Geodesic
The equivalence of controlled lagrangian and controlled hamiltonian systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 393-422

Voir la notice de l'article provenant de la source Numdam

The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity) on the hamiltonian side, which is the hamiltonian counterpart of a class of gyroscopic forces on the lagrangian side.

DOI : 10.1051/cocv:2002045
Classification : 34D20, 70H03, 70H05, 93D15
Keywords: controlled lagrangian, controlled hamiltonian, energy shaping, Lyapunov stability, passivity, equivalence 
@article{COCV_2002__8__393_0,
     author = {Chang, Dong Eui and Bloch, Anthony M. and Leonard, Naomi E. and Marsden, Jerrold E. and Woolsey, Craig A.},
     title = {The equivalence of controlled lagrangian and controlled hamiltonian systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {393--422},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002045},
     mrnumber = {1932957},
     zbl = {1070.70013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002045/}
}
TY  - JOUR
AU  - Chang, Dong Eui
AU  - Bloch, Anthony M.
AU  - Leonard, Naomi E.
AU  - Marsden, Jerrold E.
AU  - Woolsey, Craig A.
TI  - The equivalence of controlled lagrangian and controlled hamiltonian systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2002
SP  - 393
EP  - 422
VL  - 8
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002045/
DO  - 10.1051/cocv:2002045
LA  - en
ID  - COCV_2002__8__393_0
ER  - 
%0 Journal Article
%A Chang, Dong Eui
%A Bloch, Anthony M.
%A Leonard, Naomi E.
%A Marsden, Jerrold E.
%A Woolsey, Craig A.
%T The equivalence of controlled lagrangian and controlled hamiltonian systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2002
%P 393-422
%V 8
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002045/
%R 10.1051/cocv:2002045
%G en
%F COCV_2002__8__393_0
Chang, Dong Eui; Bloch, Anthony M.; Leonard, Naomi E.; Marsden, Jerrold E.; Woolsey, Craig A. The equivalence of controlled lagrangian and controlled hamiltonian systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 393-422. doi: 10.1051/cocv:2002045

Cité par Sources :