and high-dimensional uncertainties. For instance, gradient descent algorithms often become trapped in local optima in high-noise environments. Zeroing Neural Networks (ZNN), a dynamic solver grounded in differential equation theory, achieve real-time tracking and high-precision solutions for time-varying optimization problems by constructing evolution equations for error functions. By combining the mathematical structure of dynamic systems with the adaptive features of neural computation, ZNN overcomes the slow convergence of conventional recurrent networks and improves robustness and real-time performance through noise-tolerant designs and efficient discretization. This paper provides a systematic and accessible review of recent advances in ZNN across a range of problems, including time-varying quadratic programming, quaternion least squares, redundant manipulator trajectory planning, and other nonlinear and linear optimization tasks. Furthermore, ZNN addresses the noise sensitivity of traditional methods in time-varying matrix inversion through dynamic error functions (e.g. exponential convergence mechanisms), variable gain adjustment strategies, and integral enhancement techniques, demonstrating exceptional adaptability in fields such as robotic control and high-frequency trading. Despite its outstanding performance across multiple problem types, ZNN still faces limitations in global convergence analysis for non-convex optimization, computational complexity control in ultra-high-dimensional problems, and energy efficiency optimization for hardware deployment. Future research should integrate non-smooth optimization theory, in-memory computing hardware architectures, and adaptive dynamic activation functions to push theoretical boundaries and advance ZNN’s deep applications in real-time decision-making, autonomous system optimization, intelligent manufacturing, and multimodal information fusion.</p>

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A review of research progress and multi-field applications of Zeroing neural networks in optimization problems

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Lu Wang,
  • Yun Huang

摘要

As the optimization demands of dynamic systems grow increasingly complex, traditional static optimization methods face significant challenges in addressing time-varying parameters, nonlinear constraints, and high-dimensional uncertainties. For instance, gradient descent algorithms often become trapped in local optima in high-noise environments. Zeroing Neural Networks (ZNN), a dynamic solver grounded in differential equation theory, achieve real-time tracking and high-precision solutions for time-varying optimization problems by constructing evolution equations for error functions. By combining the mathematical structure of dynamic systems with the adaptive features of neural computation, ZNN overcomes the slow convergence of conventional recurrent networks and improves robustness and real-time performance through noise-tolerant designs and efficient discretization. This paper provides a systematic and accessible review of recent advances in ZNN across a range of problems, including time-varying quadratic programming, quaternion least squares, redundant manipulator trajectory planning, and other nonlinear and linear optimization tasks. Furthermore, ZNN addresses the noise sensitivity of traditional methods in time-varying matrix inversion through dynamic error functions (e.g. exponential convergence mechanisms), variable gain adjustment strategies, and integral enhancement techniques, demonstrating exceptional adaptability in fields such as robotic control and high-frequency trading. Despite its outstanding performance across multiple problem types, ZNN still faces limitations in global convergence analysis for non-convex optimization, computational complexity control in ultra-high-dimensional problems, and energy efficiency optimization for hardware deployment. Future research should integrate non-smooth optimization theory, in-memory computing hardware architectures, and adaptive dynamic activation functions to push theoretical boundaries and advance ZNN’s deep applications in real-time decision-making, autonomous system optimization, intelligent manufacturing, and multimodal information fusion.