Weighted H∞ mixed-sensitivity minimization for stable MIMO distributed-parameter plants

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Abstract

This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. 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 proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.

Original languageEnglish (US)
Pages (from-to)219-233
Number of pages15
JournalIMA Journal of Mathematical Control and Information
Volume12
Issue number3
DOIs
StatePublished - 1995

Fingerprint

Multiple-input multiple-output (MIMO)
Computer Communication Networks
Controllers
Factorization
Spectral Factorization
Controller
Distributed Parameter Systems
Optimization
Compensator
Control Design
performance
parameter
Optimality

ASJC Scopus subject areas

  • Molecular Biology
  • Statistics and Probability
  • Computational Mathematics
  • Development
  • Control and Optimization
  • Control and Systems Engineering
  • Applied Mathematics

Cite this

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title = "Weighted H∞ mixed-sensitivity minimization for stable MIMO distributed-parameter plants",
abstract = "This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. 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 proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.",
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T1 - Weighted H∞ mixed-sensitivity minimization for stable MIMO distributed-parameter plants

AU - Rodriguez, Armando

PY - 1995

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N2 - This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. 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 proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.

AB - This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. 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 proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.

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