This study investigates an adaptive chattering-free sliding-mode control method for n-order nonlinear systems with unknown external disturbances and uncertain models. The proposed method takes the advantage of finite-time fast convergence to avoid singularity problem and ensure its robustness against system uncertainty and unknown disturbance. To achieve fast convergence from any initial condition to system origin, a full-order terminal sliding-mode controller containing differential terms is proposed based on the property of n-order nonlinear systems. Then the continuous and smooth actual control law is obtained by integrating the differential control law containing the discontinuous sign function to realize chattering free. Meanwhile, instead of evaluating the fixed upper bound of system uncertainty and interference in practical implementations, an adaptive method is utilized for its unknown upper bound estimation. The convergence of the adaptive terminal sliding-mode controller in finite time is verified based on Lyapunov stability theory. Finally, two simulation results demonstrate the effectiveness of the proposed control method.

中文翻译：

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具有未知扰动和模型不确定性的全阶非线性系统的自适应无颤动终端滑模控制

本研究研究了一种用于未知外部扰动和不确定模型的 n 阶非线性系统的自适应无颤动滑模控制方法。所提出的方法利用有限时间快速收敛的优点来避免奇异性问题，并确保其对系统不确定性和未知扰动的鲁棒性。为了实现从任何初始条件到系统原点的快速收敛，基于n阶非线性系统的性质，提出了一种包含微分项的全阶终端滑模控制器。然后对包含不连续符号函数的微分控制律进行积分，得到连续平滑的实际控制律，实现无颤振。同时，与其在实际实现中评估系统不确定性和干扰的固定上限，一种自适应方法被用于其未知的上限估计。基于Lyapunov稳定性理论验证了自适应终端滑模控制器在有限时间内的收敛性。最后，两个仿真结果证明了所提出的控制方法的有效性。