As a typical kind of nonlinear system, pendulum systems have drawn attention of numerous researchers for a very long time. This paper focuses mainly on dealing with the discrete-time tracking control problem of both the simple pendulum system and inverted-pendulum-on-a-cart (IPOAC) system. Based on zeroing neural dynamics (ZND), controllers of z2 type are designed respectively for the effective tracking control of the above two pendulum systems. Then, with the aim of possible digital hardware implementation, a 4-node discretization (4ND) formula, which is of square precision in terms of truncation error, is employed to discretize the continuous-time pendulum systems with high precision (i.e., with discretization error being proportional to the cube of the sampling gap). By comparing with Euler-type discretization, simulative results further substantiate the feasibility, accuracy and superiority of the discrete-time control of both the simple pendulum system and IPOAC system with the 4ND formula.

摆系统作为一种典型的非线性系统，在很长一段时间内一直受到众多研究人员的关注。本文主要关注简单摆系统和购物车倒摆系统（IPOAC）的离散时间跟踪控制问题。基于调零神经动力学（ZND），分别设计了z2型控制器，以对上述两个摆系统进行有效的跟踪控制。然后，以可能的数字硬件实现为目标，采用截断误差为平方精度的4节点离散化（4ND）公式对高精度的连续时间摆系统进行离散化（即离散化）。误差与采样间隙的立方成正比）。与Euler型离散化相比，