Morse families in optimal control problems Articles uri icon

authors

  • BARBERO LI√ĎAN, MARIA
  • IGLESIAS PONTE, DAVID
  • DE DIEGO DAVID, MARTIN

publication date

  • February 2015

start page

  • 414

end page

  • 433

issue

  • 1

volume

  • 53

International Standard Serial Number (ISSN)

  • 0363-0129

Electronic International Standard Serial Number (EISSN)

  • 1095-7138

abstract

  • We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point to run an integrability algorithm. Moreover the integrability algorithm is adapted to optimal control problems in such a way that the trajectories originated by discontinuous controls are also obtained. From the Hamiltonian viewpoint we obtain the equations of motion for optimal control problems in the Lagrangian formalism by means of a proper Lagrangian submanifold. Singular optimal control problems and overdetermined ones are also studied in the paper.