Para acceder a los documentos con el texto completo, por favor, siga el siguiente enlace: http://hdl.handle.net/2117/1987

Geometric approach to Pontryagin's Maximum Principle
Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
Since the second half of the 20th century, Pontryagin’s Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self–contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.
Peer Reviewed
Differential equations
Mathematical optimization
System theory
Pontryagin's Maximum Principle
perturbation vectors
tangent perturbation cones
optimal control problems
Equacions diferencials ordinàries
Optimització matemàtica
Sistemes de control
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::49 Calculus of variations and optimal control; optimization::49J Existence theories
Classificació AMS::49 Calculus of variations and optimal control; optimization::49K Necessary conditions and sufficient conditions for optimality
Classificació AMS::93 Systems Theory; Control::93C Control systems, guided systems
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Artículo
Springer Netherlands
         

Mostrar el registro completo del ítem

Documentos relacionados

Otros documentos del mismo autor/a

Barbero Liñán, María; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos
Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos
Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso