Generating Series for Drawing the Output of Dynamical Systems
Identifieur interne : 000588 ( France/Analysis ); précédent : 000587; suivant : 000589Generating Series for Drawing the Output of Dynamical Systems
Auteurs : Farida Benmakrouha [France] ; Christiane Hespel [France] ; Edouard Monnier [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2012.
Abstract
Abstract: We provide the drawing of the output of dynamical system (Σ), particularly when the output is rough or near instability points. (Σ) being analytical in a neighborhood of the initial state q(0) and described by its state equations, its output y(t) in a neighborhood of t = 0 is obtained by “evaluating” its generating series. Our algorithm consists in juxtaposing local approximating outputs on successive time intervals [t i ,t i + 1]0 ≤ i ≤ n − 1, to draw y(t) everywhere as far as possible. At every point t i + 1 we calculate at order k an approximated value of each component q r of the state; on every interval [t i ,t i + 1]0 ≤ i ≤ n − 1 we calculate an approximated output. These computings are obtained from the symbolic expressions of the generating series of q r and y, truncated at order k, specified for t = t i and “evaluated”. A Maple package is built, providing a suitable result for oscillating outputs or near instability points when a Runge-Kutta method is wrong.
Url:
DOI: 10.1007/978-3-642-27413-8_11
Affiliations:
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ISTEX:232E0B62D3D2E39E67B54A58A2FA07955C40A566Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Generating Series for Drawing the Output of Dynamical Systems</title><author><name sortKey="Benmakrouha, Farida" sort="Benmakrouha, Farida" uniqKey="Benmakrouha F" first="Farida" last="Benmakrouha">Farida Benmakrouha</name></author><author><name sortKey="Hespel, Christiane" sort="Hespel, Christiane" uniqKey="Hespel C" first="Christiane" last="Hespel">Christiane Hespel</name></author><author><name sortKey="Monnier, Edouard" sort="Monnier, Edouard" uniqKey="Monnier E" first="Edouard" last="Monnier">Edouard Monnier</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:232E0B62D3D2E39E67B54A58A2FA07955C40A566</idno><date when="2012" year="2012">2012</date><idno type="doi">10.1007/978-3-642-27413-8_11</idno><idno type="url">https://api.istex.fr/document/232E0B62D3D2E39E67B54A58A2FA07955C40A566/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001157</idno><idno type="wicri:Area/Istex/Curation">001157</idno><idno type="wicri:Area/Istex/Checkpoint">000067</idno><idno type="wicri:doubleKey">0302-9743:2012:Benmakrouha F:generating:series:for</idno><idno type="wicri:Area/Main/Merge">000668</idno><idno type="wicri:Area/Main/Curation">000668</idno><idno type="wicri:Area/Main/Exploration">000668</idno><idno type="wicri:Area/France/Extraction">000588</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Generating Series for Drawing the Output of Dynamical Systems</title><author><name sortKey="Benmakrouha, Farida" sort="Benmakrouha, Farida" uniqKey="Benmakrouha F" first="Farida" last="Benmakrouha">Farida Benmakrouha</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>INSA-IRISA, 20 avenue des Buttes de Coesmes, 35043, Rennes cedex</wicri:regionArea><placeName><region type="region" nuts="2">Région Bretagne</region><settlement type="city">Rennes</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Hespel, Christiane" sort="Hespel, Christiane" uniqKey="Hespel C" first="Christiane" last="Hespel">Christiane Hespel</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>INSA-IRISA, 20 avenue des Buttes de Coesmes, 35043, Rennes cedex</wicri:regionArea><placeName><region type="region" nuts="2">Région Bretagne</region><settlement type="city">Rennes</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Monnier, Edouard" sort="Monnier, Edouard" uniqKey="Monnier E" first="Edouard" last="Monnier">Edouard Monnier</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>INSA-IRISA, 20 avenue des Buttes de Coesmes, 35043, Rennes cedex</wicri:regionArea><placeName><region type="region" nuts="2">Région Bretagne</region><settlement type="city">Rennes</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2012</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">232E0B62D3D2E39E67B54A58A2FA07955C40A566</idno><idno type="DOI">10.1007/978-3-642-27413-8_11</idno><idno type="ChapterID">11</idno><idno type="ChapterID">Chap11</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We provide the drawing of the output of dynamical system (Σ), particularly when the output is rough or near instability points. (Σ) being analytical in a neighborhood of the initial state q(0) and described by its state equations, its output y(t) in a neighborhood of t = 0 is obtained by “evaluating” its generating series. Our algorithm consists in juxtaposing local approximating outputs on successive time intervals [t i ,t i + 1]0 ≤ i ≤ n − 1, to draw y(t) everywhere as far as possible. At every point t i + 1 we calculate at order k an approximated value of each component q r of the state; on every interval [t i ,t i + 1]0 ≤ i ≤ n − 1 we calculate an approximated output. These computings are obtained from the symbolic expressions of the generating series of q r and y, truncated at order k, specified for t = t i and “evaluated”. A Maple package is built, providing a suitable result for oscillating outputs or near instability points when a Runge-Kutta method is wrong.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Région Bretagne</li></region><settlement><li>Rennes</li></settlement></list><tree><country name="France"><region name="Région Bretagne"><name sortKey="Benmakrouha, Farida" sort="Benmakrouha, Farida" uniqKey="Benmakrouha F" first="Farida" last="Benmakrouha">Farida Benmakrouha</name></region><name sortKey="Benmakrouha, Farida" sort="Benmakrouha, Farida" uniqKey="Benmakrouha F" first="Farida" last="Benmakrouha">Farida Benmakrouha</name><name sortKey="Hespel, Christiane" sort="Hespel, Christiane" uniqKey="Hespel C" first="Christiane" last="Hespel">Christiane Hespel</name><name sortKey="Hespel, Christiane" sort="Hespel, Christiane" uniqKey="Hespel C" first="Christiane" last="Hespel">Christiane Hespel</name><name sortKey="Monnier, Edouard" sort="Monnier, Edouard" uniqKey="Monnier E" first="Edouard" last="Monnier">Edouard Monnier</name><name sortKey="Monnier, Edouard" sort="Monnier, Edouard" uniqKey="Monnier E" first="Edouard" last="Monnier">Edouard Monnier</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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