Constraint algorithm for extremals in optimal control problems
A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determin...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1167 |
| Acceso en línea: | https://hdl.handle.net/2117/1167 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations Optimization (Mathematics) Lagrangian functions Hamiltonian dynamical systems Pontryagin’s Maximum Principle abnormality optimal control problems presymplectic Equacions diferencials ordinàries Control òptim, Teoria del Sistemes dinàmics diferenciables Lagrange, Funcions de Classificació AMS::34 Ordinary differential equations::34A General theory Classificació AMS::49 Calculus of variations and optimal control optimization::49J Existence theories optimization::49K Necessary conditions and sufficient conditions for optimality Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand. |
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