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A unified framework for solving a general class of conditional and robust set-membership estimation problems

Cerone, Vito and Lasserre, Jean-Bernard and Piga, Dario and Regruto, Diego A unified framework for solving a general class of conditional and robust set-membership estimation problems. IEEE Transactions on Automatic Control , 59 (11). pp. 2897-2909. ISSN 0018-9286 (2014)

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In this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.

Item Type: Article
Identification Number: 10.1109/TAC.2014.2351695
Uncontrolled Keywords: Convex relaxation; robust optimization; set-membership identification
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 13 Jan 2015 14:42
Last Modified: 13 Jan 2015 14:42
URI: http://eprints.imtlucca.it/id/eprint/2478

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