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Constraint algorithm for extremals in optimal control problems
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
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística
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
Classificació AMS::49 Calculus of variations and optimal control; 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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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