Observer-based switched-linear system identification

Abstract

In this paper, we present a framework to identify discrete-time, single-input/single-output, switched linear systems (SISO-SLSs) from input–output data measurements. Continuous state is not assumed to be measured. The key step is a deadbeat observer-based transformation of the SLS model to a switched auto-regressive with exogenous input (SARX) model. Discrete states are estimated by a three-stage algorithm from input–output data. First, a sparse optimization problem is solved to detect segments with large dwell times. Then, a clustering algorithm is applied to midpoint estimates in these segments, revealing the system order, the number of discrete states, and the observer discrete states. In the third stage, back-transformation from the observer to a finite set of SLS Markov parameters is carried out and a subspace algorithm extracts discrete states from SLS Markov parameters. A MOESP subspace algorithm is also proposed to estimate discrete states directly from input–output data in segments with large dwell times. Switch and discrete-state identifiability issues are carefully examined and persistence of excitation (PE) conditions on input–output data, switching signal, and system structure are derived to retrieve discrete states. Monte Carlo simulations and case studies are presented to illustrate the derived results.