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On optimal deterministic identification with uncertain data treated as exact data

Technische Hogeschool Eindhoven
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  • Incertainty
  • Fuzzy Sets
  • Adaptive Control Systems - Optimisation


tlB Eindhoven University of Technology Faculty of Electrical Engineering On Optimal Deterministic Identification with Uncertain Data Treated as Exact Data L.J.J.M. Ariaans, S. Weiland, A.A.H. Darnen Internal report, 941/04 Group Measurement and Control Eindhoven, September 26, 1994 On Optimal Deterministic Identification with Uncertain Data Treated as Exact Data L.J.J .M. Ariaans, S. Weiland, A.A.H. Darnen Department of Electrical Engineering, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, The Netherlands Tel: +31 4047 3795 Fax: +31 40 434 582 e-Mail: [email protected] September 26, 1994 Abstract Experimental data obtained from a real plant is always contaminated by various disturbance effects. For the model identification problem this in- variably leads to uncertainty in the identified model with respect to the true process data. In this paper, we assume deterministic bounds on the uncertainty of the data which are expressed as norm bounds. Three classes of identification problems are considered. One in which data is assumed to be exact, not corrupted by noise, and two identification problems in which data uncertainty is explicitly taken into account. For very general model sets and for any norm bound of the data uncertainty, we show that an optimal solution of the identification problem without data uncertainty also solves the more complex problems with data uncertainty. Keywords: Identification, Uncertain Data, Deterministic Bounds, Norm Bounds, Optimization 1 Introduction One of the difficulties inherent to process identification is that the data from which we try to identify the process is corrupted by measurement noise or pro- cess disturbances. The relationships among the process variables that we wish to uncover are further blurred by the influence of unmodelled process inputs (i.e. disturbances) or by relationships whose complexity is not contained in the model set. All these effects mak

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