Theory, development, and applications of zeroing neural network: a review

The zeroing neural network (ZNN) possesses core characteristics such as a simple architecture and fast response speed. These advantages have earned it widespread research attention and spurred the generation of high-quality outcomes in related studies. This paper presents a comprehensive introduction to ZNN. It begins with an elaboration on the core principles of ZNN, clarifying its underlying operational mechanisms from a theoretical perspective. The evolution of ZNN is discussed, and an in-depth analysis is conducted on continuous-time ZNN (CTZNN) and discrete-time ZNN (DTZNN) respectively. Subsequently, the paper systematically reviews and summarizes ZNN’s application practices in various fields, including mathematical applications, robot control, and image processing. Finally, this paper summarizes the current challenges faced by ZNN, proposes targeted future research directions, and provides new perspectives for researchers to understand and apply ZNN.