Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 29 May 2020 18:10:00 GMT2020-05-29T18:10:00Z5091Optimal control and quasi-velocitieshttp://hdl.handle.net/10316/13713Title: Optimal control and quasi-velocities
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Cariñena, José F.; Clemente-Gallardo, Jesús; Martínez, Eduardo; Santos, Patricia
Abstract: In this paper we study optimal control problems for nonholonomic systems
defined on Lie algebroids by using quasi-velocities. We consider both kinemactic,
i.e. systems whose cost functional depends only on position and velocities, and
dynamic optimal control problems, i.e. systems whose cost functional depends also
on accelarations. Formulating the problem directly at the level of Lie algebroids
turns out to be the correct framework to explain in detail similar results appeared
recently [48]. We also provide several examples to illustrate our construction
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137132010-01-01T00:00:00ZCorrigendum: Cubic polynomials on Lie groups: reduction of the Hamiltonian systemhttp://hdl.handle.net/10316/44963Title: Corrigendum: Cubic polynomials on Lie groups: reduction of the Hamiltonian system
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Clemente-Gallardo, Jesús
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449632013-01-01T00:00:00ZGeometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Accelerationhttp://hdl.handle.net/10316/44982Title: Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Clemente-Gallardo, Jesús
Abstract: In this work we consider a second order variational problem depending on the covariant acceleration, which is related with the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of the Pontryagin's maximum principle, allows us to study the dynamics of the control problem.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449822013-01-01T00:00:00ZRelating Lagrangian and Hamiltonian formalisms of LC circuitshttp://hdl.handle.net/10316/12913Title: Relating Lagrangian and Hamiltonian formalisms of LC circuits
Authors: Clemente-Gallardo, Jesús; Scherpen, Jacquelien M. A.
Abstract: The Lagrangian formalism defined by Scherpen et al. (2000) for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other Hamiltonian approaches is also analyzed and interpreted
Wed, 01 Oct 2003 00:00:00 GMThttp://hdl.handle.net/10316/129132003-10-01T00:00:00ZMotion on lie groups and its applications in control theoryhttp://hdl.handle.net/10316/4074Title: Motion on lie groups and its applications in control theory
Authors: Cariñena, José F.; Clemente-Gallardo, Jesús; Ramos, Arturo
Abstract: The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the method proposed by Wei and Norman for linear systems, and a reduction procedure. This last method allows us to reduce the equation on a Lie group G to that on a subgroup H, provided a particular solution of an associated problem in G/H is known. These methods are shown to be very appropriate to deal with control systems on Lie groups and homogeneous spaces, through the specific examples of the planar rigid body with two oscillators and the front-wheel driven kinematic car.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/40742003-01-01T00:00:00ZCubic polynomials and optimal control on compact Lie groupshttp://hdl.handle.net/10316/11187Title: Cubic polynomials and optimal control on compact Lie groups
Authors: Abrunheiro, L.; Camarinha, M.; Clemente-Gallardo, J.
Abstract: This paper analyzes the Riemannian cubic polynomials’s problem from
a Hamiltonian point of view. The description of the problem on compact Lie groups
is particulary explored. The state space of the second order optimal control problem
considered is the tangent bundle of the Lie group which also has a group structure.
The dynamics of the problem is described by a presymplectic formalism associated
with the canonical symplectic form on the cotangent bundle of the tangent bundle.
Using these control geometrical tools, the equivalence between the Hamiltonian
approach developed here and the known variational one is verified. Moreover, the
equivalence allows us to deduce two invariants along the cubic polynomials which
are in involution.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111872009-01-01T00:00:00ZDirac-Nijenhuis structureshttp://hdl.handle.net/10316/11433Title: Dirac-Nijenhuis structures
Authors: Clemente-Gallardo, J.; Costa, J. M. Nunes da
Abstract: We introduce the concept of Dirac-Nijenhuis structures as those manifolds
carrying a Dirac structure and admitting a deformation by Nijenhuis operators
which is compatible with it. This concept generalizes the notion of Poisson-Nijenhuis
structure and can be adapted to include the Jacobi-Nijenhuis case.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114332003-01-01T00:00:00ZJacobi manifolds, Dirac structures and Nijenhuis operatorshttp://hdl.handle.net/10316/11406Title: Jacobi manifolds, Dirac structures and Nijenhuis operators
Authors: Clemente-Gallardo, J.; Costa, J. M. Nunes da
Abstract: In a recent paper [2], we studied the concept of Dirac-Nijenhuis structures.
We de ned them as deformations of the canonical Lie algebroid structure of
a Dirac bundle D de ned in the double of a Lie bialgebroid (A;A¤) which satisfy
certain properties. In this paper, we introduce the concept of generalized Dirac-
Nijenhuis structures as the natural analogue when we replace the double of the Lie
bialgebroid by the double of a generalized Lie bialgebroid. We also show the usefulness
of the concept by proving that a Jacobi-Nijenhuis manifold has an associated
generalized Dirac-Nijenhuis structure of a certain type.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114062004-01-01T00:00:00ZDirac structures for generalized Lie bialgebroidshttp://hdl.handle.net/10316/11434Title: Dirac structures for generalized Lie bialgebroids
Authors: Costa, M. Nunes da; Clemente-Gallardo, J.
Abstract: We introduce the notion of Dirac structure for a generalized Courant
algebroid. We show that the double of a generalized Lie bialgebroid is a generalized
Courant algebroid. We present some examples and we obtain, as a particular case
of our definition, the notion of E1(M)-Dirac structure introduced by Wade.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114342003-01-01T00:00:00Z