Structural Risk Minimization for Switched System Identification

This paper deals with the identification of hybrid dynamical systems that switch arbitrarily between modes. In particular, we focus on the critical issue of estimating the number of modes. A novel method inspired by model selection techniques in statistical learning is proposed. Specifically, the method implements the structural risk minimization principle, which relies on the minimization of an upper bound on the expected prediction error of the model. This so-called generalization error bound is first derived for static switched systems using Rademacher complexities. Then, it is extended to handle non independent observations from a single trajectory of a dynamical system. Finally, it is further tailored to the needs of model selection via a uniformization step. An illustrative example of the behavior of the method and its ability to recover the true number of modes is presented.