The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
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 kine...
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| Veröffentlicht in: | ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2002-06, Vol.8, p.393-422 |
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| container_title | ESAIM. Control, optimisation and calculus of variations |
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| creator | Chang, Dong Eui Bloch, Anthony M. Leonard, Naomi E. Marsden, Jerrold E. Woolsey, Craig A. |
| description | 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. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1051/cocv:2002045 |
| format | Article |
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| identifier | ISSN: 1292-8119 |
| ispartof | ESAIM. Control, optimisation and calculus of variations, 2002-06, Vol.8, p.393-422 |
| issn | 1292-8119 1262-3377 |
| language | eng |
| recordid | cdi_proquest_journals_896418560 |
| source | EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection; NUMDAM |
| subjects | Aerospace engineering Closed loop systems Energy Grants |
| title | The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems |
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