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  • k -Symplectic Pontryagin¿s Maximum Principle for some families of PDEs

     Barbero Liñan, Maria; Muñoz Lecanda, Miguel Carlos
    Calculus of variations and partial differential equations
    Date of publication: 2014-03-04
    Journal article

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    An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature k -symplectic formalism is used to provide the optimal control problems associated to some families of partial differential equations with a geometric formulation. A parallel between the classic formalism of optimal control theory with ordinary differential equations and the one with particular families of partial differential equations is established. This description allows us to state and prove Pontryagin¿s Maximum Principle on k -symplectic formalism. We also consider the unified Skinner-Rusk formalism for optimal control problems governed by an implicit partial differential equation.

  • The generating function of a canonical transformation

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2013-01-14
    Journal article

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  • Invariant forms and automorphisms of locally homogeneous multisymplectic manifolds

     Echeverría-Enríquez, Arturo; Ibort, Alberto; Muñoz Lecanda, Miguel Carlos; Román-Roy, Narciso
    Journal of Geometric Mechanics
    Date of publication: 2012-12
    Journal article

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    Kinematic reduction and the Hamilton-Jacobi equation  Open access

     Barbero Liñan, Maria; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos
    Journal of Geometric Mechanics
    Date of publication: 2012
    Journal article

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    A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces.

    A close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces.

  • Geometría de sistemas físicos y de control y aplicaciones

     Gracia Sabate, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Franch Bullich, Jaime; Roman Roy, Narciso
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  • Variational principles for spin systems and the Kirchhoff rod

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2011-05
    Journal article

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  • Routhian reduction for quasi-invariant Lagrangians

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2011-09
    Journal article

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  • Presymplectic high order maximum principle

     Barbero-Liñán, María; Muñoz Lecanda, Miguel Carlos
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
    Date of publication: 2011
    Journal article

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  • Review on the paper "Null Lagrangian forms and Euler-Lagrange PDEs. "

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2010-05
    Journal article

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    Strict abnormal extremals in nonholonomic and kinematic control systems  Open access

     Barbero-Liñán, María; Muñoz Lecanda, Miguel Carlos
    Discrete and continuous dynamical systems. Series S (paper)
    Date of publication: 2010-03
    Journal article

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    In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost function. We focus on control systems such as nonholonomic control mechanical systems and the associated kinematic systems as long as they are equivalent. With all this in mind, first we study conditions to relate an optimal control problem for the mechanical system with another one for the associated kinematic system. Then, Pontryagin's Maximum Principle will be used to connect the abnormal extremals of both optimal control problems. An example is given to glimpse what the abnormal solutions for kinematic systems become when they are considered as extremals to the optimal control problem for the corresponding nonholonomic mechanical systems.

  • GEOMETRIC HAMILTON-JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS

     Cariñena Marzo, José Fernando; Gracia Sabate, Francesc Xavier; Marmo, Giusseppe; Muñoz Lecanda, Miguel Carlos; Martínez, E; Roman Roy, Narciso
    International journal of geometric methods in modern physics
    Date of publication: 2010-05
    Journal article

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  • A class of self-concordant functions on Riemannian manifolds

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2010-12
    Journal article

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  • K-symplectic and k-cosymplectic lagrangian field theories: some interesting examples and applications

     Muñoz Lecanda, Miguel Carlos; Salgado Seco, Modesto; Vilariño, Silvia
    International journal of geometric methods in modern physics
    Date of publication: 2010-06
    Journal article

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  • Ciencia en Acción 2010

     Ros Ferre, Rosa Maria; Muñoz Lecanda, Miguel Carlos; Lazaro Ochoa, Jose Tomas
    Participation in a competitive project

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    Hamilton-Jacobi theory and the evolution operator  Open access

     Cariñena Marzo, José Fernando; Gracia Sabate, Francesc Xavier; Martínez Fernández, Eduardo; Marmo, Giuseppe; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date of publication: 2009
    Book chapter

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    We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in [7], and can be applied to the case of singular Lagrangian dynamical systems.

