In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

在这篇论文中，鲁棒的有限时间跟踪问题针对的是一类完全平方的非线性系统，它受到扰动和不确定性的影响。首先，推导了两个适用的引理，并通过应用这些引理定义了新颖的非线性滑动表面（流形）。其次，通过开发非奇异终端滑模控制，设计了两种不同类型的鲁棒非线性控制输入，以满足并实现上述有限时间跟踪目标。通过分析和数学评估闭环非线性系统的全局有限时间稳定性。拟议的控制输入用于解决两个有趣的问题，其中包括（a）：统一混沌系统的有限时间跟踪问题，以及（b）：两个不同的超混沌系统的有限时间同步。最后，基于MATLAB软件，进行了两个数值模拟，以说明和证明所提出的鲁棒有限时非线性控制方案的有效性和性能。