Adaptive control for a class of second-order nonlinear systems with unknown input nonlinearities

An adaptive controller is developed for a class of second-order nonlinear dynamic systems with input nonlinearities using artificial neural networks (ANNs). The unknown input nonlinearities are continuous and monotone and satisfy a sector constraint. In contrast to conventional Lyapunov-based design techniques, an alternative Lyapunov function, which depends on both system states and control input variable, is used for the development of a control law and a learning algorithm. The proposed adaptive controller guarantees the stability of the closed-loop system and convergence of the output tracking error to an adjustable neighborhood of the origin.