Worst Case System Identification in B∞ : Validation of a Priori Information Essentially Optimal Algorithms, and Error Bounds

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Detail(s)

Original languageEnglish
Pages (from-to)1260-1265
Journal / PublicationIEEE Transactions on Automatic Control
Volume40
Issue number7
Publication statusPublished - Jul 1995
Externally publishedYes

Abstract

In this paper we resolve several important open issues pertaining to a worst-case control-oriented system identificadon problem known as identification in H∞, First, a method is presented for developing confidence that certain a priori information available for identification is not invalid. This method requires the solution of a certain nondifferendable convex program. Second, an essentially optimal identification algorithm is constructed. This algorithm is (worst-case strongly) optimal to within a factor of two. Finally new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm. Interestingly, the development of each of these results draws heavily upon the classical Nevanlinna—Pick interpolation theory. As such, our results establish a clear link between the areas of system identification and optimal interpolation theory. Boda the formulation and techniques in this paper are applicable to problems where the flquency data available for identification may essentially be arbitrarily distributed. © 1995 IEEE