On the geometry and topology of singular optimal control problems and their solutions

Pages: 223 - 233, Issue Special, July 2003

 Abstract        Full Text (194.9K)              

M. Delgado-Téllez - Departmento de Matemáticas, Universidad Carlos III de Madrid, Leganés 28911, Madrid, Spain (email)
Alberto Ibort - Department de Matemáticas, Universidad Carlos III De Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid, Spain (email)

Abstract: The existence of singular arcs for optimal control problems is studied by using a geometric recursive algorithm inspired in Dirac’s theory of constraints. It is shown that singular arcs must lie in the singular locus of a projection map into the coestate space. After applying the geometrical recursive constraints algorithm, we arrive to a reduced set of hamiltonian equations that replace Pontriaguine’s maximum principle. Finally, a global singular perturbation theory is used to obtain nearly optimal solutions.

Keywords:  Singular optimal control theory, implicit differential equations, geometrical constraints algorithm, global singular perturbations.
Mathematics Subject Classification:  49J15, 34A09, 34K35.

Received: September 2002;      Revised: April 2003;      Published: April 2003.