Adaptive Second-Order Sliding Mode Controller Design Subject to Mismatched Uncertainties

In this article, a novel adaptive second-order sliding mode (ASOSM) control law is constructed for a general category of sliding mode control (SMC) systems with mismatched uncertainties, including a nonvanishing external disturbance. This innovative control design proposal is accomplished through three key mechanisms. First, the new sliding mode dynamics subject to mismatched uncertainties is derived by selecting the appropriate sliding variables, which can significantly increase the uncertainties existing in the control input channel and relax the strict requirement on the relative degree assumption of the sliding variable. Second, a novel ASOSM controller, which contains some adaptive parameters generated via a three-layer nested adaptive mechanism, is constructed by utilizing the modified adding power integrator (API) approach and the adaptive control technique. Third, the practical finite-time stability of the closed-loop sliding mode system is confirmed by means of the systematic Lyapunov stability theory. The technical advancement of the developed adaptive control scheme lies in its ability to effectively deal with a more general sliding mode dynamics containing multiple uncertainties and guarantee that the practical second-order sliding mode (SOSM) is established in a finite time. Finally, simulation results, incorporating a practical application case, are provided to illustrate the effectiveness of the designed adaptive control scheme.