Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators

The design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered. The Lyapunov synthesis approach is used to develop state-feedback adaptive control schemes based on a general class of nonlinearly parametrized on-line approximation models. The key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher-order terms of the on-line approximator (with respect to the network weights) satisfy certain bounding conditions. An adaptive bounding design is used to show that the overall neural control system guarantees semi-global uniform ultimate boundedness within a neighbourhood of zero tracking error. The theoretical results are illustrated through a simulation example.