A survey on zeroing neural dynamics: models, theories, and applications

Extensive research has been conducted in dynamic mathematical problems and real-time industrial control applications, leading to the emergence of zeroing neural dynamics (ZND) as a significant approach. This approach is guided by the fluctuating tendency of state errors, and a link is established between the stability of the zero solution in the neurodynamic system and the convergence of neuron states in a zeroing neural network. Over the last two decades, considerable efforts have been made by numerous scholars to advance the development of ZND, resulting in the formation of a series of ZND models for various mathematical issues and real-world applications. In this paper, the advances in ZND are synthesised from three aspects: models, theories, and applications. Specifically, ZND models are categorised into two main frameworks based on their structures and further classified into different types depending on the dynamics of the specific models under each framework. The two main frameworks identified are the foundational ZND framework and the integral ZND framework. The former serves as the basic structure for exponential type ZND, finite-time type ZND, fixed-time type ZND, and predefined-time type ZND, while the latter is extended with the single-integral type ZND and the double-integral type ZND. Furthermore, the primary analytical methods for the dynamics of each type of ZND are summarised, and the current applications of ZND, including robot manipulator control, multi-agent consistency, dynamic positioning, chaos synchronisation, and image processing, are introduced. Through this survey, a comprehensive understanding of the development history of ZND research, the current research focuses and challenges in ZND models, theories, and applications, as well as future directions and key breakthroughs in ZND research, will be provided to readers.