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Infimum gaps for limit solutions

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Aronna2015_Article_InfimumGapsForLimitSolutions.pdf (412.4Kb)
Date
2015
Author
Soledad Aronna, Maria
Motta, Monica
Rampazzo, Franco
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Abstract
After recalling the notion of L1 limit solution for a dynamics which is affine in the (unbounded) derivative of the control, we focus on the possible occurrence of the Lavrentiev phenomenon for a related optimal control problem. By this we mean the possibility that the cost functional evaluated along L1 inputs (and the corresponding limit solutions) assumes values strictly smaller than the infimum over AC inputs. In fact, it turns out that no Lavrentiev phenomenon may take place in the unconstrained case, while the presence of an end-point constraint may give rise to an actual gap. We prove that a suitable transversality condition, here called Quick 1-Controllability, is sufficient for this gap to be avoided. Meanwhile, we also investigate the issue of trajectories’ approximation through implementation of inputs with bounded variation.
URI
https://hdl.handle.net/10438/28304
Collections
  • FGV EMAp - Artigos [18]
Knowledge Areas
Matemática
Subject
Equações diferenciais
Cálculo integral
Keyword
Fenômeno de Lavrentiev
Optimal control
Impulsive control
Lavrentiev phenomenon
Controllability

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