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Global optimization in stabilizing controller design

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Abstract

In this paper, we develop a global optimization methodology to solve stabilization problems. We first formulate stabilization problems as bilevel programming problems. By invoking the Hurwitz stability conditions, we reformulate these bilevel programs to equivalent single-level nonconvex optimization programs. The branch-and-reduce global optimization algorithm is finally applied to these problems. Using the proposed methodology, we report improved solutions for two feedback stabilization problems from the literature. In addition, we improve the lower bound of the stabilizability parameter of the Belgian chocolate problem from the previous best known 0.96 to 0.973974.

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Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL, 61801, USA

    YoungJung Chang & Nikolaos V. Sahinidis

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  1. YoungJung Chang
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  2. Nikolaos V. Sahinidis
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Correspondence to Nikolaos V. Sahinidis.

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Chang, Y., Sahinidis, N.V. Global optimization in stabilizing controller design. J Glob Optim 38, 509–526 (2007). https://doi.org/10.1007/s10898-006-9092-2

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  • DOI: https://doi.org/10.1007/s10898-006-9092-2

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