# The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems

Dong Eui Chang; Anthony M. Bloch; Naomi E. Leonard; Jerrold E. Marsden; Craig A. Woolsey

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 8, page 393-422
- ISSN: 1292-8119

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topChang, Dong Eui, et al. "The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 393-422. <http://eudml.org/doc/90654>.

@article{Chang2010,

abstract = {
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.
},

author = {Chang, Dong Eui, Bloch, Anthony M., Leonard, Naomi E., Marsden, Jerrold E., Woolsey, Craig A.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Controlled Lagrangian; controlled Hamiltonian; energy
shaping; Lyapunov stability; passivity; equivalence.; gyroscopic forces; equivalence; almost Poisson structures},

language = {eng},

month = {3},

pages = {393-422},

publisher = {EDP Sciences},

title = {The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems},

url = {http://eudml.org/doc/90654},

volume = {8},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 393

EP - 422

AB -
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.

LA - eng

KW - Controlled Lagrangian; controlled Hamiltonian; energy
shaping; Lyapunov stability; passivity; equivalence.; gyroscopic forces; equivalence; almost Poisson structures

UR - http://eudml.org/doc/90654

ER -

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