A Nonlinear Subspace Identification Algorithm with Positive Definite Kernels

Abstract

Subspace identification is a paradigm for estimating the parameters of dynamical systems by geometric operations on subspaces spanned by the column or row vectors of certain block Hankel matrices formed by input and output data. In this paper, we develop a theoretical underpinning for generalization of the predictor-based subspace identification method to nonlinear with reproducing kernel Hilbert spaces (RKHSs). As well known in the machine learning community, a stochastic process generate an unique congruent reproducing kernel Hilbert space. Based on this relationship, we derive a subspace identification method which gives an optimal prediction on the RKHS generated by given data sequences.