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


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
Number of pages6
StatePublished - 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


Other2009 American Control Conference, ACC 2009
Country/TerritoryUnited States
CitySt. Louis, MO

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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