An algorithm for sampling subsets of H∞ with applications to risk-adjusted performance analysis and model (In)validation

Mario Sznaier, Constantino Manuel Lagoa, Maria Cecilia Mazzaro

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H∞. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.

    Original languageEnglish (US)
    Pages (from-to)410-416
    Number of pages7
    JournalIEEE Transactions on Automatic Control
    Volume50
    Issue number3
    DOIs
    StatePublished - Mar 1 2005

    Fingerprint

    Set theory
    Sampling
    Robust control
    Mathematical operators
    Computational complexity
    Uncertainty

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Computer Science Applications
    • Electrical and Electronic Engineering

    Cite this

    @article{81319a67346e47eda32d722faff744ca,
    title = "An algorithm for sampling subsets of H∞ with applications to risk-adjusted performance analysis and model (In)validation",
    abstract = "In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H∞. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.",
    author = "Mario Sznaier and Lagoa, {Constantino Manuel} and Mazzaro, {Maria Cecilia}",
    year = "2005",
    month = "3",
    day = "1",
    doi = "10.1109/TAC.2005.843852",
    language = "English (US)",
    volume = "50",
    pages = "410--416",
    journal = "IEEE Transactions on Automatic Control",
    issn = "0018-9286",
    publisher = "Institute of Electrical and Electronics Engineers Inc.",
    number = "3",

    }

    An algorithm for sampling subsets of H∞ with applications to risk-adjusted performance analysis and model (In)validation. / Sznaier, Mario; Lagoa, Constantino Manuel; Mazzaro, Maria Cecilia.

    In: IEEE Transactions on Automatic Control, Vol. 50, No. 3, 01.03.2005, p. 410-416.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - An algorithm for sampling subsets of H∞ with applications to risk-adjusted performance analysis and model (In)validation

    AU - Sznaier, Mario

    AU - Lagoa, Constantino Manuel

    AU - Mazzaro, Maria Cecilia

    PY - 2005/3/1

    Y1 - 2005/3/1

    N2 - In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H∞. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.

    AB - In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H∞. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.

    UR - http://www.scopus.com/inward/record.url?scp=16244403372&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=16244403372&partnerID=8YFLogxK

    U2 - 10.1109/TAC.2005.843852

    DO - 10.1109/TAC.2005.843852

    M3 - Article

    AN - SCOPUS:16244403372

    VL - 50

    SP - 410

    EP - 416

    JO - IEEE Transactions on Automatic Control

    JF - IEEE Transactions on Automatic Control

    SN - 0018-9286

    IS - 3

    ER -