Zhang Neural Network Models and Tables Summarized and Compared for Different Time-Dependent Problems Solving in Addition to DDD (Direct Derivative Dynamics) Method

Zhang neural network (ZNN, also called zeroing neural network) is considered as an effective method to solve time-dependent problems (i.e., time-varying problems). Different continuous-time ZNN models of various time-dependent problems solving are obtained by exploiting the ZNN design formula. Before applying on digital equipment, the acquired continuous-time ZNN models are generally discretized by using Zhang time discretization (ZTD) formula. To provide readers with the choice of various ZNN models and different ZTD formulas for time-dependent problems solving, this paper summarizes ZNN models and ZTD formulas, and presents them in tables. Specifically, four categories and seventeen subcategories of time-dependent problems are summarized and presented after studying related literatures. In addition, ZTD formulas from the 2-instant ZTD through the 10-instant ZTD formula are also summarized and compared in a table. With the direct derivative dynamics (DDD) method as a special situation, this paper also introduces the process of solving time-dependent problems with the ZNN method, especially the time-dependent matrix problem.