Abstract: In order to solve the problem that the conventional nonsingular fast terminal sliding mode (NFTSM) control converges slower than classical terminal sliding mode (TSM) control. A novel NFTSM is proposed for nonlinear uncertain systems and faster convergence rate is achieved especially in the neighbor of equilibrium points in comparison with the classical TSM control. Then, a novel NFTSM control with adaptive boundary layer is proposed so as to make systematic variables converge to a residual set in finite time. Furthermore, the application of adaptive boundary layers achieves higher precision and stronger robustness. The stability of closed loop systems is confirmed by Lyapunov theory. Finally, the simulation results verify that higher control precision and superior systematic robustness can be obtained simultaneously by the proposed approach for nonlinear uncertain systems.

Key words: Nonsingular fast terminal sliding mode, residual set, adaptive, boundary layer, nonlinear uncertain system

摘要： 针对传统非奇异快速终端滑模在平衡点附近收敛速率比经典终端滑模收敛速率慢的问题，提出了一种非线性不确定系统改进型非奇异快速终端滑模，在平衡点附近获得比经典终端滑模更快的收敛速率。其次，设计了一种自适应边界层非奇异快速终端滑模算法, 使系统状态能有限时间收敛到一个剩余集。自适应边界层的应用进一步提高了系统控制精度，改善了系统鲁棒性。同时，根据Lyapunov理论证明系统的闭环稳定性。最后，通过Matlab仿真表明，对非线性不确定系统，该算法能大大提高系统的控制精度，改善系统鲁棒性。

关键词: 非奇异快速终端滑模, 剩余集, 自适应, 边界层, 非线性不确定系统