A statistical learning perspective on switched linear system identification

Abstract

Hybrid systems form a particularly rich class of dynamical systems based on the combination of multiple continuous subsystems and a discrete mechanism deciding which one of these is active at a given time. Their identification from input–output data involves nontrivial issues that were partly solved over the last twenty years thanks to numerous approaches. However, despite this effort, estimating the number of modes (or subsystems) of hybrid systems remains a critical and open issue. This paper focuses on switched linear systems and proposes an analysis of their identification based on statistical learning theory. This leads to new theoretically sound bounds on the prediction error of switched models on the one hand, and a practical method for the estimation of the number of modes on the other hand. The latter is inspired by the structural risk minimization principle developed in statistical learning for model selection. The proposed analysis is conducted under various assumptions on the model class and regularization schemes for which new algorithms are presented. Numerical experiments are also provided to illustrate the accuracy of the proposed method.