Adaptive Backstepping Control for a Class of Nonlinear Systems

Tracking control of nonlinear uncertain Chua´s chaotic systems is studied. Based on coordinate transform, the paper deduced the principle with which Chua´s chaotic system can be translated into the so-called general strict-feedback form. Combining the back stepping method with robust control technology, an adaptive parameter control law is developed and thus the output tracking is successfully accomplished for the system with unknown parameters and dynamic uncertainties. It is proved that the derived robust adaptive controller based on Lyapunov stability theory can guarantee that all states of the closed-loop system are globally uniformly ultimately bounded, and lead the system tracking error to a small neighborhood. Finally simulation results are provided to show the effectiveness of the proposed approach.