On the relationship between the energy shaping and the lyapunov constraint based methods

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 eq...

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Detalles Bibliográficos
Autores principales: Grillo, Sergio, Salomone, Leandro Martín, Zuccalli, Marcela
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2016
Materias:
Ciencias Exactas
Matemática
Control systems
Energy shaping
Hamiltonian systems
Higher-order constraints
Lyapunov function
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/87297
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-87297
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Matemática
Control systems
Energy shaping
Hamiltonian systems
Higher-order constraints
Lyapunov function
spellingShingle Ciencias Exactas
Matemática
Control systems
Energy shaping
Hamiltonian systems
Higher-order constraints
Lyapunov function
Grillo, Sergio
Salomone, Leandro Martín
Zuccalli, Marcela
On the relationship between the energy shaping and the lyapunov constraint based methods
topic_facet Ciencias Exactas
Matemática
Control systems
Energy shaping
Hamiltonian systems
Higher-order constraints
Lyapunov function
description 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.
format Articulo
Preprint
author Grillo, Sergio
Salomone, Leandro Martín
Zuccalli, Marcela
author_facet Grillo, Sergio
Salomone, Leandro Martín
Zuccalli, Marcela
author_sort Grillo, Sergio
title On the relationship between the energy shaping and the lyapunov constraint based methods
title_short On the relationship between the energy shaping and the lyapunov constraint based methods
title_full On the relationship between the energy shaping and the lyapunov constraint based methods
title_fullStr On the relationship between the energy shaping and the lyapunov constraint based methods
title_full_unstemmed On the relationship between the energy shaping and the lyapunov constraint based methods
title_sort on the relationship between the energy shaping and the lyapunov constraint based methods
publishDate 2016
url http://sedici.unlp.edu.ar/handle/10915/87297
work_keys_str_mv AT grillosergio ontherelationshipbetweentheenergyshapingandthelyapunovconstraintbasedmethods
AT salomoneleandromartin ontherelationshipbetweentheenergyshapingandthelyapunovconstraintbasedmethods
AT zuccallimarcela ontherelationshipbetweentheenergyshapingandthelyapunovconstraintbasedmethods
bdutipo_str Repositorios
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