  • Ciencia en Acción: Trabajos de divulgación científica en soportes adecuados

     Roman Roy, Narciso; Muñoz Lecanda, Miguel Carlos; Padrón Fernández, Edith
    Award or recognition

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  • Lie algebroids and optimal control: abnormality

     Barbero Liñan, Maria; Diego, de DM; Muñoz Lecanda, Miguel Carlos
    AIP Conference proceedings
    Date of publication: 2009-01
    Journal article

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    Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems  Open access

     Gracia Sabate, Francesc Xavier; Giuseppe, Marmo; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2009-08
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    The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered.

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    Constraint algorithm for extremals in optimal control  Open access

     Barbero-Liñán, María; Muñoz Lecanda, Miguel Carlos
    International journal of geometric methods in modern physics
    Date of publication: 2009-07
    Journal article

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    A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand.

  • ALGORITMOS GEOMETRICOS DE LIGADURAS Y REDUCCION EN SISTEMAS DINAMICOS, FISICA Y CONTROL

     Herrero Izquierdo, Jose; Gracia Sabate, Francesc Xavier; Barbero Liñan, Maria; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
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  • GEOMETRIA DIFERENCIAL SISTEMES DINAMICS I APLIC

     Herrero Izquierdo, Jose; Roman Roy, Narciso; Gracia Sabate, Francesc Xavier; Barbero Liñan, Maria; Ros Ferre, Rosa Maria; Muñoz Lecanda, Miguel Carlos
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  • A GEOMETRIC STUDY OF ABNORMALITY IN OPTIMAL CONTROL PROBLEMS FOR CONTROL AND MECHANICAL CONTROL SYSTEMS  Open access  awarded activity

     Barbero Liñan, Maria
    Defense's date: 2008-12-19
    School of Mathematics and Statistics (FME), Universitat Politècnica de Catalunya
    Theses

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    Durant els darrers quaranta anys la geometria diferencial ha estat una eina fonamental per entendre la teoria de control òptim. Habitualment la millor estratègia per resoldre un problema és transformar-lo en un altre problema que sigui més tractable. El Principi del Màxim de Pontryagin proporciona al problema de control òptim d’una estructura Hamiltoniana. Les solucions del problema Hamiltonià que satisfan unes determinades propietats són candidates a ésser solucions del problema de control òptim. Aquestes corbes candidates reben el nom d’extremals. Per tant, el Principi del Màxim de Pontryagin aixeca el problema original a l’espai cotangent. En aquesta tesi desenvolupem una demostració completa i geomètrica del Principi del Màxim de Pontryagin. Investiguem cuidadosament els punts més delicats de la demostració, que per exemple inclouen les perturbacions del controls, l’aproximació lineal del conjunt de punts accessibles i la condició de separació. Entre totes les solucions d’un problema de control òptim, existeixen les corbes anormals. Aquestes corbes no depenen de la funció de cost que es vol minimitzar, sinó que només depenen de la geometria del sistema de control. En la literatura de control òptim, existeixen estudis sobre l’anormalitat, tot i que només per a sistemes lineals o afins en el controls i sobretot amb funcions de cost quadràtiques en els controls. Nosaltres descrivim un mètode geomètric nou per caracteritzar tots els diferents tipus d’extremals (no només les anormals) de problemes de control òptim genèrics. Aquest mètode s’obté com una adaptació d’un algoritme de lligadures presimplèctic. El nostre interès en les corbes anormals es degut a les corbes òptimes estrictament anormals, les quals també queden caracteritzades mitjançant l’algoritme descrit en aquesta tesi. Com aplicació del mètode mencionat, caracteritzem les extremals d’un problema de control òptim lliure, aquell on el domini de definició no està donat. En concret, els problemes de temps mínim són problemes de control òptim lliures. A més a més, som capaços de donar una corba extremal estrictament anormal aplicant el mètode descrit per a un sistema mecànic. Un cop la noció d’anormalitat ha estat estudiada en general, ens concentrem en l’estudi de l’anormalitat per a sistemes de control mecànics, perquè no existeixen resultats sobre l’existència de corbes òptimes estrictament anormals per a problemes de control òptim associats a aquests sistemes. En aquesta tesi es donen resultats sobre les extremals anormals quan la funció de cost és quadràtica en els controls o si el funcional a minimitzar és el temps. A més a més, la caracterització d’anormals en casos particulars és descrita mitjançant elements geomètrics com les formes quadràtiques vector valorades. Aquests elements geomètrics apareixen com a resultat d’aplicar el mètode descrit en aquesta tesi. També tractem un altre enfocament de l’estudi de l’anormalitat de sistemes de control mecànics, que consisteix a aprofitar l’equivalència que existeix entre els sistemes de control noholònoms i els sistemes de control cinemàtics. Provem l’equivalència entre els problemes de control òptim associats a ambdós sistemes de control i això permet establir relacions entre les corbes extremals del problema nonholònom i del cinemàtic. Aquestes relacions permeten donar un example d’una corba òptima estrictament anormal en un problema de temps mínim per a sistemes de control mecànics. Finalment, i deixant de banda per un moment l’anormalitat, donem una formulació geomètrica dels problemes de control òptim no autònoms mitjançant la formulació unificada de Skinner-Rusk. La formulació descrita en aquesta tesis és fins i tot aplicable a sistemes de control implícits que apareixen en un gran nombre de problemes de control òptim dins de l’àmbit de l’enginyeria, com per exemple els sistemes Lagrangians controlats i els sistemes descriptors.

