Identification of nonlinear state-space systems using zero-input responses

This paper studies the generalization of linear subspace identification techniques to nonlinear systems. The basic idea is to combine nonlinear minimal realization techniques based on the Hankel operator with embedding theory used in time-series modeling. We show that under the assumption of zero-state observability, a collection of several zero-input responses can be used to construct a state sequence of the nonlinear system. This state sequence can then be used to estimate a state-space model via nonlinear regression. We also discuss how the zero-input responses can be obtained. The proposed method is illustrated using a pendulum as an example system