Identification of polynomial nonlinear systems based on center manifold

Abstract

A center-manifold (CM) based system identification (SID) method is developed to identify multi-input-multi-output continuous-time polynomial nonlinear systems in the state–space form. On one hand, the CM method is a natural extension of the frequency-domain subspace method to nonlinear SID problems. It decomposes the nonlinear SID problem into a series of linear least-square problems (in a precise sense), which can be solved analytically. This is in contrast to many existing methods that rely on iterative search of the global minimum. On the other hand, it is also a generalization of the invariant-subspace (ISP) based SID method. It inherits the nice property of the ISP method that the advantages of time-domain and frequency-domain SID methods are combined. In the paper, a persistence of excitation (PE) condition for the CM method is derived, which is described by the rank of certain Khatri–Rao product. Under the PE condition, the identification error is shown to be bounded within an arbitrarily small neighborhood of the origin when measurement noise is presented.