Control Theory and Calculus of Variations

cotg MR Papers

Project's objectives:

  • To obtain new versions of Pontryagin s maximum principle covering classes of generalized controls; to give geometric characterizations of generalized extremals and accessible sets; to investigate singular optimal control problems; to obtain explicit formulas for the Chen logarithm and develop a formal control theory with applications to stabilizability and noncommutative symmetric functions; to obtain conditions for boundedness of optimal controls; to investigate the role of symmetry and conservation laws.

  • Extension of Noether s theorem of the calculus of variations to the wider class of Lipschitz functions, and obtain a corresponding formulation for higher-order variational problems; to obtain conserved quantities along all minimizers of the problems; to identify new and more general classes of well and bad behaved problems in the calculus of variations.

  • To study systems of rolling bodies by designing time-variant feedback stabilizers with possible application to robotic manipulators; to develop a computer algebra package for determining symmetries and conservation laws in the calculus of variations and optimal control; to prove convergence of digital arithmetic algorithms by using results on feedback stabilization; develop numerical and asymptotical methods to study nonlinear dynamical control systems with distributed and discrete parameters, decreasing the effect of vibrations.


  • Members

    Scientific Reports

  • Research plans for 2003-2005 and cotg Final Report 2003 (Details)

  • cotg Final Report 2004 (Details)

  • cotg Final Report 2005 (Details)

  • cotg Final Report 2006 (Details)

  • cotg Report 2003-2006 (Details)

  • cotg Future Research for the period 2007-2010 (Details)



  • Post-Docs

  • 2004-2007 Olena Vladlenivna Mul
    Associate Professor of Physics and Mathematics
    Ternopil Academy of National Economy, Ukraine

    Scientific Coordinator: Delfim F. M. Torres

    Title of Project: Analysis of Vibrations in Nonlinear Dynamical Systems

    Funding: FCT SFRH/BPD/14946/2004

    Project for 2004-2005 (Details)

    Final report 2004-2005 and Working plans for 2005-2006 (Details)

    Final report 2005-2006 and Working plans for 2006-2007 (Details)

    Final report 2007 (Details)



  • 2005-2008 Rachid Sidi Ammi

    Scientific Coordinator: Delfim F. M. Torres

    Funding: FCT SFRH/BPD/20934/2004

    Project for 2005-2006 (Details)

    Final Report 2005-2006 and Working plans for 2006-2007 (Details)



  • European Projects for PhD students

  • January-July 2005
    Ilona Dzenite ( Doctoral student certificate)
    PhD student at Riga Technical University, Latvia
    Home Supervisor: Prof. Maximilian Ya. Antimirov
    Scientific Coordinator (Host Supervisor): Delfim F. M. Torres
    Title of Project: Impedance Change and the Calculus of Variations
    Funding: Marie Curie Fellowship, CTS (Control Training Site)

    Project for 2004-2005 (Details and Annex 3)

    Final report 2005 (Details)

    Project for 2005-2006 (Details)



  • March-July 2005
    Elena Ligere
    PhD student at Riga Technical University, Latvia
    Home Supervisor: Prof. Maximilian Ya. Antimirov
    Scientific Coordinator (Host Supervisor): Delfim F. M. Torres
    Title of Project: Analytical solutions to some magnetohydrodynamical control problems on a flow of conducting fluid
    Funding: Marie Curie Fellowship, CTS (Control Training Site)

    Project Details

    Final report 2005 (Details)



  • Projects

  • Project "Application of Conservation Laws to Space Trajectography"

    between the University of Aveiro and the University Paris XI, Actions Universitaires Intégrées Luso-Françaises

    Project Details

    Final Report (Details)



  • Cooperation with the Faculty of Computer Science of the Bialystok Technical University

    Framework Agreement on Cooperation (Details)

    Work plan for 2007-2008 (Details)



  • PhD projects

  • Concluded with success in 2008
    Paulo Duarte Ferreira Gouveia
    Symbolic Computation in Static and Dynamic Optimization
    Supervisor: Delfim F. M. Torres and Alexander Plakhov

    Project Details (1 and 2)


  • Since 2005
    Cristiana Silva
    Optimal syntheses of nonlinear optimal control problems involving state constraints, and conjugate points
    Supervisors: Delfim F. M. Torres and Emmanuel Trélat
    Funding: FCT SFRH/BD/27272/2006

    Project Details


  • Since 2005
    Gastão Silves Ferreira Frederico
    Supervisors: Delfim F. M. Torres
    Funding: IPAD (Instituto Português de Apoio ao Desenvolvimento)


  • MSc projects

  • Concluded with success in 2005
    Cristiana Silva
    MSc on Mathematics - Analysis and Geometry
    Thesis: On the Calculus of Variations and Optimal Control Approaches to Newton's Problem of Minimal Resistance
    Supervisor: Delfim F. M. Torres

    Details


  • Concluded with success in 2006
    Andreia M. F. Louro
    MSc on Mathematics
    Thesis: Computação Simbólica em Maple no Cálculo das Variações
    Supervisor: Delfim F. M. Torres

    Details


  • Concluded with success in 2006
    Joana F. Costa
    MSc on Mathematics
    Thesis: Teorema de Noether do Cálculo das Variações e do Controlo Óptimo na Economia
    Supervisor: Delfim F. M. Torres

    Details


  • Since 2006 (in progress)
    Célia Teresa Ligeiro Mendes Pereira
    MSc on Mathematics
    Thesis: Computação no Cálculo das Variações e Controlo Óptimo
    Supervisor: Pedro Cruz and Delfim F. M. Torres