Basis transform in switched linear system state-space models from input-output data

Abstract

This paper tackles the basis selection issue in the context of state-space hybrid system identification from input-output data. It is often the case that an identification scheme responsible for state-space switched linear system (SLS) estimation from input-output data operates on local levels. Such individually identified local estimates reside in distinct state bases, which call for the need to perform some basis correction mechanism that facilitates their coherent patching for the ultimate goal of performing output predictions for predefined input test signals. We derive necessary and sufficient conditions on the submodel set, the switching sequence, and the dwell times that guarantee the presented approach's success. Such conditions turn out to be relatively mild, which contributes to the application potential of the devised algorithm. We also provide a linkage between this work and the existing literature by providing several insightful remarks that highlight the discussed method's favorability. We supplement the theoretical findings by an elaborative numerical simulation that puts our methodology into action.

Observer-based switched-linear system identification

“…A framework is proposed to identify the discrete states and the switching sequences of the SLSs in the state-space form from the input-output measurements. This framework followed by the basis construction procedure in (Bencherki et al, 2021) proposed by the authors of this paper delivers final models suitable for predicting time responses of the SLSs to prescribed inputs. The proposed identification framework is demonstrated to be consistent under some assumptions on the system structure, the dwell times of the discrete states, and noise amplitude in a completely deterministic setting.…”

“…The rest of the transformations are fixed and can be calculated from the input-output data, P, and χ. See (Bencherki et al, 2021) for details.…”