In this paper, the finite-time control problem for a class of double integrator systems under state constraints is investigated. Different from the traditional finite-time control methods with constant gains, an improved finite-time controller with state-dependent gains is designed. The main challenges lie in the finite-time stability analysis of the resultant closed-loop system caused by state-dependent control gains and how to make the system states keep in the constrained region. Based on the homogeneous system theory, the finite-time stability of the closed-loop system under state constraints is proved. In addition to the finite-time convergence, it is also shown that the states of the system always are kept in the constrained region. Finally, the developed finite-time controller is applied to buck converter and the validity of the proposed method is verified through a DC–DC buck converter under voltage and current constraints.

本文研究了一类状态约束下的双积分系统的有限时间控制问题。与传统的具有恒定增益的有限时间控制方法不同，设计了一种改进的具有状态相关增益的有限时间控制器。主要挑战在于由状态相关控制增益引起的合成闭环系统的有限时间稳定性分析以及如何使系统状态保持在约束区域内。基于齐次系统理论，证明了闭环系统在状态约束下的有限时间稳定性。除了有限时间收敛外，还表明系统的状态始终保持在约束区域内。最后，