    Durante los últimos cuarenta años la geometría diferencial ha sido una herramienta para entender la teoría de control óptimo. Habitualmente la mejor estrategia para resolver un problema es transformarlo en otro problema que sea más tratable. El Principio del Máximo de Pontryagin dota al problema de control óptimo de una estructura Hamiltoniana. Las soluciones del problema Hamiltoniano que satisfagan determinadas propiedades son candidatas a ser soluciones del problema de control óptimo. Estas curvas candidatas se llaman extremales. Por lo tanto, el Principio del Máximo de Pontryagin levanta el problema original al espacio cotangente. En esta tesis doctoral, desarrollamos una demostración completa y geométrica del Principio del Máximo de Pontryagin. Investigamos minuciosamente los puntos delicados de la demostración, como son las perturbaciones de los controles, la aproximación lineal del conjunto de puntos alcanzables y la condición de separación. Entre todas las soluciones de un problema de control óptimo, existen las curvas anormales. Estas curvas no dependen de la función de coste que se quiere minimizar, sino que sólo dependen de la geometría del sistema de control. En la literatura de control óptimo existen estudios sobre la anormalidad, aunque sólo para sistemas lineales o afines en los controles y fundamentalmente con funciones de costes cuadráticas en los controles. Nosotros presentamos un método geométrico nuevo para caracterizar todos los distintos tipos de extremales (no sólo las anormales) de problemas de control óptimo genéricos. Este método es resultado de adaptar un algoritmo de ligaduras presimpléctico. Nuestro interés en las extremales anormales es debido a las curvas óptimas estrictamente anormales, las cuales también pueden ser caracterizadas mediante el algoritmo descrito en esta tesis. Como aplicación del método mencionado en el párrafo anterior, caracterizamos las extremales de un problema de control óptimo libre, aquél donde el dominio de definición de las curvas no está dado. En particular, los problemas de tiempo óptimo son problemas de control óptimo libre. Además, somos capaces de dar un ejemplo de una curva extremal estrictamente anormal aplicando el método descrito. Una vez la noción de anormalidad en general ha sido estudiada, nos centramos en el estudio de la anormalidad para sistemas de control mecánicos, ya que no existen resultados sobre la existencia de curvas óptimales estrictamente anormales para problemas de control óptimo asociados a estos sistemas. En esta tesis, se dan resultados sobre las extremales anormales cuando la función de coste es cuadrática en los controles o el funcional a minimizar es el tiempo. Además, la caracterización de las anormales en casos particulares es descrita por medio de elementos geométricos como las formas cuadráticas vector valoradas. Dichos elementos geométricos aparecen como consecuencia del método descrito para caracterizar las extremales. También se considera otro enfoque para el estudio de la anormalidad de sistemas de control mecánicos, que consiste en aprovechar la equivalencia que existe entre sistemas de control noholónomos y sistemas de control cinemáticos. Se prueba la equivalencia entre problemas de control óptimo asociados a ambos sistemas de control, lo que permite establecer relaciones entre las extremales del problema noholónomo y las extremales del problema cinemático. Estas relaciones permiten dar un ejemplo de una curva optimal estrictamente anormal en un problema de tiempo óptimo para sistemas de control mecánicos. Por último, olvidándonos por un momento de la anormalidad, se describe una formulación geométrica de los problemas de control óptimo no autónomos aprovechando la formulación unificada de Skinner-Rusk. Esta formulación es incluso válida para sistemas de control implícitos que aparecen en numerosos problemas de control óptimo de ámbito ingenieril, como por ejemplo, los sistemas Lagrangianos controlados y los sistemas descriptores.

