Observer-based direct adaptive neural control for a class of nonlinear non-affine systems with unknown control direction

This paper presents a direct adaptive neural controller for a class of SISO non-affine nonlinear systems. Based on the implicit function theorem, the existence of an ideal controller is proved, and neural network is employed to approximate the unknown ideal controller. Since all the states may not be available for measurements, an observer is designed to estimate the states of the system. In this method a priori knowledge about the sign of control gain are not required. To deal with the unknown sign of the control direction, the Nussbaum-type function is used. In this approach, to reduce the effect of external disturbances and approximation errors, a robustifying term is utilized. Stability of the closed-loop system is proved by Lyapunov method. The effectiveness of the adaptive neural control method is demonstrated by a simulation example.