Robust and adaptive non-homogeneous higher order sliding mode control for a class of uncertain nonlinear systems

An adaptive non-homogeneous higher order sliding mode control (HOSMC) method for a class of uncertain nonlinear systems is proposed in this paper. The HOSMC problem can be viewed as the finite time stabilization of a higher order input-output dynamic system with bounded uncertainties. Given a large initial tracking error, the proposed HOSMC algorithm provide fast convergence rate by using non-homogeneous finite time stabilization. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of bounds needed in the conventional design. To solve the overestimation problem, equivalent control technique is used in this paper, and then the switching gain can be designed as a small constant. Numerical simulation on an omnidirectional mobile vehicle demonstrates the effectiveness of the proposed HOSMC algorithm.