Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties and nonlinearities. This paper addresses for the first time unknown control coefficients without any known bound, and meanwhile extends system nonlinearities, within the framework of continuous adaptive feedback. The success is typically due to several sets of disparate powers in control design and analysis. Specifically, the nonidentical power-type parameters are introduced in high-gain dynamics, instead of an identical one in the literature, to ensure the stabilizing terms have lower powers than the terms containing uncertainties, enabling finite-time convergence. Thus an adaptive finite-time controller is achieved. New integral-type functions are exploited to make up the important Lyapunov function, which are equipped with different powers to make possible the anticipated performance analysis. The effectiveness of the proposed controller is demonstrated by a simulation example.

有限时间控制具有精确、快速的优点，受到许多对性能要求高的应用的青睐。它的实现需要微妙的处理，例如，具有低阶项和具有负次数的同质性的Lyapunov 方法。然而，可用于有限时间控制的方法是基于对系统不确定性和非线性的一些基本排除和基本限制。本文首次解决了没有任何已知界限的未知控制系数，同时在连续自适应反馈的框架内扩展了系统非线性。成功通常归功于控制设计和分析中的几组不同的权力。具体来说，在高增益动态中引入了不同的功率型参数，而不是文献中的相同参数，确保稳定项的幂低于包含不确定性的项，从而实现有限时间收敛。从而实现自适应有限时间控制器。利用新的积分型函数组成重要的李亚普诺夫函数，这些函数具有不同的幂，使预期的性能分析成为可能。所提出的控制器的有效性通过仿真示例进行了论证。