Skinner-Rusk unified formalism for optimal control systems and applications
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessar...
| Autores: | , , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2007 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1013 |
| Acesso em linha: | https://hdl.handle.net/2117/1013 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Hamiltonian systems Lagrange equations Lagrangian and Hamiltonian formalisms jet bundles implicit optimal control systems descriptor systems Hamilton, Sistemes de Lagrange, Equacions de Control òptim, Teoria del Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods Classificació AMS::49 Calculus of variations and optimal control optimization::49J Existence theories Classificació AMS::34 Ordinary differential equations::34A General theory optimization::49K Necessary conditions and sufficient conditions for optimality Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| Resumo: | A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by Pontryagin’s Maximum Principle, providing that the differentiability with respect to controls is assumed and the space of controls is open. Furthermore, our method is also valid for implicit optimal control systems and, in particular, for the so-called descriptor systems (optimal control problems including both differential and algebraic equations). |
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