Abstract This article addresses a fixed-time tracking problem of uncertain nonlinear system. Firstly, a sufficient condition for practical fixed-time stability is given. Secondly, on the basis of the sufficient condition, a novel adaptive control strategy is proposed. The designed parameter adaptive law is expressed as a nonlinear differential equation, which is different from the existing adaptive design method. Under the proposed adaptive control scheme, the system performance can be guaranteed in a fixed time, and the upper bound of the settling time is merely affected by the control design parameters, which is independent on the initial states of system. Then, based on the new established inequalities, the fixed-time stability of the closed-loop system is proved. Finally, an example is provided to illustrate the effectiveness of the main result.

中文翻译：

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基于自适应方法的非线性不确定系统的定时控制设计

摘要 本文解决了一个不确定非线性系统的固定时间跟踪问题。首先，给出了实际固定时间稳定的充分条件。其次，在充分条件的基础上，提出了一种新的自适应控制策略。设计的参数自适应律表示为非线性微分方程，不同于现有的自适应设计方法。在提出的自适应控制方案下，系统性能可以在固定时间内得到保证，稳定时间的上限仅受控制设计参数的影响，与系统的初始状态无关。然后，基于新建立的不等式，证明了闭环系统的固定时间稳定性。最后，