Neural network approximation for periodically disturbed functions and applications to control design

This paper addresses the approximation problem of functions affected by unknown periodically time-varying disturbances. By combining Fourier series expansion into multilayer neural network or radial basis function neural network, we successfully construct two kinds of novel approximators, and prove that over a compact set, the new approximators can approximate a continuously and periodically disturbed function to arbitrary accuracy. Then, we apply the proposed approximators to disturbance rejection in the first-order nonlinear control systems with periodically time-varying disturbances, but it is straightforward to extend the proposed design methods to higher-order systems by using adaptive backstepping technique. A simulation example is provided to illustrate the effectiveness of control schemes designed in this paper.