Robust and chance-constrained optimization under polynomial uncertainty

F. Dabbene, C. Feng, C. M. Lagoa

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

    3 Scopus citations

    Abstract

    A chance-constrained optimization problem, induced from a robust design problem with polynomial dependence on the uncertainties, is, in general, non-convex and difficult to solve. By introducing a novel concept - the kinship function - an easily computable convex relaxation of this problem is proposed. In particular, optimal polynomial kinship functions, which can be computed a priori and once for all, are introduced and used to bound the probability of constraint violation. Moreover, it is proven that the solution of the relaxed problem converges to that of the original robust optimization problem as the degree of the polynomial kinship function increases. Finally, by relying on quadrature formulae for computation of integrals of polynomials, it is shown that the computational complexity of the proposed approach is polynomial on the number of uncertainty parameters.

    Original languageEnglish (US)
    Title of host publication2009 American Control Conference, ACC 2009
    Pages379-384
    Number of pages6
    DOIs
    StatePublished - Nov 23 2009
    Event2009 American Control Conference, ACC 2009 - St. Louis, MO, United States
    Duration: Jun 10 2009Jun 12 2009

    Publication series

    NameProceedings of the American Control Conference
    ISSN (Print)0743-1619

    Other

    Other2009 American Control Conference, ACC 2009
    CountryUnited States
    CitySt. Louis, MO
    Period6/10/096/12/09

    All Science Journal Classification (ASJC) codes

    • Electrical and Electronic Engineering

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