Research

• Geometric structures in Physics
  • Lagrangian and hamiltonian formalisms
  • Higher-order systems, time-dependent systems
  • Classical field theory
  • Singular differential equations
  • Symmetries and reduction
  • Geometric quantization
  • Supermanifolds
• Geometric methods in control theory
  • Control of mechanical systems
  • Geometric and algebraic control
  • Optimal control
  • Singular systems

Title: Geometry and Control: Applications in Physics and Technology (MTM2005-04947)
Supported by: Ministerio de Ciencia y Tecnología

Duration: 2006-2008

Main reseacher: Narciso Román Roy

• [FILE] M. Barbero-Liñan, A. Echeverria-Enriquez, D. Martin de Diego, M.C. Muñoz-Lecanda, N. Roman-Roy:  Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications, Preprint 2007

• [FILE] J.F. Cariñena, X. Gracia, G. Marmo, E. Martinez, M. Munoz-Lecanda, N.Roman-Roy: Geometric Hamilton-Jacobi Theory, Preprint (2006)

• [FILE] A. Echeverría-Enríquez, M. de León, M.C. Muñoz-Lecanda, N. Román-Roy: Hamiltonian systems in multisymplectic filed theory, Preprint 2005

• [FILE] A. Echeverría-Enríquez, L.A. Ibort, M.C. Muñoz-Lecanda, N. Román-Roy: Invariant forms and automorphisms of a class of multisymplectic manifolds, 2004

• [FILE] J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy : A new geometrical setting for the Hamilton-Jacobi equation, Procs. of the XIV Fall Workshop on Geometry and Physics, Bilbao (Spain), 2004.  to appear in  Publicaciones de la RSME (2006)

• [FILE] M.C. Muñoz-Lecanda, J. Yániz-Fernández: Control and Kinematic Systems, IEEE Transactions on Automatic control

  VOL. X, NO. X, X X, (2006)

• [FILE] M.C.Muñoz-Lecanda, M. Salgado, S. Vilariño: Nonstandar connections in k-cosymplectic field theory, J. Math. Phys. 46 (2005), 122901.

• [FILE] M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy: Pre-multisymplectic constraint algorithm for field theories, Int. J. Geom. Meth. Mod. Phys. 5(2) (2005) 839-871

• [FILE] A. Echeverría-Enríquez, M. de León, M.C. Muñoz-Lecanda, N. Román-Roy: Extended Hamiltonian formalism on fields theories: variational aspects and other topics, Seventh International Conference on Geometry, Integrability and Quantization June 2–10, 2005, Varna, Bulgaria Ivaïlo M. Mladenov and Manuel De Leon, Editors SOFTEX, Sofia 2005, pp 1–11

•  M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy: Constraint algorithm for singular field theories, Publicaciones de la Real Sociedad Matemática Española, 10 (2005), 233-239

• A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy: Symmetries and reduction in optimal control theory, Publicaciones de la Real Sociedad Matemática Española, 6 (2004), 203-208

• [FILE] M.C. Muñoz-Lecanda, F.J. Yániz Fernández: Mechanical Control Systems and Kinematic Systems,  Proceedings of the XI Fall Workshop on Differential Geometry and Applications, Publ. de la RSME (2004)

• [FILE] A. Echeverría-Enríquez, C. López, J. Marín-Solano, M.C. Muñoz-Lecanda and N. Román-Roy: Skinner-Rusk formulation in Classical Field Theory, Publicaciones de la Real Sociedad Matemática Española, 7 (2004), 211-216

• [FILE] X. Gràcia, M.C. Muñoz-Lecanda, N. Román-Roy: On some aspects of the geometry of differential geometry in Physics, Int. J. Geom.Meth. Mod. Phys. 1(3) (2004) 265-284

• [FILE] A. Echeverría-Enríquez, C. López, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy: Lagrangian-Hamiltonian unified formalism for field theory, J. Math. Phys. 45(1) (2004) 360-380

• [FILE] A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy: Geometric reduction in optimal control theory with symmetries, Rep. Math. Phys. 52(1) (2003) 89-113

• [FILE] X. Gràcia, J. Marín-Solano and M.C. Muñoz-Lecanda: Some geometric aspects of variational principles in constrained mechanics, Reports on Mathematical Physics,  51 (1) (2003), 127-148

• [FILE] A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy: On the construction of K-operators in field theories as sections along Legendre maps', Acta Appl. Math. 77(1) (2003) 1-40

• [FILE] A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy: On a kind of field operators in field theories, Publicaciones de la Real Sociedad Matemática Española, 4 (2003), 105-115

• [FILE] M.C. Muñoz-Lecanda, F.J. Yániz-Fernández: A global study of the stability of nonholonomic dynamical systems,  Lagrangian and Hamiltonian Methods in Nonlinear Control 2003 Proceedings of the 2nd IFAC Workshop, Seville, Spain, April 3-5 2003, Elsevier IFAC Publications (2003)

• M.C. Muñoz-Lecanda, N. Román-Roy, F.J. Yániz: Time-dependent Lagrangians invariant by a connection, Publicaciones de la Real Sociedad Matemática Española, 4 (2003), 215-223

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: A geometrical analysis of the field equations in field theories, Int. J. Math. and Math. Sciences 29(12) (2002), 687-700

• [FILE] M.C. Muñoz-Lecanda, J. Yániz-Fernández: Dissipative control of mechanical systems: A geometric approach, SIAM J. Control Optim. 40(5) (2002) 1505-1518.

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: Multivector Fields and Connections. Applications to field theories, Rev. R. Acad. Cien. Ser. A Math. 96(1) (2002), 83-93

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: A geometrical analysis of the field equations in field theories, Int. J. Maths. and Math. Sciences 29(12) (2002) 687-700

• [FILE] M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy: Singular Lagrangian systems on jet bundles, Fortsch. Phys. 50(2) (2002) 105-169

• [FILE] M.C. Muñoz-Lecanda, N. Román-Roy, F.J. Yániz: Time-dependent Lagrangians invariant by a vector field, Lett. Math. Phys. 57(2) (2001) 107-121

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: Equations and symmetries in covariant Hamiltonian field theories, Publicaciones de la Real Sociedad Matemática Española, 2 (2001), 55-66

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: Geometry of Multisymplectic Hamiltonian First-order Field Theories, J. Math. Phys. 41(11) (2000) 7402-7444

•  X. Gràcia, J. Marín-Solano, M.C. Muñoz-Lecanda: Variational principles in mechanics: Geometric aspects, in  Proceedings of the VII Fall Workshop on Differential Geometry and Applications, (2000), Publ. de la RSME I, ed., RSME, Madrid (2000) 81-94

• [FILE] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy: On the Multimomentum Bundles and the Legendre Maps in Field Theories, Rep. Math. Phys. 45(1) (2000) 85-105

• ALL PAPERS