High-order control for symplectic maps

Marco Sansottera, Antonio Giorgilli, Timoteo Carletti

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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
Etat de la publicationPublié - 1 janv. 2015

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur

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