High-Order Sliding Mode Control Design Subject to Unknown Nonvanishing Uncertainties
针对一类具有非消失不确定性的非线性系统，提出一种无需已知不确定性上界的高阶滑模控制方法，通过引入低阶虚拟积分动力学重构系统，并基于Lyapunov理论设计控制律，保证闭环系统有限时间收敛，在Buck变换器系统中验证了有效性。
In this article, a high-order sliding mode control (SMC) method is proposed for a class of nonlinear systems with nonvanishing uncertainties. Unlike most methods, which treat the upper bound of disturbances and their time derivatives as known or unknown, the proposed approach does not require an upper bound for nonvanishing uncertainties. Moreover, these uncertainties and their time derivatives are usually time-invariant, such as the exogenous time-varying disturbances of unknown magnitude and the modeling uncertainties of unknown system parameters. First, a low-order virtual integral dynamics is introduced such that the system dynamics are reconstructed. Second, based on the introduced integral dynamics, an SMC law incorporating correction terms is designed using Lyapunov theory to handle the various disturbances with an unknown upper bound. Finally, the finite-time convergence of the closed-loop system is guaranteed, and the effectiveness of the method is verified by the application of the Buck converter system.