Asymptotic expansion of the optimal control under logarithmic penalty: worked example and open problems

Felipe Alvarez 1 J. Frederic Bonnans 2 Julien Laurent-Varin 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : We discuss the problem of expansion of optimal control, state and costate when a logarithmic penalty is applied to constraints. We show that, in a simple case, that the variation of (a regular) junction point, and of the optimal control, state and costate is of order $\eps\log \eps$, where $\eps$ is the penalty parameter.
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https://hal.inria.fr/inria-00143515
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Submitted on : Thursday, April 26, 2007 - 9:57:04 AM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM
Long-term archiving on : Monday, June 27, 2011 - 3:48:56 PM

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Felipe Alvarez, J. Frederic Bonnans, Julien Laurent-Varin. Asymptotic expansion of the optimal control under logarithmic penalty: worked example and open problems. [Research Report] RR-6170, INRIA. 2007. ⟨inria-00143515v2⟩

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