Fuzzy adaptive backstepping sliding mode control of the cart-pendulum system

A novel adaptive backstepping sliding mode control (ABSMC) law with fuzzy monitoring strategy is proposed for the tracking control of a cart-pendulum system. The proposed ABSMC scheme combining the sliding mode control and the backstepping technique, ensure that the occurrence of the sliding motion in finite time and the trajectory of the tracking error converge to equilibrium point. Furthermore, we introduce fuzzy monitoring strategy to approximate the unknown nonlinear functions of the system model and moreover to approximate the switching control term of the sliding control in order to resolve the chattering problem. The convergence and stability of the proposed control scheme are proved using Lyapunov´s method. Finally many simulation results for the cart-Pendulum system are given to illustrate the good tracking performances.