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 interest in the modeling and control of uncertain systems, such as those met in biotechnological processes. A kernel-based nonparametric estimator is proposed whose almost sure convergence is studied by means of a Lyapunov stabilizability assumption and laws of large numbers for martingales. We then adapt the general result to several classes of deterministic or random functional model uncertainties.