Equivalence of regularizations in abstract problems with different classes of admissible controls
type: Item
instance of: scholarly article
title: Equivalence of regularizations in abstract problems with different classes of admissible controls
zbMATH Open document ID: 0930.93005
DOI: 10.1007/BF02666979
author: A. G. Chentsov
author: Yu. I. Berdyshev
published in: Cybernetics and Systems Analysis
publication date: 2000-01-31T00:00:00Z
review text: The authors consider a finite dimensional control system with a single input. Admissible control functions are constrained by integral equality and integral inclusion. It is demonstrated on examples that there are situations where the attainable set for a traditional class of piecewise continuous admissible controls is different from the attainable set for the class of pulse controls, i.e. controls expressed as weighted sums of Dirac's \(\delta\)-functions. In the considered example both attainable sets are closed. Using a technique based on finite additive measures developed earlier by the second author [see e.g. Autom. Remote Control 53, No. 5, pt. 1, 646-655 (1992; Zbl 0794.93041)], the class of admissible controls is extended. The conventional controls in the new settings are step-function with respect to the introduced measure whereas pulse controls are analogs of weighted sums of \(\delta\)-functions. It is obtained that in the relaxed problem the respective analogs of attainable sets both for conventional admissible controls and for purely impulse controls are equal.
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 28A25
zbMATH DE Number: 1283630
zbMATH Keywords: linear control system
zbMATH Keywords: attainable set
zbMATH Keywords: pulse control
zbMATH Keywords: finite additive measure
zbMATH Keywords: impulse controls
reviewed by: D. B. Silin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1283630