This paper is concerned with functional observer-based finite-time adaptive integral sliding mode control (ISMC) for continuous systems with unknown nonlinear function. First, a novel finite-time ISMC framework is established based on the functional observer whose parameters can be directly found. Second, an adaptive compensator is designed to counteract the effect of the unknown nonlinear function such that the composite integral sliding mode controller ensures that the closed-loop system reaches boundedness in a predefined finite time. Moreover, some sufficient conditions in the form of matrix inequalities are proposed to guarantee the finite-time boundedness with $H_{\infty }$ performance (FTB-$H_{\infty }$) over the sliding phase and the reaching phase of the closed-loop system. Then the FTB-$H_{\infty }$ conditions over the whole finite-time interval are also provided. Due to introducing more degrees of freedom in the functional observer, the designed finite-time integral sliding mode controller is more flexible and less conservative. Finally, a simulation example is given to show the validity of the proposed method.

本文涉及具有未知非线性函数的连续系统的基于功能观测器的有限时间自适应积分滑模控制（ISMC）。首先，基于可直接找到其参数的功能观测器，建立了一个新颖的有限时间ISMC框架。其次，设计了自适应补偿器来抵消未知非线性函数的影响，以使复合积分滑模控制器确保闭环系统在预定的有限时间内达到有界。此外，以矩阵不等式的形式提出了一些充分的条件，以保证有限时间的有界性。$H_{\infty }$ 性能（FTB-$H_{\infty }$）在闭环系统的滑动阶段和到达阶段。然后FTB-$H_{\infty }$还提供了整个有限时间间隔内的条件。由于在功能观测器中引入了更多的自由度，因此设计的有限时间积分滑模控制器更加灵活，不那么保守。最后，通过仿真实例验证了该方法的有效性。