High-order control for symplectic maps

Résultats de recherche: Livre/Rapport/RevueAutre rapport

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Résumé

We revisit the problem of control for devices that can be modeled via a symplectic
map in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
langue originaleAnglais
EditeurNamur center for complex systems
Nombre de pages30
Volume2
Edition15
étatPublié - 1 janv. 2015

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur
Numéro15
Volume2

Empreinte digitale

Higher Order
Normal Form
Dynamical Behavior
Heuristics
Transform
Numerical Examples
Invariant
Term
Estimate

Citer ceci

Sansottera, M., Giorgilli, A., & Carletti, T. (2015). High-order control for symplectic maps. (15 Ed.) (naXys Technical Report Series; Vol 2, Numéro 15). Namur center for complex systems.
Sansottera, Marco ; Giorgilli, Antonio ; Carletti, Timoteo. / High-order control for symplectic maps. 15 Ed. Namur center for complex systems, 2015. 30 p. (naXys Technical Report Series; 15).
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title = "High-order control for symplectic maps",
abstract = "We revisit the problem of control for devices that can be modeled via a symplecticmap in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of H{\'e}non type.",
keywords = "dynamical systems, Normal forms method, Control of chaos, Hamiltonian control, Symplectic maps",
author = "Marco Sansottera and Antonio Giorgilli and Timoteo Carletti",
year = "2015",
month = "1",
day = "1",
language = "English",
volume = "2",
series = "naXys Technical Report Series",
publisher = "Namur center for complex systems",
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Sansottera, M, Giorgilli, A & Carletti, T 2015, High-order control for symplectic maps. naXys Technical Report Series, Numéro 15, VOL. 2, VOL. 2, 15 edn, Namur center for complex systems.

High-order control for symplectic maps. / Sansottera, Marco; Giorgilli, Antonio; Carletti, Timoteo.

15 Ed. Namur center for complex systems, 2015. 30 p. (naXys Technical Report Series; Vol 2, Numéro 15).

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

T1 - High-order control for symplectic maps

AU - Sansottera, Marco

AU - Giorgilli, Antonio

AU - Carletti, Timoteo

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We revisit the problem of control for devices that can be modeled via a symplecticmap in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.

AB - We revisit the problem of control for devices that can be modeled via a symplecticmap in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.

KW - dynamical systems

KW - Normal forms method

KW - Control of chaos

KW - Hamiltonian control

KW - Symplectic maps

M3 - Other report

VL - 2

T3 - naXys Technical Report Series

BT - High-order control for symplectic maps

PB - Namur center for complex systems

ER -

Sansottera M, Giorgilli A, Carletti T. High-order control for symplectic maps. 15 Ed. Namur center for complex systems, 2015. 30 p. (naXys Technical Report Series; 15).