Adaptive Control for a Class of Unknown Nonlinear Systems Without Using Function Approximators

This paper is concerned with the problem of universal control for a class of second order nonlinear systems with unknown dynamics. Without utilizing function approximators, a universal adaptive control scheme is developed via backstepping approach, where the system nonlinearities are adaptively compensated at each step. Based on Lyapunov stability theory, it is proven that, for any initial system condition, all the resulting closed loop signals are globally uniformly ultimately bounded. Finally, simulation results are presented to validate the effectiveness of the proposed design method.