Discrete-time zeroing neural network of O(τ4) pattern for online solving time-varying nonlinear optimization problem: Application to manipulator motion generation

In this paper, a new Taylor-type differentiation formula is investigated for the first-order derivative approximation to generate higher numerical accuracy in the implementation of zeroing neural network model discretization. Then, two novel discrete-time zeroing neural network models are first developed, analyzed and verified for online solving time-varying nonlinear optimization problem. Moreover, the 0-stability, consistency and convergence reveal that the developed discrete-time zeroing neural network models converge to the theoretical solution to the time-varying nonlinear optimization problem with the residual error O(tau(4)), where tau signifies the sampling gap. In addition, according to the smooth solution accuracy, the proposed discrete-time zeroing neural network models have better performance than traditional computing models by adopting the Taylor-type computational differentiation formula with O(tau(3)) pattern. Finally, two illustrative numerical examples are further provided to demonstrate the efficiency and superiority of the proposed discrete-time zeroing neural network models for time varying nonlinear optimization problems solving compared with the classical neural network models, furthermore, the proposed models are also applied on two-link mechanical arm with motion generation. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.