Convergent relaxations of polynomial matrix inequalities and static output feedback
Didier Henrion (henrionlaas.fr)
Abstract: Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to the global optimum. Results from the theory of moments are used to detect whether the global optimum is reached at a given LMI relaxation, and if so, to extract global minimizers that satisfy the PMI. The approach is successfully applied to PMIs arising from static output feedback design problems.
Keywords: Polynomial matrix, nonconvex optimization, convex optimization, static output feedback design
Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )
Category 2: Applications -- Science and Engineering (Control Applications )
Citation: LAAS-CNRS Research Report, November 2004, submitted for publication.
Entry Submitted: 11/15/2004
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