Optimal control problems for affine connection control systems: characterization of extremals
| Autor: | Barbero Liñán, María, Muñoz Lecanda, Miguel Carlos |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Differential equations
Matemàtiques i estadística [Àrees temàtiques de la UPC] abnormal extremals 49 Calculus of variations and optimal control [Classificació AMS] Pontryagin's Maximum Principle Optimization (Mathematics) Hamilton Sistemes de optimal control problems 34 Ordinary differential equations::34A General theory [Classificació AMS] 70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS] Hamiltonian dynamical systems Equacions diferencials ordinàries affine connection control systems 49 Calculus of variations and optimal control optimization::49K Necessary conditions and sufficient conditions for optimality [Classificació AMS] Optimització 49K Necessary conditions and sufficient conditions for optimality [optimization] |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | Pontryagin’s Maximum Principle [8] is considered as an outstanding achievement of optimal control theory. This Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary conditions. Thus only candidates to be optimal trajectories, called extremals, are found. Maximum Principle gives rise to different kinds of them and, particularly, the so-called abnormal extremals have been studied because they can be optimal, as Liu and Sussmann, and Montgomery proved in subRiemannian geometry [5, 7]. We build up a presymplectic algorithm, similar to those defined in [2, 3, 4, 6], to determine where the different kinds of extremals of an optimal control problem can be. After describing such an algorithm, we apply it to the study of extremals, specially the abnormal ones, in optimal control problems for affine connection control systems [1]. These systems model the motion of different types of mechanical systems such as rigid bodies, nonholonomic systems and robotic arms [1]. |
| Databáze: | OpenAIRE |
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