This paper seeks to address the problem of finite-time stabilization for a class of uncertain Hamiltonian systems via sliding mode control approach. A novel sliding function in connection with the state and energy function of the considered system is constructed, and then, a suitable controller is designed to drive the state trajectories onto the specified sliding surface before the given finite-time. Moreover, the finite-time boundedness of the closed-loop system over both reaching phase and sliding motion phase are analyzed and the corresponding conditions are obtained. Furthermore, two optimization problems are formed to enhance the performance of finite-time boundedness, which will be solved via genetic optimization algorithm. Finally, a simulation example is provided to illustrate the proposed control strategy.

本文试图通过滑模控制方法解决一类不确定的哈密顿系统的有限时间稳定问题。构造了与所考虑系统的状态和能量函数相关的新颖滑动函数，然后设计了一个合适的控制器，以在给定的有限时间之前将状态轨迹驱动到指定的滑动表面上。此外，分析了闭环系统在到达阶段和滑动阶段的有限时间有界性，并得到了相应的条件。此外，形成了两个优化问题以提高有限时间有界性的性能，这将通过遗传优化算法解决。最后，提供了一个仿真示例来说明所提出的控制策略。