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dc.contributor.author
Grillo, Sergio Daniel  
dc.contributor.author
Salomone, Leandro Martin  
dc.contributor.author
Zuccalli, Marcela  
dc.date.available
2019-06-12T23:19:14Z  
dc.date.issued
2017-12  
dc.identifier.citation
Grillo, Sergio Daniel; Salomone, Leandro Martin; Zuccalli, Marcela; On the relationship between the energy shaping and the Lyapunov constraint based methods; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 9; 4; 12-2017; 411-437  
dc.identifier.issn
1941-4889  
dc.identifier.uri
http://hdl.handle.net/11336/78163  
dc.description.abstract
In this paper, we make a review of the controlled Hamiltonians (CH) method and its related matching conditions, focusing on an improved version recently developed by D.E. Chang. Also, we review the general ideas around the Lyapunov constraint based (LCB) method, whose related partial differential equations (PDEs) were originally studied for underactuated systems with only one actuator, and then we study its PDEs for an arbitrary number of actuators. We analyze and compare these methods within the framework of Differential Geometry, and from a purely theoretical point of view. We show, in the context of control systems defined by simple Hamiltonian functions, that the LCB method and the Chang’s version of the CH method are equivalent stabilization methods (i.e. they give rise to the same set of control laws). In other words, we show that the Chang’s improvement of the energy shaping method is precisely the LCB method. As a by-product, coordinate-free and connection-free expressions of Chang’s matching conditions are obtained.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
American Institute of Mathematical Sciences  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
Control Systems  
dc.subject
Energy Shaping  
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Hamiltonian Systems  
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Higher-Order Constraints  
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Lyapunov Function  
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Matemática Pura  
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Matemáticas  
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CIENCIAS NATURALES Y EXACTAS  
dc.title
On the relationship between the energy shaping and the Lyapunov constraint based methods  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2019-06-11T15:22:19Z  
dc.identifier.eissn
1941-4897  
dc.journal.volume
9  
dc.journal.number
4  
dc.journal.pagination
411-437  
dc.journal.pais
Estados Unidos  
dc.description.fil
Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina  
dc.description.fil
Fil: Salomone, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina  
dc.description.fil
Fil: Zuccalli, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina  
dc.journal.title
Journal of Geometric Mechanics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3934/jgm.2017018  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://aimsciences.org//article/doi/10.3934/jgm.2017018  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1601.03975