The Lanczos Algorithm for Model Order Reduction of Nonlinear Systems

This paper considers the problem of model order reduction of nonlinear affine systems by using Krylov subspace projection. The nonlinear affine system is described with the concepts of differential geometry. The main properties of such systems are shown and the tools for reachability and observability analysis are provided. The main features of the Krylov subspace projection methods are presented and the extension of these methods in the nonlinear case are developed. The presented method uses the concept of nonlinear reachability and observability distributions and implements the Gram-Schmidt orthogonalization procedure on the members of these distributions. The main difference with the linear methods is that the orthogonalization procedure is implemented directly on the distribution elements, while in the linear case the orthogonalization is performed iteratively by using the system matrices. The performance of the presented method is demonstrated by numerical examples.