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Optimality properties in finite sample l i identification with bounded noise
Author(s) -
Kacewicz B.,
Milanese M.
Publication year - 1995
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480090109
Subject(s) - bounded function , mathematics , impulse (physics) , norm (philosophy) , upper and lower bounds , lti system theory , noise (video) , invariant (physics) , algorithm , control theory (sociology) , mathematical optimization , linear system , mathematical analysis , computer science , physics , control (management) , quantum mechanics , artificial intelligence , political science , law , image (mathematics) , mathematical physics
In this paper we investigate finite sample optimality properties for worst‐case l 2 identification of the impulse response of discrete time, linear, time‐invariant systems. the experimental conditions we consider consist of m experiments of length N. the measured outputs are corrupted by component‐wise bounded additive disturbances with known bounds. the quantification of the identification error is given by the maximum l 1 ‐norm of the difference between the true impulse response samples and the estimated ones, where the maximum is taken with respect to all admissible plants and all admissible disturbances. First we show that for any given experimental condition, almost‐optimal (within a factor of two) estimates can be obtained by solving suitable linear programmes. Then we study how experimental conditions affect the identification error. Optimality of the experimental data is measured by the diameter of information, a quantity which is at most twice as large as the minimal worst‐case error. We show that the minimum number of experiments allowing us to minimize the diameter of information is m − = 2 −N . the values of the diameter of information and the corresponding optimal inputs are derived for the two extreme experimental conditions m = 1 and m = 2 −N .