Unified Solution of Different-Kind Future Matrix Equations Using New Nine-Instant Discretization Formula and Zeroing Neural Dynamics
本文提出一种基于九步离散公式和归零神经动力学的统一求解模型，用于处理未来视角下的时变矩阵方程，包括Lyapunov方程、矩阵求逆等，并通过机器人运动生成等数值实验验证其有效性。
In this article, time-varying matrix equation problems, including the Lyapunov equation, matrix inversion, and generalized matrix inversion are investigated in a future (or say, discrete time-varying) perspective. Then, in order to develop a unified solution model for the above three future problems, a future matrix equation (FME) is investigated. The discrete-time unified solution (DTUS) model, which is based on the zeroing neural dynamics (ZND) method and a new nine-instant Zhang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> discretization (ZeaD) formula, is thus proposed and termed the nine-instant DTUS (9IDTUS) model. Meanwhile, theoretical analyses on the stability and precision of the 9IDTUS model are provided. In addition, conventional DTUS models obtained from the Euler forward formula, Taylor–Zhang discretization formula, and a seven-instant discretization formula are also presented for comparisons. Furthermore, numerical experiments including the robot motion generation, are conducted and analyzed to substantiate the efficacy and superiority of the proposed 9IDTUS model.