Robustifying nonlinear systems using high-order neural network controllers

A robust control methodology for affine control of nonlinear dynamical systems is developed in this paper. A correction control signal is added to a nominal controller (designed to guarantee a desired performance for the corresponding nominal system), to render the actual system uniformly and ultimately bounded. The control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and/or optimal weight values. Simulations performed on a simple nonlinear system illustrate the approach.