Taylor O(h^) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators

• Published in: IEEE transaction on neural networks and learning systems Vol. 27; no. 2; pp. 225 - 237
• Main Authors: Liao, Bolin, Zhang, Yunong, Jin, Long
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2016
• Subjects: Analytical models; Computational accuracy; Computational modeling; discrete-time Zhang neural network (ZNN); Discretization; Dynamic programming; Dynamical systems; Dynamics; equality constraint; Iterative methods; Mathematical model; Mathematical models; Neural networks; numerical differentiation; Numerical models; online dynamic quadratic programming; Quadratic programming; Sampling; numerical differentiation; equality constraint; Computational accuracy; discrete-time Zhang neural network (ZNN); online dynamic quadratic programming
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2015.2435014

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylortype discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discretetime ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h 3 ), O(h 2 ), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.