Strict abnormal extremals in nonholonomic and kinematic control systems
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost function. We focus on control systems such as nonholonomic control...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2008 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2100 |
| Acesso em linha: | https://hdl.handle.net/2117/2100 |
| Access Level: | acceso abierto |
| Palavra-chave: | Differential equations Optimization (Mathematics) Mechanics Hamiltonian dynamical systems Lagrangian functions nonholonomic control mechanical systems kinematic control systems Pontryagin's Maximum Principle extremals abnormality Equacions diferencials ordinàries Optimització Sistemes dinàmics diferenciables Hamilton, Sistemes de 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 |
| Resumo: | In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost function. We focus on control systems such as nonholonomic control mechanical systems and the associated kinematic systems as long as they are equivalent. With all this in mind, first we study conditions to relate an optimal control problem for the mechanical system with another one for the associated kinematic system. Then, Pontryagin's Maximum Principle will be used to connect the abnormal extremals of both optimal control problems. An example is given to glimpse what the abnormal solutions for kinematic systems become when they are considered as extremals to the optimal control problem for the corresponding nonholonomic mechanical systems. |
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