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Informative data and identifiability in LPV-ARX prediction-error identification

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  • Chemistry
  • Computer Science


Informative Data and Identifiability in LPV-ARX Prediction-Error Identification Informative Data and Identifiability in LPV-ARX Prediction-Error Identification Arne G. Dankers, Roland To´th, Peter S. C. Heuberger, Xavier Bombois and Paul M. J. Van den Hof Abstract— In system identification, the concepts of infor- mative data and identifiable model structures are important for addressing the statistical properties of estimated models. In this paper, these two concepts are generalized from the classical LTI prediction-error identification framework to the situation of LPV model structures and appropriate definitions are introduced. For two particular cases (piecewise constant and periodic scheduling trajectories) conditions are derived for the data sets to be informative w.r.t. the LPV-ARX model structure. Moreover, conditions are derived under which the LPV-ARX model structure is globally identifiable. I. INTRODUCTION Efficient control of high-tech systems such as precision mechatronic devices, aircrafts, and chemical plants, requires accurate but simple models of the nonlinear and/or time- varying behavior of these applications. For many nonlin- ear systems, the linear parameter-varying (LPV) framework offers a nice trade-off between accuracy and parsimony. Moreover, it offers convex control synthesis for nonlinear systems in a computationally attractive setting [1]. In the LPV framework, signal relations are considered to be linear just as in the LTI case, but these relations are assumed to be varying as a function of a measurable signal, the so-called scheduling variable. Recently an LPV prediction-error identification framework has been developed in [1] providing a theoretical basis which can be used for the estimation of LPV predictor models. In this framework LPV-ARX, LPV-ARMAX, etc. model structures are defined which are generalizations of the LTI model structures. In the LTI prediction-error identification theory, it is well known that the data set must be informativ

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