H sensitivity minimization for unstable infinite-dimensional plants

Armando Rodriguez, James R. Cloutier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

This paper considers the problem of designing near-optimal finite-dimensional compensators for unstable infinite-dimensional plants. Standard weighted H sensitivity measures are used to define the notion of optimality. The method of solution is based on finite-dimensional techniques applied to finite-dimensional approximants of the original plant. The difficulties which arise from such an approach can be attributed to two factors. First, there is the lack of continuity of the performance measures with respect to perturbations in the plant, even with the graph topology. Second, there are many infinite-dimensional plants which cannot be approximated uniformly in the graph topology. It is shown in this paper, for the sensitivity minimization problem, that it is sufficient to obtain approximants of the plant on compact sets, provided that the inner part of the plant's `numerator coprime factor' is approximated in some sense. Constructive algorithms are presented. New results on the convergence of actual closed loop transfer functions are also given.

Original languageEnglish (US)
Title of host publicationAmerican Control Conference
Place of PublicationPiscataway, NJ, United States
PublisherPubl by IEEE
Pages2155-2159
Number of pages5
ISBN (Print)0780308611
StatePublished - 1993
EventProceedings of the 1993 American Control Conference - San Francisco, CA, USA
Duration: Jun 2 1993Jun 4 1993

Other

OtherProceedings of the 1993 American Control Conference
CitySan Francisco, CA, USA
Period6/2/936/4/93

Fingerprint

Topology
Transfer functions

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Rodriguez, A., & Cloutier, J. R. (1993). H sensitivity minimization for unstable infinite-dimensional plants. In American Control Conference (pp. 2155-2159). Piscataway, NJ, United States: Publ by IEEE.

H sensitivity minimization for unstable infinite-dimensional plants. / Rodriguez, Armando; Cloutier, James R.

American Control Conference. Piscataway, NJ, United States : Publ by IEEE, 1993. p. 2155-2159.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rodriguez, A & Cloutier, JR 1993, H sensitivity minimization for unstable infinite-dimensional plants. in American Control Conference. Publ by IEEE, Piscataway, NJ, United States, pp. 2155-2159, Proceedings of the 1993 American Control Conference, San Francisco, CA, USA, 6/2/93.
Rodriguez A, Cloutier JR. H sensitivity minimization for unstable infinite-dimensional plants. In American Control Conference. Piscataway, NJ, United States: Publ by IEEE. 1993. p. 2155-2159
Rodriguez, Armando ; Cloutier, James R. / H sensitivity minimization for unstable infinite-dimensional plants. American Control Conference. Piscataway, NJ, United States : Publ by IEEE, 1993. pp. 2155-2159
@inproceedings{65c78f3a9eaa421bb9ee6c93dd570fe3,
title = "H∞ sensitivity minimization for unstable infinite-dimensional plants",
abstract = "This paper considers the problem of designing near-optimal finite-dimensional compensators for unstable infinite-dimensional plants. Standard weighted H∞ sensitivity measures are used to define the notion of optimality. The method of solution is based on finite-dimensional techniques applied to finite-dimensional approximants of the original plant. The difficulties which arise from such an approach can be attributed to two factors. First, there is the lack of continuity of the performance measures with respect to perturbations in the plant, even with the graph topology. Second, there are many infinite-dimensional plants which cannot be approximated uniformly in the graph topology. It is shown in this paper, for the sensitivity minimization problem, that it is sufficient to obtain approximants of the plant on compact sets, provided that the inner part of the plant's `numerator coprime factor' is approximated in some sense. Constructive algorithms are presented. New results on the convergence of actual closed loop transfer functions are also given.",
author = "Armando Rodriguez and Cloutier, {James R.}",
year = "1993",
language = "English (US)",
isbn = "0780308611",
pages = "2155--2159",
booktitle = "American Control Conference",
publisher = "Publ by IEEE",

}

TY - GEN

T1 - H∞ sensitivity minimization for unstable infinite-dimensional plants

AU - Rodriguez, Armando

AU - Cloutier, James R.

PY - 1993

Y1 - 1993

N2 - This paper considers the problem of designing near-optimal finite-dimensional compensators for unstable infinite-dimensional plants. Standard weighted H∞ sensitivity measures are used to define the notion of optimality. The method of solution is based on finite-dimensional techniques applied to finite-dimensional approximants of the original plant. The difficulties which arise from such an approach can be attributed to two factors. First, there is the lack of continuity of the performance measures with respect to perturbations in the plant, even with the graph topology. Second, there are many infinite-dimensional plants which cannot be approximated uniformly in the graph topology. It is shown in this paper, for the sensitivity minimization problem, that it is sufficient to obtain approximants of the plant on compact sets, provided that the inner part of the plant's `numerator coprime factor' is approximated in some sense. Constructive algorithms are presented. New results on the convergence of actual closed loop transfer functions are also given.

AB - This paper considers the problem of designing near-optimal finite-dimensional compensators for unstable infinite-dimensional plants. Standard weighted H∞ sensitivity measures are used to define the notion of optimality. The method of solution is based on finite-dimensional techniques applied to finite-dimensional approximants of the original plant. The difficulties which arise from such an approach can be attributed to two factors. First, there is the lack of continuity of the performance measures with respect to perturbations in the plant, even with the graph topology. Second, there are many infinite-dimensional plants which cannot be approximated uniformly in the graph topology. It is shown in this paper, for the sensitivity minimization problem, that it is sufficient to obtain approximants of the plant on compact sets, provided that the inner part of the plant's `numerator coprime factor' is approximated in some sense. Constructive algorithms are presented. New results on the convergence of actual closed loop transfer functions are also given.

UR - http://www.scopus.com/inward/record.url?scp=0027335283&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027335283&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027335283

SN - 0780308611

SP - 2155

EP - 2159

BT - American Control Conference

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -