Nonparametric output prediction for nonlinear fading memory systems

The authors construct a class of elementary nonparametric output predictors of an unknown discrete-time nonlinear fading memory system, Their algorith ms predict asymptotically well for every bounded input sequence, every dist urbance sequence in certain classes, and every linear or nonlinear system t hat is continuous and asymptotically time-invariant, causal, and with fadin g memory, The predictor is based on k(n)-nearest neighbor estimators from n onparametric statistics. It uses only previous input and noisy output data of the system without any knowledge of the structure of the unknown system, the bounds on the input, or the properties of noise, Under additional smoo thness conditions the authors provide rates of convergence for the time-ave rage errors of their scheme. Finally, they apply their results to the speci al case of stable linear time-invariant (LTI) systems.