This paper proposes a novel fast terminal sliding mode (FTSM) control scheme, which accelerates convergence of the controlled system both in its approaching and after reaching the sliding manifold. The novelty lies in the design of time-varying sliding surface without a priori knowledge of the initial system states, so achieving insensitivity to the uncertainty of the initial states. Based on this, we design a corresponding FTSM control strategy, where the singularity problem of conventional terminal sliding mode (TSM) control systems is overcome by restricting the TSM surfaces to non-singular areas. We prove stability and finite-time convergence of the system with the proposed controller. Furthermore, we extend the proposed FTSM control scheme to high-order systems and discuss its application in practical systems. Preliminary simulation results and comparative studies demonstrate the validity of the proposed FTSM control scheme with the designed sliding surface.

本文提出了一种新颖的快速终端滑模 (FTSM) 控制方案，该方案在接近和到达滑动流形之后加速了受控系统的收敛。新颖之处在于时变滑动面的设计没有初始系统状态的先验知识，因此对初始状态的不确定性不敏感。基于此，我们设计了相应的 FTSM 控制策略，通过将 TSM 表面限制为非奇异区域来克服传统终端滑模 (TSM) 控制系统的奇异性问题。我们用所提出的控制器证明了系统的稳定性和有限时间收敛性。此外，我们将所提出的 FTSM 控制方案扩展到高阶系统并讨论其在实际系统中的应用。