Universal prediction of nonlinear systems

We construct a class of elementary nonparametric output predictors of an unknown nonlinear system. Our algorithms predict asymptotically well for every bounded input sequence, every disturbance sequence in certain classes, and every nonlinear system that is bounded, continuous, and asymptotically time-invariant, causal, with decaying memory. The predictor uses only previous input and noisy output data of the system without any knowledge of the structure of the nonlinear system. Under additional smoothness conditions we provide rates of convergence for our scheme. Finally, we apply our results to the special case of stable LTI systems.