Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems

A fast self-adapting high-order sliding mode (FSH-OSM) controller is designed for a class of nonlinear systems with unknown uncertainties. As for uncertainty-free nonlinear system, a new switching condition is introduced into the standard geometric homogeneity. Different from the existing geometric homogeneity method, both state variables and their derivatives are considered to bring a reasonable effective switching condition. As a result, a faster convergence rate of state variables is achieved. Furthermore, based on the integral sliding mode (ISM) and above geometric homogeneity, a self-adapting high-order sliding mode (HOSM) control law is proposed for a class of nonlinear systems with uncertainties. The resulting controller allows the closed-loop system to conduct with the expected properties of strong robustness and fast convergence. Stable analysis of the nonlinear system is also proved based on the Lyapunov approach. The effectiveness of the resulting controller is verified by several simulation results.