A high order sliding mode control scheme based on adaptive radial basis function neural network

A high order sliding mode control algorithm for uncertain nonlinear systems is presented. This problem can be considered as finite time stabilization of higher order input-output dynamic systems with bounded uncertainties. The algorithm developed is based on the concept of integral sliding mode and includes two steps. One is the controller for nominal system using geometric homogeneity. The other is one compensating for uncertainties utilizing sliding mode control. In addition, to overcome the difficulty in determining the boundaries of uncertainties, the adaptive radial basis function neural network is designed to estimate bounded uncertainties. The proposed procedure ensures establishment of high order sliding mode and provides easy implementation. An illustrative example of a car control shows feasibility of the approach.