AI 中文总结
本文利用简谐运动等时性建立精确预设时间控制框架，提出李雅普诺夫分析方法实现标量系统镇定，扩展出非奇异滑模控制律，仿真验证了方法有效性。
AI 中文摘要
本文研究精确预设时间控制的稳定性分析与非奇异滑模镇定问题。利用简谐运动的等时性，本文建立了一种新颖的精确预设时间控制框架。首先，提出了一种用于精确预设时间控制的新颖李雅普诺夫分析方法，基于该方法实现了标量系统的精确预设时间镇定，从理论上证明对于任意非零初始条件，收敛时间精确等于预设时间。接着，将该框架扩展为一种新颖的滑模控制律，该控制律即使在存在外部扰动的情况下，也能保证几乎所有初始条件下的精确预设时间收敛，值得注意的是，所提出的控制律在整个状态空间均为非奇异，且增益保持一致有界。最后，仿真结果验证了所提方法的有效性。
英文摘要
This paper investigates the problems of stability analysis and nonsingular sliding mode stabilization for exact prescribed-time control. By exploiting the isochronism of simple harmonic motion, this paper establishes a novel exact prescribed-time control framework. First, a novel Lyapunov analysis method for exact prescribed-time control is proposed, based on which the exact prescribed-time stabilization of scalar systems is achieved. It is theoretically established that for arbitrary non-zero initial conditions, the settling time is exactly equal to the prescribed time. Next, the framework is extended to a novel sliding mode control law. It guarantees exact prescribed-time convergence for almost all initial conditions even in the presence of external disturbances. Notably, the proposed control law is nonsingular across the entire state space and maintains uniformly bounded gains. Finally, simulation results validate the effectiveness of the proposed methods.