    For the last forty years, differential geometry has provided a means of understanding optimal control theory. Usually the best strategy to solve a difficult problem is to transform it into a different problem that can be dealt with more easily. Pontryagin's Maximum Principle provides the optimal control problem with a Hamiltonian structure. The solutions to the Hamiltonian problem, satisfying particular conditions, are candidates to be solutions to the optimal control problem. These candidates are called extremals. Thus, Pontryagin's Maximum Principle lifts the original problem to the cotangent bundle. In this thesis, we develop a complete geometric proof of Pontryagin's Maximum Principle. We investigate carefully the crucial points in the proof such as the perturbations of the controls, the linear approximation of the reachable set and the separation condition. Among all the solutions to an optimal control problem, there exist the abnormal curves. These do not depend on the cost function we want to minimize, but only on the geometry of the control system. Some work has been done in the study of abnormality, although only for control-linear and control-affine systems with mainly control-quadratic cost functions. Here we present a novel geometric method to characterize all the different kinds of extremals (not only the abnormal ones) in general optimal control problems. This method is an adaptation of the presymplectic constraint algorithm. Our interest in the abnormal curves is with the strict abnormal minimizers. These last minimizers can be characterized by the geometric algorithm presented in this thesis. As an application of the above-mentioned method, we characterize the extremals for the free optimal control problems that include, in particular, the time-optimal control problem. Moreover, an example of an strict abnormal extremal for a control-affine system is found using the geometric method. Furthermore, we focus on the description of abnormality for optimal control problems for mechanical control systems, because no results about the existence of strict abnormal minimizers are known for these problems. Results about the abnormal extremals are given when the cost function is control-quadratic or the time must be minimized. In this dissertation, the abnormality is characterized in particular cases through geometric constructions such as vectorvalued quadratic forms that appear as a result of applying the previous geometric procedure. The optimal control problems for mechanical control systems are also tackled taking advantage of the equivalence between nonholonomic control systems and kinematic control systems. In this thesis, it is found an equivalence between time-optimal control problems for both control systems. The results allow us to give an example of a local strict abnormal minimizer in a time-optimal control problem for a mechanical control system. Finally, setting aside the abnormality, the non-autonomous optimal control problem is described geometrically using the Skinner-Rusk unified formalism. This approach is valid for implicit control systems that arise in optimal control problems for the controlled Lagrangian systems and for descriptor systems. Both systems are common in engineering problems.

  • Abnormality for a?ne connection control systems in the Special Session

     Muñoz Lecanda, Miguel Carlos
    Mathematical Theory of Networks and Systems MTNS
    Presentation's date: 2008-07-28
    Presentation of work at congresses

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  • Unified formalism for nonautonomous mechanical systems

     Barbero-Linan, M; Barbero Liñan, Maria; Echeverria-Enriquez, A; Diego, De D M; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Journal of mathematical physics
    Date of publication: 2008-06
    Journal article

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  • Mechanical control systems and kinematic systems

     Muñoz Lecanda, Miguel Carlos; Yániz-Fernández, F J
    IEEE transactions on automatic control
    Date of publication: 2008-06
    Journal article

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  • Geometric approach to Pontryagin's Maximum Principle

     Barbero Liñan, Maria; Muñoz Lecanda, Miguel Carlos
    Acta applicandae mathematicae
    Date of publication: 2008-10
    Journal article

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  • Review on the book "Mechanics in differential geometry"

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2008-03
    Journal article

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  • Unified formalism for non-autonomous mechanical systems

     Barbero-Liñán, María; a-Enríquez, Arturo Echeverrí; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2008-03
    Report

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  • Review on "Chetaev versus vakonomic prescriptions in constrained field theories with parametrized variational calculus "

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2008-10
    Journal article

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  • La mujer: elemento innovador en la ciencia

     Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2008
    Report

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    El proyecto "La mujer, innovadora en la Ciencia" se puso en marcha con motivo del año de la Ciencia (2007) como una iniciativa de la Comisión de Mujeres Matemáticas de la Real Sociedad Matemática Española, encargándose del desarrollo un equipo de trabajo integrado por Ainhoa Berciano (Universidad del País Vasco), Carmen Jalón (CEP Luisa Revuelta de Córdoba), Josefina Ling (Universidad de Santiago de Compostela), Marta Macho (Universidad del País Vasco), Mª Isabel Marrero (Universidad de La Laguna), Miguel Muñoz (Universidad Politécnica de Cataluña), Edith Padrón (Universidad de La Laguna), Narciso Román (Universidad Politécnica de Cataluña), Mónika Sánchez (IES Beatriz Galindo), Teresa Valdecantos (SIPFA Algeciras, Cádiz) y Elena Vázquez (Universidad de Santiago de Compostela).

