In this study, the authors present an overview of closed-loop subspace identification methods found in the recent literature. Since a significant number of algorithms has appeared over the last decade, the authors highlight some of the key algorithms that can be shown to have a common origin in autoregressive modelling. Many of the algorithms found in the literature are variants on the algorithms that are discussed here. In this study, the aim is to give a clear overview of some of the more successful methods presented throughout the last decade. Furthermore, the authors retrace these methods to a common origin and show how they differ. The methods are compared both on the basis of simulation examples and real data. Although the main focus in the literature has been on the identification of discrete-time models, identification of continuous-time models is also of practical interest. Hence, the authors also provide an overview of the continuous-time formulation of the identification framework
A new subspace identification method for systems operating either in open-loop or in closed-loop is presented. The method obtains an estimate of the innovation sequence by performing an RQ-factorization of the measurement data, thereby avoiding explicitly solving a least-squares problem. In a second step, the estimated innovation sequence is used to perform ordinary MOESP [1] to find the system matrices up to a similarity transformation. The closed-loop identification algorithm also applies to cases where certain disturbance inputs are present that can be parametrised in terms of suitable basis functions. All computations are performed using orthogonal factorisations of the data. The method is illustrated by applying it to a system operating in closed-loop and to measurements from a real system with periodic disturbances.
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