Nonlinear system identification by affine coordinate unification of locally identified MIMO linear systems

Abstract

In this study, an identification method of a state-space model, which describes the quasi-steady behavior of a multi-input-multi-output (MIMO) nonlinear system, is investigated. At several steady points, local linear statespace models with input and output offsets are identified by a subspace identification method. We propose a state-space unification method of the identified local linear models, where an affine transformation is introduced for each pair of adjacent local systems. The affine transformations are chosen by using similarities of the system expressions. The matrices and offsets of the affine transformations are uniquely calculated by the least-squares method. Our method considers the change of steady points by the offset terms in the affine transformations. By the transformations, a linear parameter-varying system model with bias terms is obtained. The parameter is determined by the value of the unified state, and therefore we can finally obtain a nonlinear dynamical model, which is valid around the equilibria set. A numerical simulation is shown for confirming an availability of this method.