Identification of hybrid linear time-invariant systems via subspace embedding and segmentation (SES)

This paper considers the offline identification of hybrid linear time-invariant (LTI) systems that are based on state-space models. This includes the identification of the number of LTI systems involved, the orders of the systems, and the switching times. By embedding the input/output data in a higher dimensional space, the problem of finding the switching times of the hybrid system becomes one of segmenting the data into distinct subspaces. Since these subspaces correspond to the original linear systems, their number and dimension must be found automatically. We examine and compare two different embedding methods. One is based on the well-known subspace method and the other is based on a direct input/output relationship. A robust and deterministic generalized principal component analysis (GPCA) algorithm is presented to solve the multiple-subspace identification problem. In addition, we show that data from near the switching points corresponds to points outside the subspaces under the embedding, and are thus readily identified by the GPCA algorithm. Although the resulting algorithm is purely algebraic, it is numerically robust and can tolerate moderate amounts of noise. Extensive simulations and experiments are presented to demonstrate the performance of the proposed algorithm and methods.