@prefix rdf: . @prefix prodotto: . @prefix retescientifica: . prodotto:ID20753 rdf:type retescientifica:ProdottoDellaRicerca , prodotto:TIPO1101 . @prefix rdfs: . prodotto:ID20753 rdfs:label "A Kinship Function Approach to Robust and Probabilistic Optimization Under Polynomial Uncertainty (Articolo in rivista)"@en . @prefix xsd: . @prefix pubblicazioni: . prodotto:ID20753 pubblicazioni:anno "2011-01-01T00:00:00+01:00"^^xsd:gYear ; pubblicazioni:doi "10.1109/TAC.2010.2099734"^^xsd:string . @prefix skos: . prodotto:ID20753 skos:altLabel "
C. Feng, F. Dabbene, C. M. Lagoa (2011)
A Kinship Function Approach to Robust and Probabilistic Optimization Under Polynomial Uncertainty
in IEEE transactions on automatic control (Print)
"^^rdf:HTML ; pubblicazioni:autori "C. Feng, F. Dabbene, C. M. Lagoa"^^xsd:string ; pubblicazioni:paginaInizio "1509"^^xsd:string ; pubblicazioni:paginaFine "1523"^^xsd:string ; pubblicazioni:url "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5669338&tag=1"^^xsd:string ; pubblicazioni:numeroVolume "56"^^xsd:string . @prefix ns7: . prodotto:ID20753 pubblicazioni:rivista ns7:ID394449 ; pubblicazioni:note " DOI: 10.1109/TAC.2010.2099734"^^xsd:string ; pubblicazioni:pagineTotali "15"^^xsd:string ; pubblicazioni:numeroFascicolo "7"^^xsd:string ; skos:note "copus"^^xsd:string , "ISI Web of Science (WOS)"^^xsd:string ; pubblicazioni:affiliazioni "C. Feng, C. M. Lagoa : Pennsylvania State University, University Park, PA 16802, United States\nF. Dabbene : CNR-IEIIT"^^xsd:string ; pubblicazioni:titolo "A Kinship Function Approach to Robust and Probabilistic Optimization Under Polynomial Uncertainty"^^xsd:string . @prefix prodottidellaricerca: . prodotto:ID20753 prodottidellaricerca:abstract "In this paper, we study a class of robust design problems with polynomial dependence on the uncertainty. One of the main motivations for considering these problems comes from robust controller design, where one often encounters systems that depend polynomially on the uncertain parameters. This paper can be seen as integrated in the emerging area of probabilistic robustness, where a probabilistic relaxation of the original robust problem is adopted, thus requiring the satisfaction of the constraints not for all possible values of the uncertainty, but for most of them. Different from the randomized approach for tackling probabilistic relaxations, which is only guaranteed to provide soft bounds on the probability of satisfaction, we present a deterministic approach based on the novel concept of kinship function introduced in this paper. This allows the development of an original framework, which leads to easily computable deterministic convex relaxations of the probabilistic problem. In particular, optimal polynomial kinship functions are introduced, which can be computed a priori and once for all and provide the \\\"best convex bound\\\" on the probability of constraint violation. More importantly, it is proven that the solution of the relaxed problem converges to that of the original robust optimization problem as the degree of the optimal polynomial kinship function increases. Furthermore, by relying on quadrature formulas for computation of integrals of polynomials, it is shown that the computational complexity of the proposed approach is polynomial in the number of uncertain parameters. Finally, unlike other deterministic approaches to robust polynomial optimization, the number of variables in the ensuing optimization problem is not increased by the proposed approximation. An important feature of this approach is that a significant amount of the computational burden is shifted to a one-time offline computation whose results can be stored and provided to the end-user."@en . @prefix istituto: . prodotto:ID20753 prodottidellaricerca:prodottoDi istituto:CDS029 . @prefix modulo: . prodotto:ID20753 prodottidellaricerca:prodottoDi modulo:ID2244 . @prefix unitaDiPersonaleInterno: . prodotto:ID20753 pubblicazioni:autoreCNR unitaDiPersonaleInterno:MATRICOLA8494 . istituto:CDS029 prodottidellaricerca:prodotto prodotto:ID20753 . unitaDiPersonaleInterno:MATRICOLA8494 pubblicazioni:autoreCNRDi prodotto:ID20753 . modulo:ID2244 prodottidellaricerca:prodotto prodotto:ID20753 . ns7:ID394449 pubblicazioni:rivistaDi prodotto:ID20753 .