Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 3

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Some geometrical properties of infinite-dimensional bilinear controlled systems

100%
Bensalem N., Pelletier F.
Banach Center Publications
|
1999
|
tom 50
|
nr 1
41-59
EN
The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim of this paper is to study "infinite bilinear systems" on Hilbert spaces for which such a solution always exists. Moreover, to this particular class of controlled systems a nilpotent Lie algebra of degree 2 is naturally associated. On the other hand, given a Hilbertian nilpotent Lie algebra G of degree 2 we can associate to it in a natural way a bilinear system corresponding to left invariant distributions on a connected Lie groups G whose Lie algebra is G. The first result we obtain is an accessibility one which can be considered as a version of Chow's theorem in this situation. If we consider infinite-dimensional time optimal controlled systems the optimal trajectories are always abnormal curves which can be defined as in the finite-dimensional case. The second result of this paper is to give a "localization" of such curves: each of them is actually "normal" in some induced system on a submanifold. Finally we illustrate these results in the case of classical infinite generalized Heisenberg algebras.
2
Content available remote

Singularities of implicit differential systems and maximum principle

100%
Janeczko S., Pelletier F.
Banach Center Publications
|
2003
|
tom 62
|
nr 1
117-132
EN
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 differential caustics are calculated.
3
Content available remote

Generalized PN manifolds and separation of variables

100%
Pelletier F., Cabau P.
Banach Center Publications
|
2008
|
tom 82
|
nr 1
163-181
EN
The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.