American Institute of Mathematical Sciences

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2003, 2003(Special): 223-233. doi: 10.3934/proc.2003.2003.223

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, Spain
2. 

Department de Matemáticas, Universidad Carlos III De Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid, Spain

Received  September 2002 Revised  April 2003 Published  April 2003

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: geometrical constraints algorithm, Singular optimal control theory, global singular perturbations., implicit differential equations.
Mathematics Subject Classification: 49J15, 34A09, 34K3.
Citation: M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223
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