Polytopic outer approximations of semialgebraic sets

V. Cerone; D. Piga; D. Regruto

Polytopic outer approximations of semialgebraic sets

V. Cerone, D. Piga, D. Regruto

Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

7 Citations (Scopus)

Abstract

This paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ¿ Rn. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties of the presented algorithm and its possible applications in the analysis, identification and control of uncertain systems are discussed.

Original language	English
Title of host publication	Proceedings of the 51st IEEE Conference on decision and control (CDC 2012), 10-13 December 2012, Maui, Hawai
Pages	7793-7798
Publication status	Published - 2012

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abstract = "This paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ¿ Rn. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties of the presented algorithm and its possible applications in the analysis, identification and control of uncertain systems are discussed.",

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AB - This paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ¿ Rn. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties of the presented algorithm and its possible applications in the analysis, identification and control of uncertain systems are discussed.

M3 - Conference contribution

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EP - 7798

BT - Proceedings of the 51st IEEE Conference on decision and control (CDC 2012), 10-13 December 2012, Maui, Hawai

ER -

Polytopic outer approximations of semialgebraic sets

Abstract

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