Zhang Yunong, Ling Yihong, Yang Min, Yang Song, Zhang Zhijun
IEEE Trans Neural Netw Learn Syst. 2021 Jun;32(6):2663-2675. doi: 10.1109/TNNLS.2020.3007509. Epub 2021 Jun 2.
Time-varying matrix pseudoinverse (TVMP) problem has been investigated by many researchers in recent years, but a new class of matrix termed Zhang matrix has been found and not been handled by some conventional models, e.g., Getz-Marsden dynamic model. On the other way, future matrix pseudoinverse (FMP), as a more challenging and intractable discrete-time problem, deserves more attention due to its significant role-playing on some engineering applications, such as redundant manipulator. Based on the zeroing neural network (ZNN), this article concentrates on designing new discrete ZNN models appropriately for computing the FMPs of all matrices of full rank, including the Zhang matrix. First, an inverse-free continuous ZNN model for computing TVMP is derived. Subsequently, Zhang et al. discretization (ZeaD) formulas and equidistant extrapolation formulas are used to discretize the continuous ZNN model to two discrete ZNN models for computing FMPs with different truncation errors. The numerical experiments are conducted for the five conventional discrete models and two new discrete ZNN models. Distinct numerical results substantiate the effectiveness and choiceness of newly proposed models. Finally, one of the newly proposed models is implemented on simulating and physical instances of robot manipulators, respectively, to show its practicability.
近年来，时变矩阵伪逆（TVMP）问题受到了许多研究人员的关注，但一类新的矩阵——张矩阵已被发现，一些传统模型，如Getz - Marsden动态模型，并未对其进行处理。另一方面，未来矩阵伪逆（FMP）作为一个更具挑战性和难以处理的离散时间问题，因其在一些工程应用，如冗余机械手等方面发挥的重要作用，值得更多关注。基于归零神经网络（ZNN），本文专注于设计合适的新型离散ZNN模型，以计算包括张矩阵在内的所有满秩矩阵的FMP。首先，推导了一个用于计算TVMP的无逆连续ZNN模型。随后，利用张等人的离散化（ZeaD）公式和等距外推公式，将连续ZNN模型离散化为两个具有不同截断误差的用于计算FMP的离散ZNN模型。对五个传统离散模型和两个新型离散ZNN模型进行了数值实验。不同的数值结果证实了新提出模型的有效性和优良性。最后，将新提出的模型之一分别应用于机器人机械手的仿真和物理实例，以展示其实用性。
