Nonparametric identification of controlled nonlinear time varying processes

We are interested in the identification of an unknown time varying additive component of a controlled nonlinear autoregressive model, a problem of int erest in the modeling and control of uncertain systems, such as those met i n biotechnological processes. A kernel-based nonparametric estimator is pro posed whose almost sure convergence is studied by means of a Lyapunov stabi lizability assumption and laws of large numbers for martingales. We then ad apt the general result to several classes of deterministic or random functi onal model uncertainties.