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Master's Dissertation
DOI
10.11606/D.45.2008.tde-05052009-111117
Document
Author
Full name
Eduardo Oda
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Tonelli, Pedro Aladar (President)
Garcia, Manuel Valentim de Pera
Pait, Felipe Miguel
Title in Portuguese
Fenômeno Fuller em problemas de controle ótimo: trajetórias em tempo mínino de veículos autônomos subaquáticos
Keywords in Portuguese
bang-bang.
chattering
controle ótimo
controle singular
Fenômeno Fuller
Princípio do Máximo de Pontryagin
sistemas hamiltonianos
teoria geométrica de controle
Abstract in Portuguese
As equações do modelo bidimensional de veículos autônomos subaquáticos fornecem um exemplo de sistema de controle não linear com o qual podemos ilustrar propriedades da teoria de controle ótimo. Apresentamos, sistematicamente, como os conceitos de formalismo hamiltoniano e teoria de Lie aparecem de forma natural neste contexto. Para tanto, estudamos brevemente o Princípio do Máximo de Pontryagin e discutimos características de sistemas afins. Tratamos com cuidado do Fenômeno Fuller, fornecendo critérios para decidir quando ele está ou não presente em junções, utilizando para isso uma linguagem algébrica. Apresentamos uma abordagem numérica para tratar problemas de controle ótimo e finalizamos com a aplicação dos resultados ao modelo bidimensional de veículo autônomo subaquático.
Title in English
Fuller Phenomenon in optimal control problems: minimum time path of autonomous underwater vehicles.
Keywords in English
bang-bang
chattering
Fuller Phenomenon
geometric control theory
Hamiltonian systems
optimal control
Pontryagin Maximum Principle
singular control
Abstract in English
The equations of the two-dimensional model for autonomous underwater vehicles provide an example of a nonlinear control system which illustrates properties of optimal control theory. We present, systematically, how the concepts of the Hamiltonian formalism and the Lie theory naturally appear in this context. For this purpose, we briefly study the Pontryagin's Maximum Principle and discuss features of affine systems. We treat carefully the Fuller Phenomenon, providing criteria to detect its presence at junctions with an algebraic notation. We present a numerical approach to treat optimal control problems and we conclude with an application of the results in the bidimesional model of autonomous underwater vehicle.
 
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dissertacao.pdf (550.85 Kbytes)
Publishing Date
2009-06-26
 
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