Multiobjective optimization applied to robust ℋ2/ℋ∞ state-feedback control synthesis

This paper presents an algorithm for robust H2/H1 state-feedback control synthesis, with regional pole placement, based on a multiobjective optimization algorithm with non-smooth problem-solving capability. The problem is formulated with the state-feedback matrix coefficients as optimization parameters. The closed-loop performance ob- tained by means of the proposed strategy is assessed for the whole uncertainty-set through an LMI-based H2 and H1 guaranteed cost computation. The proposed strategy is compared with three former LMI approaches, for systems with polytope-bounded uncertainties, and presents better results. Index Terms— Robust H2/H1 control, regional pole place- ment, uncertain systems, multiobjective optimization. x(t) = Ax(t) + Buu(t) + Bww(t) z1(t) = Cz1x(t) + Dzu1u(t) + Dzw1w(t) z2(t) = Cz2x(t) + Dzu2u(t) y(t) = Cyx(t)

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