Taylor O(h3) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators
Taylor O(h3) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators
复制标题
用于动态等式约束二次规划的 ZNN 模型的泰勒 O(h(3)) 离散化及其在机械臂中的应用
DOI：
10.1109/tnnls.2015.2435014
复制
发表时间：
2016-02-01
影响因子：
10.4
通讯作者：
Jin, Long
中科院分区：
文献类型：
--
作者：
Liao, Bolin;Zhang, Yunong;Jin, Long
本文首次提出了一种新的泰勒型数值微分公式，将连续时间张氏神经网络（ZNN）离散化，获得了更高的计算精度。基于泰勒型公式，泰勒型离散时间ZNN模型（称为泰勒型离散时间ZNNK和泰勒型离散时间ZNNU模型），然后提出和讨论执行在线动态等式约束二次规划。为了比较，欧拉型离散时间ZNN模型（称为欧拉型离散时间ZNNK和欧拉型离散时间ZNNU模型）和牛顿迭代，有趣的链接被发现，也提出。本文证明了泰勒型离散时间ZNN模型、欧拉型离散时间ZNN模型和牛顿迭代的稳态残差分别具有O（h（3））、O（h（2））和O（h）的模式，h表示采样间隙。数值实验，包括应用实例，其中的结果进一步证实了理论研究结果和泰勒型离散时间ZNN模型的有效性。最后，通过与Taylor型离散时间导数模型和其他Lagrange型离散时间ZNN模型求解动态等式约束二次规划问题的比较，再次验证了本文提出的Taylor型离散时间ZNN模型的优越性.
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 Taylor-type 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 discrete-time 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.