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Title: Sliding modes for a phase-field system
Authors: Barbu, ViorelColli, PierluigiGilardi, GianniMarinoschi, GabrielaRocca, Elisabetta
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2133, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In the present contribution the sliding mode control (SMC) problem for a phasefield model of Caginalp type is considered. First we prove the well-posedness and some regularity results for the phase-field type state systems modified by the statefeedback control laws. Then, we show that the chosen SMC laws force the system to reach within finite time the sliding manifold (that we chose in order that one of the physical variables or a combination of them remains constant in time). We study three different types of feedback control laws: the first one appears in the internal energy balance and forces a linear combination of the temperature and the phase to reach a given (space dependent) value, while the second and third ones are added in the phase relation and lead the phase onto a prescribed target phi*. While the control law is non-local in space for the first two problems, it is local in the third one, i.e., its value at any point and any time just depends on the value of the state.
Keywords: Phase field system; nonlinear boundary value problems; phase transition; sliding mode control; state-feedback control law
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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