Weighted ℋ ∞ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control

Delano R. Carter; Armando A. Rodriguez

Kybernetika (1999)

  • Volume: 35, Issue: 5, page [527]-554
  • ISSN: 0023-5954

Abstract

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This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted ℋ ∞ -style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite- dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.

How to cite

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Carter, Delano R., and Rodriguez, Armando A.. "Weighted $\mathcal {H}_\infty $ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control." Kybernetika 35.5 (1999): [527]-554. <http://eudml.org/doc/33445>.

@article{Carter1999,
abstract = {This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted $ \{\mathcal \{H\}\}^\infty $-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite- dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.},
author = {Carter, Delano R., Rodriguez, Armando A.},
journal = {Kybernetika},
keywords = {MIMO; distributed parameter system; sampled-data control; finite-dimensional controllers; finite-dimensional systems; MIMO; distributed parameter system; sampled-data control; finite-dimensional controllers; finite-dimensional systems},
language = {eng},
number = {5},
pages = {[527]-554},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Weighted $\mathcal \{H\}_\infty $ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control},
url = {http://eudml.org/doc/33445},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Carter, Delano R.
AU - Rodriguez, Armando A.
TI - Weighted $\mathcal {H}_\infty $ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 5
SP - [527]
EP - 554
AB - This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted $ {\mathcal {H}}^\infty $-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite- dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.
LA - eng
KW - MIMO; distributed parameter system; sampled-data control; finite-dimensional controllers; finite-dimensional systems; MIMO; distributed parameter system; sampled-data control; finite-dimensional controllers; finite-dimensional systems
UR - http://eudml.org/doc/33445
ER -

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