Nonlinear output regulation based on RBF neural network approximation

The regulator equations arising from the nonlinear output regulation problem are a set of mixed partial differential and algebraic equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. In this paper, an approximation method based on a class of radial basis function (RBF) neural networks was investigated for solving the regulator equations. It is shown that the RBF neural networks can solve the regulator equations up to a prescribed arbitrarily small error, and this small error can be translated into a guaranteed steady-state tracking error for the closed-loop system. Simulation studies, which are conducted to compare with MNN method, show that the RBF NN method has good properties such as rapid training speed and overcoming local minimal value.