Yang Min, Zhang Yunong, Tan Ning, Mao Mingzhi, Hu Haifeng
IEEE Trans Cybern. 2022 Aug;52(8):8366-8375. doi: 10.1109/TCYB.2021.3051035. Epub 2022 Jul 19.
Differing from the common linear matrix equation, the future different-level linear matrix system is considered, which is much more interesting and challenging. Because of its complicated structure and future-computation characteristic, traditional methods for static and same-level systems may not be effective on this occasion. For solving this difficult future different-level linear matrix system, the continuous different-level linear matrix system is first considered. On the basis of the zeroing neural network (ZNN), the physical mathematical equivalency is thus proposed, which is called ZNN equivalency (ZE), and it is compared with the traditional concept of mathematical equivalence. Then, on the basis of ZE, the continuous-time synthesis (CTS) model is further developed. To satisfy the future-computation requirement of the future different-level linear matrix system, the 7-instant discrete-time synthesis (DTS) model is further attained by utilizing the high-precision 7-instant Zhang et al. discretization (ZeaD) formula. For a comparison, three different DTS models using three conventional ZeaD formulas are also presented. Meanwhile, the efficacy of the 7-instant DTS model is testified by the theoretical analyses. Finally, experimental results verify the brilliant performance of the 7-instant DTS model in solving the future different-level linear matrix system.
与常见的线性矩阵方程不同，本文考虑了未来不同层级的线性矩阵系统，该系统更具趣味性和挑战性。由于其结构复杂且具有未来计算特性，传统的静态和同层级系统方法在此情况下可能无效。为解决这一困难的未来不同层级线性矩阵系统，首先考虑连续不同层级线性矩阵系统。基于归零神经网络（ZNN），提出了物理数学等效性，称为ZNN等效性（ZE），并将其与传统的数学等效概念进行比较。然后，基于ZE，进一步开发了连续时间合成（CTS）模型。为满足未来不同层级线性矩阵系统的未来计算要求，利用高精度的7点张等人离散化（ZeaD）公式进一步获得了7点离散时间合成（DTS）模型。为作比较，还给出了使用三种传统ZeaD公式的三种不同DTS模型。同时，通过理论分析验证了7点DTS模型的有效性。最后，实验结果验证了7点DTS模型在解决未来不同层级线性矩阵系统方面的出色性能。
