High-Order Sliding Mode Control Design Subject to Unknown Nonvanishing Uncertainties

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.