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Authors: Jean-Baptiste Thevenet 1 ; Dominikus Noll 2 and Pierre Apkarian 3

Affiliations: 1 ONERA-CERT; UPS-MIP (Mathmatiques pour l’Industrie et la Physique), CNRS UMR 5640, France ; 2 UPS-MIP (Mathmatiques pour l’Industrie et la Physique), France ; 3 ONERA-CERT; UPS-MIP, France

Keyword(s): Bilinear matrix inequality, spectral penalty function, trust-region, control synthesis.

Related Ontology Subjects/Areas/Topics: Informatics in Control, Automation and Robotics ; Intelligent Control Systems and Optimization ; Optimization Algorithms ; Robot Design, Development and Control ; Robotics and Automation

Abstract: The purpose of this paper is to examine a nonlinear spectral semidefinite programming method to solve problems with bilinear matrix inequality (BMI) constraints. Such optimization programs arise frequently in automatic control and are difficult to solve due to the inherent non-convexity. The method we discuss here is of augmented Lagrangian type and uses a succession of unconstrained subproblems to approximate the BMI optimization program. These tangent programs are solved by a trust region strategy. The method is tested against several difficult examples in feedback control synthesis.

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Paper citation in several formats:
Thevenet, J.; Noll, D. and Apkarian, P. (2004). NON LINEAR SPECTRAL SDP METHOD FOR BMI-CONSTRAINED PROBLEMS : APPLICATIONS TO CONTROL DESIGN. In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 972-8865-12-0; ISSN 2184-2809, SciTePress, pages 237-248. DOI: 10.5220/0001128402370248

@conference{icinco04,
author={Jean{-}Baptiste Thevenet. and Dominikus Noll. and Pierre Apkarian.},
title={NON LINEAR SPECTRAL SDP METHOD FOR BMI-CONSTRAINED PROBLEMS : APPLICATIONS TO CONTROL DESIGN},
booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2004},
pages={237-248},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001128402370248},
isbn={972-8865-12-0},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - NON LINEAR SPECTRAL SDP METHOD FOR BMI-CONSTRAINED PROBLEMS : APPLICATIONS TO CONTROL DESIGN
SN - 972-8865-12-0
IS - 2184-2809
AU - Thevenet, J.
AU - Noll, D.
AU - Apkarian, P.
PY - 2004
SP - 237
EP - 248
DO - 10.5220/0001128402370248
PB - SciTePress

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