Necessary conditions involving Lie brackets for impulsive optimal control problems; the commutative case

Maria Soledad Aronna 1, 2 Franco Rampazzo 3
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are considered as classical controls. This kind of system is called 'impulsive system'. We assume that the vector fields multiplying the derivatives of each component of the control are commutative. We derive new necessary conditions in terms of the adjoint state and the Lie brackets of the data functions.
Type de document :
Pré-publication, Document de travail
2012
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https://hal.inria.fr/hal-00800531
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 13 mars 2013 - 19:22:02
Dernière modification le : jeudi 12 avril 2018 - 01:45:37

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  • HAL Id : hal-00800531, version 1
  • ARXIV : 1210.4532

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Maria Soledad Aronna, Franco Rampazzo. Necessary conditions involving Lie brackets for impulsive optimal control problems; the commutative case. 2012. 〈hal-00800531〉

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