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 algorithms predict asymptotically well for every bounded input sequence, every disturbance sequence in certain classes, and every linear or nonlinear system that is continuous and asymptotically time-invariant, causal, and with fading memory. The predictor is based on k_n-nearest neighbor estimators from nonparametric 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 smoothness conditions the authors provide rates of convergence for the time-average errors of their scheme. Finally, they apply their results to the special case of stable linear time-invariant (LTI) systems.