A general convergence result for kernel-based nonparametric identification of nonlinear stochastic systems

Abstract

In this paper we consider nonparametric identification of nonlinear autoregressive systems with exogenous inputs. Using a kernel function, a general criterion is introduced for estimating the values of the nonlinear function within the system at any fixed point. The criterion function includes the classical kernel based Ll, l > 1 criteria for nonparametric identification as special cases. By transforming the optimization of the criterion function into a root-finding problem, it is proved that the zero point of the root-finding function converges to the optimal value of the criterion function with probability one. A numerical example illustrating the convergence result is also given.