This paper presents a review of finite- and fixed-time convergent algorithms for dynamic systems of various dimensions and relative degrees, with or without disturbances. The review mainly focuses on finite- and fixed-time convergent algorithms, which provide explicit and easily computable upper estimates for the corresponding convergence times. The finite- and fixed-time convergent algorithms are classified according to their actions and structural properties: regulators, observers (differentiators), controllers; discontinuous and continuous, non-smooth and smooth, non-adaptive and adaptive. Some fixed-time convergent algorithms are illustrated by simulation examples displaying typical time histories of the state/estimate trajectories in each case.

本文介绍了具有各种扰动或无扰动的各种尺寸和相对程度的动态系统的有限时间和固定时间收敛算法。这篇综述主要集中在有限时间和固定时间收敛算法上，这些算法为相应的收敛时间提供了明确且易于计算的上限估计。有限时间和固定时间收敛算法根据其作用和结构特性进行分类：调节器，观察者（微分器），控制器；不连续和连续，非平滑和平滑，非自适应和自适应。通过仿真示例说明了一些固定时间收敛算法，这些示例显示了每种情况下状态/估计轨迹的典型时间历史。