Milne–Hamming Method With Zeroing Neural Network for Time-Varying Nonlinear Optimization and Redundant Manipulator Application

Continuous zeroing neural network (ZNN) and its discrete ZNN (DZNN) are comprehensively developed in many optimization systems. In this article, a Milne-Hamming method with DZNN classified as an implicit method is proposed and discussed upon the previous researches. Specifically, the Milne-Hamming discrete ZNN (MHDZNN) model is aimed for time-varying nonlinear optimization (TV-NO) problem with functional limitations. This Milne-Hamming (MH) method is a four-step discretized formula with fixed parameters and is introduced to discretize the ZNN model. Theoretical analyses of the MHDZNN model derive that MHDZNN possesses a larger stepsize domain $\mu \in (0,1/2)$ of absolute stability. Its convergent error is of order $O(\tau ^{5})$ and the corresponding truncation error constant is $1/40$ , which shows intimate relation to the accuracy. Compared with the existing DZNN models such as four-step explicit methods with the same $O(\tau ^{5})$ pattern, the convergent error constant of MHDZNN is smaller by a factor and maximal stability domain is greater. Finally, numerical simulations and application to redundant manipulators are provided and studied to verify the effectiveness of the proposed MHDZNN model.