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Singularities of implicit differential systems and maximum principle

Stanisław Janeczko, Fernand Pelletier (2003)

Banach Center Publications

The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding...

Snakes and articulated arms in an Hilbert space

Fernand Pelletier, Rebhia Saffidine (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.

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