Multi-input/multi-output switched-linear system identification from input–output data

Abstract

In this paper, we propose a scheme to identify discrete-time, multi-input/multi-output switched-linear systems (MIMO-SLSs) from input-output measurements. The key step is an observer-based transformation to a switched auto-regressive with exogenous input (SARX) model. This transformation converts the state-space (SS) identification problem into a MIMO-SARX identification problem by compressing infinite strings of system Markov parameters into finite strings of observer Markov parameters. We study switch and discrete state (submodel) identifiability and derive persistence of excitation conditions for hybrid inputs to recover discrete-states. Switching sequence and discrete-states are estimated in the observer domain by solving a convex-sparse optimization problem followed by two different subspace algorithms. Local-mode clustering then reveals discrete-states. A detailed numerical example illustrates performance of the proposed scheme