Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2013.tde-20230727-113243
Document
Author
Full name
Eduardo Oda
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Title in Portuguese
Fenômeno Fuller em problemas de controle otimo com multiplos controles
Keywords in Portuguese
Controle (Teoria De Sistemas E Controle)
Controle Ótimo
Abstract in Portuguese
Muitos problemas de controle otimo apresentam um comportamento sofisticado e ainda nao totalmente compreendido, o Fenomeno Fuller. Podemos descrever ingenuamente este fenomeno pela acumulaçao de descontinuidades no controle. Neste trabalho elaboramos extensoes dos resultados classicos de deteçao deste comportamento aos sistemas com mutiplos controles e damos uma descriçao puramente geometrica do problema que nos permite extrair informaçoes e compreender sua complexidade examinando apenas os campos vetoriais envolvidos. Aplicamos estas tecnicas a sistemas de controle que derivam de sistemas hamiltonianos, descobrindo caracteristicas surpreendentes destes problemas e dando condiçoes suficientes para existencia de Fenomeno Fuller em uma familia destes sistemas.
Title in English
not available
Abstract in English
Many optimal control problems exhibit a peculiar behavior not completely understood, the Fuller Phenomenon. In a naive way, this phenomenon can be described as the accumulation of descontinuities in the control function. In this work we elaborate extensions to multiple input control systems of classic results on the detection of this behavior, and we give a purely geometric description of the problem which allows us to extract information and best understand the complexity of the system by considering only the vector fields that define it. We apply this tecnique to control systems derived from Hamiltonian systems, leading to the observation of surprising features of this kind of behavior. Finally, we give sufficient conditions for existence of the Fuller Phenomenon in a subfamily of these systems.
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Publishing Date
2023-07-27