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

M. Delgado-Téllez; Alberto Ibort

doi:10.3934/proc.2003.2003.223

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2003, Volume 2003: 223-233. Doi: 10.3934/proc.2003.2003.223 open access

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

M. Delgado-Téllez^1, and
Alberto Ibort^2,

1.
Departmento de Matemáticas, Universidad Carlos III de Madrid, Leganés 28911, Madrid
2.
Department de Matemáticas, Universidad Carlos III De Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid

Received: August 31, 2002

Revised: March 31, 2003

Published: March 2003

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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.

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Mathematics Subject Classification: 49J15, 34A09, 34K35.

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