New Framework for Identifying Discrete-Time Switched Linear Systems

Abstract

This paper addresses the problem of offline identification of a particular class of hybrid dynamical systems that are discrete-time switched linear state space models. The identification process is carried out from data previously sampled from the system. Unlike most existing methods that prioritize identifying the switching instants first, a new framework is proposed in which the local models are identified first, and the task of identifying the switching instants is performed later. The methodology involves the iterative calculation of discrete and continuous models' a posteriori probability density function using subspace identification, clustering, data classification, and hybrid stochastic filtering methods. This strategy allows grouping the data most likely to have been generated by the same submodels, thus allowing the estimation of these local models. An essential feature of the algorithm is that the matrices of the different submodels are identified with the same state-space basis allowing them to be evaluated and, if necessary, combined. The performance of the identification procedure is evaluated through numerical examples, and a comparison with a prior method described in the literature is conducted.