  • Skinner-Rusk unified formalism for optimal control systems and applications

     Barbero, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2007-05
    Report

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  • Red Temática "Geometría, Mecánica y Control"

     Marrero González, Juan Carlos; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
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  • Skinner-Rusk unified formalism for optimal control systems and applications

     Barbero Liñan, Maria; ECHEVERRÍA-ENRÍQUEZ, ARTURO; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Journal of physics A. Mathematical and theoretical
    Date of publication: 2007-09
    Journal article

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  • Extended Hamiltonian systems in multisymplectic field theories

     ECHEVERRÍA-ENRÍQUEZ, ARTURO; Manuel, De León; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Journal of mathematical physics
    Date of publication: 2007-11
    Journal article

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  • Optimal control problems for affine connection control systems: characterization of extremals

     Barbero, M; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    GEOMETRY AND PHYSICS: XVI International Fall Workshop
    Presentation of work at congresses

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  • Skinner-Rusk formalism for optimal control

     Barbero Liñan, Maria; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2006-12
    Report

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  • Skinner-Rusk formalism for optimal control

     Barbero, M; ECHEVERRÍA-ENRÍQUEZ, A; Martín, D de Diego; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    XV Fall Workshop on Geometry and Physics
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  • Review on the papaer "A generalized Poisson algebra structure on manifold: conserved quantities in $N$-body problem. "

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2006-05
    Journal article

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  • Geometric Hamilton-Jacobi theory

     Cariñena Marzo, José Fernando; Gracia Sabate, Francesc Xavier; Marmo, G; Martínez, E; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    International journal of geometric methods in modern physics
    Date of publication: 2006-11
    Journal article

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    Geometric Hamilton?Jacobi Theory  Open access

     Cariñena Marzo, José Fernando; Gracia Sabate, Francesc Xavier; Giuseppe, Marmo; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Date: 2006-05
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    The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints. We also consider the example of the free relativistic particle, the rigid body and the electron-monopole system.

  • Review on the paper " Gauss-type curvatures and tubes for polyhedral surfaces. "

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2006-07
    Journal article

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  • Extended Hamiltonian formalism of field theories. Variational aspects and other topics

     Echeverría Enríquez, Arturo; León, Manuel de; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    7th International Conference on Geometry, Integrability and Quantization
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  • A new geometrical setting for the Hamilton-Jacobi equation

     Cariñena Marzo, José Fernando; Gracia Sabate, Francesc Xavier; Marmo, G; Martínez, E; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    XIV Fall Workshop on Geometry and Physics
    Presentation of work at congresses

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  • MTM2005-04947 GEOMETRÍA Y CONTROL: APLICACIONES EN FÍSICA Y TECNOLOGÍA

     Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    Participation in a competitive project

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  • Red Temática "Geometría, Mecánica y Control"

     Muñoz Lecanda, Miguel Carlos; Marrero González, Juan Carlos; Roman Roy, Narciso
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  • Review on the paper "Real Hamiltonian forms of Hamiltonian systems"

     Muñoz Lecanda, Miguel Carlos
    Mathematical reviews
    Date of publication: 2005-09
    Journal article

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  • Nonstandard connections in $k$-cosymplectic field theory

     Muñoz Lecanda, Miguel Carlos; Vilariño, Silvia; Modesto(E-Sacom-Gt), Salgado
    Journal of mathematical physics
    Date of publication: 2005-12
    Journal article

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  • Pre-multisymplectic constraint algorithm for field theories

     León, M de; Marín, J; Marrero, J C; Muñoz Lecanda, Miguel Carlos; Roman Roy, Narciso
    International journal of geometric methods in modern physics
    Date of publication: 2005-11
    Journal article

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