Zeroing Neural Dynamics and Models for Various Time-Varying Problems Solving with ZLSF Models as Minimization-Type and Euler-Type Special Cases [Research Frontier]

Zeroing neural dynamics (ZND), a special class of neural dynamics, is a powerful methodology for time-varying problems solving. On the basis of this methodology, different continuous-time ZND models are obtained for various time-varying problems solving. Continuous-time ZND models are supposed to be discretized for the sake of prevalent digital-equipment applications, and a discretization formula is needed to transform a continuous-time ZND model into a discrete-time ZND model. In this article, continuous-time ZND models, new discretization formulas and various discrete-time ZND models are presented. The time-varying minimization problem, which is a representative time-varying issue, is also discussed as an example throughout this article. The relationship between ZND and Zhao-Lu-Swamy-Feng (ZLSF) models is identified; i.e., the ZLSF models are minimization-type and Euler-type special cases of ZND models. In addition, ZND models are compared with other models to demonstrate their differences. The article aims to introduce the ZND methodology and illustrate the manner by which it is used, provide readers with new discretization formulas and various continuous-time and discrete-time ZND models for time-varying problems solving, discuss the factors affecting the performance of the aforementioned models, exemplify the differences between ZND models and other models, and point out future research directions.