Ponències/Comunicacions de congressos
http://hdl.handle.net/2117/3205
2019-07-16T00:34:43ZCharacterization of accessibility for affine connection control systems at some points with nonzero velocity
http://hdl.handle.net/2117/16211
Characterization of accessibility for affine connection control systems at some points with nonzero velocity
Barbero Liñán, María
Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems
2012-07-09T14:57:53ZBarbero Liñán, MaríaAffine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systemsLie-algebroid formulation of k-cosymplectic classical field theories
http://hdl.handle.net/2117/11375
Lie-algebroid formulation of k-cosymplectic classical field theories
Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
The k-cosymplectic formalism is the generalization to field theories of the cosymplectic formalism, which is the geometric framework for describing non-autonomous dynamical systems.
In [5], A. Weinstein introduced a new geometric framework for giving a more generic description of Lagrangian mechanics. This approach was followed and completed by other authors for studying different kinds of problems concerning mechanical systems (a good survey on this subject is [1]). The extension of this formalism to classical field theories has been made, in [3] for the multisymplectic formalism.
This poster, which is based on the developments made in [4], is devoted to presenting a Hamiltonian k-cosymplectic description of field theories in terms of Lie algebroids.
2011-02-14T15:44:59ZRomán Roy, NarcisoSalgado, ModestoVilariño, SilviaThe k-cosymplectic formalism is the generalization to field theories of the cosymplectic formalism, which is the geometric framework for describing non-autonomous dynamical systems.
In [5], A. Weinstein introduced a new geometric framework for giving a more generic description of Lagrangian mechanics. This approach was followed and completed by other authors for studying different kinds of problems concerning mechanical systems (a good survey on this subject is [1]). The extension of this formalism to classical field theories has been made, in [3] for the multisymplectic formalism.
This poster, which is based on the developments made in [4], is devoted to presenting a Hamiltonian k-cosymplectic description of field theories in terms of Lie algebroids.Optimal control problems for affine connection control systems: characterization of extremals
http://hdl.handle.net/2117/1646
Optimal control problems for affine connection control systems: characterization of extremals
Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos
Pontryagin’s Maximum Principle [8] is considered as an outstanding achievement of
optimal control theory. This Principle does not give sufficient conditions to compute an optimal
trajectory; it only provides necessary conditions. Thus only candidates to be optimal trajectories,
called extremals, are found. Maximum Principle gives rise to different kinds of them and, particularly,
the so-called abnormal extremals have been studied because they can be optimal, as Liu and
Sussmann, and Montgomery proved in subRiemannian geometry [5, 7].
We build up a presymplectic algorithm, similar to those defined in [2, 3, 4, 6], to determine
where the different kinds of extremals of an optimal control problem can be. After describing such
an algorithm, we apply it to the study of extremals, specially the abnormal ones, in optimal control
problems for affine connection control systems [1]. These systems model the motion of different
types of mechanical systems such as rigid bodies, nonholonomic systems and robotic arms [1].
2008-02-19T17:32:13ZBarbero Liñán, MaríaMuñoz Lecanda, Miguel CarlosPontryagin’s Maximum Principle [8] is considered as an outstanding achievement of
optimal control theory. This Principle does not give sufficient conditions to compute an optimal
trajectory; it only provides necessary conditions. Thus only candidates to be optimal trajectories,
called extremals, are found. Maximum Principle gives rise to different kinds of them and, particularly,
the so-called abnormal extremals have been studied because they can be optimal, as Liu and
Sussmann, and Montgomery proved in subRiemannian geometry [5, 7].
We build up a presymplectic algorithm, similar to those defined in [2, 3, 4, 6], to determine
where the different kinds of extremals of an optimal control problem can be. After describing such
an algorithm, we apply it to the study of extremals, specially the abnormal ones, in optimal control
problems for affine connection control systems [1]. These systems model the motion of different
types of mechanical systems such as rigid bodies, nonholonomic systems and robotic arms [1].