Adaptive Control for a Class of Pure-Feedback Nonlinear Systems with Prespecified Tracking Accuracy

A new adaptive control method is designed for a class of pure-feedback nonlinear systems with prespecified tracking accuracy. The system functions of pure-feedback nonlinear systems are allowed to be semi-bounded and continuous. As for the system functions and complicated differential terms, some compact sets are constructed to obtain their bounds on these sets. Therefore, with the help of these bounds, the complicated functions of system are tackled very well without using approximators, and the “explosion of complexity” inherently in backstepping-based methods are perfectly avoided without using any filters. Furthermore, it is proved that the designed method can guarantee the boundedness of all the closed-loop system signals and the convergence of the tracking error to arbitrarily prespecified small neighborhood of the origin. Finally, simulation results are given to show the validity of the method.