Estimation of pareto sets in the mixed H2/H∞ control problem

  • Authors:

  • Ricardo H. C. Takahashi;Reinaldo M. Palhares;Daniel A. Dutra;Leila P. S. Gonçalves

  • Affiliations:

  • Department of Mathematics, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Pampulha, 31270-010, Belo Horizonte---MG--Brazil;Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Pampulha, 31270-010, Belo Horizonte--MG--Brazil;Department of Mathematics, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Pampulha, 31270-010, Belo Horizonte---MG--Brazil;Tecnometal Engenharia e Construçẽs Mecânicas Ltda, Av. das Naçôes, 3801--Distrito Industrial de Vespasiano, 33200-000, Vespasiano--MG--Brazil

  • Venue:
  • International Journal of Systems Science
  • Year:
  • 2004

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Abstract

Multiobjective design problems give rise to a well-defined object: the Pareto-set. This paper proposes some verifiable conditions that are applicable to sets with finite number of elements, to corroborate or falsify the hypothesis of the elements of that set being samples of the Pareto set. These conditions lead to several generic criteria that can be employed in the evaluation of algorithms as multiobjective optimization mechanisms. A conceptual multiobjective genetic algorithm is proposed, exploiting the group properties of the intermediate Pareto-set estimates to generate a consistent final estimate. The methodology is applied to the case of a mixed H2/H∞ control design. Recent dedicated multiobjective algorithms are evaluated under the proposed methodology, and it is shown that they can generate sub-optimal or non-consistent solution sets. It is shown that the proposed synthesis methodology can lead to both enhanced objectives and enhanced consistency in the Pareto-set estimate.