Adaptive neural network control for nonlinear uncertain systems with high-frequency disturbances

In this work, we deal with a class of uncertain nonlinear plants along with external high-frequency disturbances. A novel controller structure consisting of two neural networks (NNs) and a low-pass filter is proposed. One NN is utilized to approximate an ideal control law and the other one to approximate the derivative of the output of the former NN. The smoothness of the control signal is guaranteed by implementing the low-pass filter. Moreover, the oscillation-like phenomena in traditional NN controllers are largely mitigated. Subsequently, the online learning algorithms of the NNs are presented without the need of a priori knowledge of the system dynamics. The tracking error is proven to be semi-global uniformly ultimately bounded (UUB) and the bound can be made arbitrarily small. Meanwhile, all other signals of the closed-loop system are bounded. Simulation results illustrate the performance of our controller and validate the theoretical outcome.