Advances in Zeroing Neural Networks: Bio-Inspired Structures, Performance Enhancements, and Applications

Zeroing neural networks (ZNN), as a specialized class of bio-Iinspired neural networks, emulate the adaptive mechanisms of biological systems, allowing for continuous adjustments in response to external variations. Compared to traditional numerical methods and common neural networks (such as gradient-based and recurrent neural networks), this adaptive capability enables the ZNN to rapidly and accurately solve time-varying problems. By leveraging dynamic zeroing error functions, the ZNN exhibits distinct advantages in addressing complex time-varying challenges, including matrix inversion, nonlinear equation solving, and quadratic optimization. This paper provides a comprehensive review of the evolution of ZNN model formulations, with a particular focus on single-integral and double-integral structures. Additionally, we systematically examine existing nonlinear activation functions, which play a crucial role in determining the convergence speed and noise robustness of ZNN models. Finally, we explore the diverse applications of ZNN models across various domains, including robot path planning, motion control, multi-agent coordination, and chaotic system regulation.