Regression techniques for subspace-based black-box state-space system identification: an overview

As far as the identification of linear time-invariant state-space representation is concerned, among all of the solutions available in the literature, the subspace-based state-space model identification techniques have proved their efficiency in many practical cases since the beginning of the 90’s as illustrated, e.g., in [95, 12, 4, 30, 51, 28, 68, 27, 89, 11]. This paper introduces an overview of these techniques by focusing on their formulation as a least-squares problem. Apart from the article [73], to the author’s knowledge, such a regression formulation is not totally investigated in the books [87, 55, 96] which can be considered as the references as far as subspace-based identification is concerned. Thus, in this paper, a specific attention is payed to the regression-based techniques used to identify systems working under open-loop as well as closed-loop conditions.