Nonlinear dynamical systems cover an immensely wide range of real-life situations. However, it is often the case that a priori structure information of the unknown system is not available. Thus, nonparametric identification is necessary for data-driven identification of nonlinear systems. In the first part of this talk, we present a recursive local linear estimator for nonparametric identification of nonlinear autoregressive systems with exogenous inputs. The strong consistency and the asymptotical mean square error properties of the recursive local linear estimator are established, and its application to an additive nonlinear system is discussed. The recursive local linear estimator provides recursive estimates not only for the function values but also their gradients at fixed points. In the second part of this talk, we present a data-driven method for identification of high-dimensional additive nonlinear dynamical systems with little a priori information. In particular, we develop a two-step method for variable selection to determine contributing additive functions and to remove non-contributing ones from the underlying nonlinear system. At the first step, we estimate each additive function by kernel-based nonparametric identification approaches without suffering from the curse of dimensionality. At the second step, we utilize a nonnegative garrote estimator to identify which additive functions are nonzero by use of the obtained nonparametric estimates of each function. We show that the proposed variable selection method can find the correct variables with probability one under weak conditions.
