Artículo
On the relationship between the energy shaping and the Lyapunov constraint based methods
Fecha de publicación:
12/2017
Editorial:
American Institute of Mathematical Sciences
Revista:
Journal of Geometric Mechanics
ISSN:
1941-4889
e-ISSN:
1941-4897
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Articulos(CCT - LA PLATA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - LA PLATA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - LA PLATA
Citación
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
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