Adaptive Neural Control for Pure-feedback Nonlinear Systems

An adaptive neural control problem of SISO fully nonaffine pure-feedback nonlinear system is considered in this paper. The main contribution of the proposed method is that it is shown that the control problem of the pure-feedback system can be viewed as that of the system in the standard normal form. As a result, proposed neural control algorithm is much simpler compared to the recently proposed backstepping-based neural controllers. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate lumped uncertain nonlinearity in the controlled system. It is shown that the Lyapunov stabilities of the NN weights and filtered tracking error are guaranteed in the semi-global sense.