This paper deals with the approximation of sets of linear time-invariant systems via orthonormal basis functions. This problem is relevant to conditional set membership identification, where a set of feasible systems is available from observed data, and a reduced-complexity model must be estimated, within a linearly parameterized model class. The basis of the model class is a collection of impulse responses of linear filters (e.g. Laguerre functions), whose poles must be chosen properly. The objective of the paper is to select the basis function pole according to a worst-case optimality criterion taking into account the uncertainty system set. This leads to complicated min-max optimization problems. Suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors.

Casini, M., Garulli, A., & Vicino, A. (2001). On Worst-Case Approximation of Feasible System Sets via Orthonormal Basis Functions. In Proc. 40th IEEE Conf. on Decision and Control (pp.2695-2700) [10.1109/.2001.980678].

On Worst-Case Approximation of Feasible System Sets via Orthonormal Basis Functions

CASINI, MARCO;GARULLI, ANDREA;VICINO, ANTONIO
2001

Abstract

This paper deals with the approximation of sets of linear time-invariant systems via orthonormal basis functions. This problem is relevant to conditional set membership identification, where a set of feasible systems is available from observed data, and a reduced-complexity model must be estimated, within a linearly parameterized model class. The basis of the model class is a collection of impulse responses of linear filters (e.g. Laguerre functions), whose poles must be chosen properly. The objective of the paper is to select the basis function pole according to a worst-case optimality criterion taking into account the uncertainty system set. This leads to complicated min-max optimization problems. Suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/21775
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