General Square-Pattern Discretization Formulas via Second-Order Derivative Elimination for Zeroing Neural Network Illustrated by Future Optimization

Previous works provide a few effective discretization formulas for zeroing neural network (ZNN), of which the precision is a square pattern. However, those formulas are separately developed via many relatively blind attempts. In this paper, general square-pattern discretization (SPD) formulas are proposed for ZNN via the idea of the second-order derivative elimination. All existing SPD formulas in previous works are included in the framework of the general SPD formulas. The connections and differences of various general formulas are also discussed. Furthermore, the general SPD formulas are used to solve future optimization under linear equality constraints, and the corresponding general discrete ZNN models are proposed. General discrete ZNN models have at least one parameter to adjust, thereby determining their zero stability. Thus, the parameter domains are obtained by restricting zero stability. Finally, numerous comparative numerical experiments, including the motion control of a PUMA560 robot manipulator, are provided to substantiate theoretical results and their superiority to conventional Euler formula.