Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloA Kinship Function Approach to Robust and Probabilistic Optimization Under Polynomial Uncertainty
Anno di pubblicazione2011
Formato
  • Elettronico
  • Cartaceo
Autore/iC. Feng, F. Dabbene, C. M. Lagoa
Affiliazioni autoriC. Feng, C. M. Lagoa : Pennsylvania State University, University Park, PA 16802, United States F. Dabbene : CNR-IEIIT
Autori CNR e affiliazioni
  • FABRIZIO DABBENE
Lingua/e
  • inglese
AbstractIn 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.
Lingua abstractinglese
Altro abstract-
Lingua altro abstract-
Pagine da1509
Pagine a1523
Pagine totali15
RivistaIEEE transactions on automatic control (Print)
Attiva dal 1963
Editore: Institute of Electrical and Electronics Engineers, - New York, N.Y.
Paese di pubblicazione: Stati Uniti d'America
Lingua: inglese
ISSN: 0018-9286
Titolo chiave: IEEE transactions on automatic control (Print)
Titolo proprio: IEEE transactions on automatic control. (Print)
Titolo abbreviato: IEEE trans. automat. contr. (Print)
Titoli alternativi:
  • Transactions on automatic control (Print)
  • Automatic control (Print)
Numero volume della rivista56
Fascicolo della rivista7
DOI10.1109/TAC.2010.2099734
Verificato da refereeSì: Internazionale
Stato della pubblicazione-
Indicizzazione (in banche dati controllate)
  • ISI Web of Science (WOS) (Codice:000293442300002)
  • Scopus (Codice:WOS:000293442300002)
Parole chiave-
Link (URL, URI)http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5669338&tag=1
Titolo parallelo-
Data di accettazione-
Note/Altre informazioni-
Strutture CNR
  • IEIIT — Istituto di elettronica e di ingegneria dell'informazione e delle telecomunicazioni
Moduli CNR
    Progetti Europei-
    Allegati
    • A Kinship Function Approach to Robust and Probabilistic Optimization Under Polynomial Uncertainty

    Dati storici
    I dati storici non sono modificabili, sono stati ereditati da altri sistemi (es. Gestione Istituti, PUMA, ...) e hanno solo valore storico.
    Area disciplinareComputer Science & Engineering
    Area valutazione CIVRIngegneria industriale e informatica
    Rivista ISIIEEE TRANSACTIONS ON AUTOMATIC CONTROL [42592J0]
    Note DOI: 10.1109/TAC.2010.2099734