On nonparametric estimation of nonlinear dynamic systems by the Fourier series estimate

Abstract

The paper deals with estimation of block oriented systems by the Fourier series estimate. Three types of systems are considered: cascade of nonlinear memoryless systems, Hammerstein system and Wiener system. The optimal model of memoryless cascade system is derived and estimated by the Fourier series regression estimate. Nonlinear dynamical systems of Hammerstein and Wiener type with arbitrary nonlinearities are estimated by means of nonparametric techniques. Convergence and the rates of estimation procedures are investigated. Convergence results are verified in computer experiments.