In this work, we introduce an adaptive neural network controller for a class
of nonlinear systems. The approach uses two Radial Basis Functions, RBF
networks. The first RBF network is used to approximate the ideal control law
which cannot be implemented since the dynamics of the system are unknown. The
second RBF network is used for on-line estimating the control gain which is a
nonlinear and unknown function of the states. The updating laws for the
combined estimator and controller are derived through Lyapunov analysis.
Asymptotic stability is established with the tracking errors converging to a
neighborhood of the origin. Finally, the proposed method is applied to
control and stabilize the inverted pendulum system.
Stability robustness to unstructured uncertainty for nonlinear systems under feedback linearization