Higher order adaptive sliding mode control for a class of SISO systems

A higher order sliding mode control with self-tuning law algorithm is proposed for a class of uncertain nonlinear systems. This problem can be viewed as the finite time stabilization of a higher order dynamic system with unknown but bounded system uncertainties. An adaptation tuning approach without high frequency switching is developed based on geometric homogeneity and sliding mode control. The stability of proposed procedure is proven by using the Lyapunov theory and guarantees robustness against uncertainties. The upper bounds of uncertainties are not required to be known in advance. An illustrative example demonstrates the advantages of the strategy.