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A max-plus finite element method for solving finite horizon deterministic optimal control problems

Abstract : We introduce a max-plus analogue of the Petrov-Galerkin finite element method, to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation, and exploits the properties of projectors on max-plus semimodules. We obtain a nonlinear discretized semigroup, corresponding to a zero-sum two players game. We give an error estimate of order $\sqrt{\Dta t}+\Dta x(\Dta t)^{-1}$, for a subclass of problems in dimension 1. We compare our method with a max-plus based discretization method previously introduced by Fleming and McEneaney.
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https://hal.inria.fr/inria-00071426
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Submitted on : Tuesday, May 23, 2006 - 5:29:21 PM
Last modification on : Friday, February 4, 2022 - 3:09:58 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:12:48 PM

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• HAL Id : inria-00071426, version 1

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Marianne Akian, Stéphane Gaubert, Asma Lakhoua. A max-plus finite element method for solving finite horizon deterministic optimal control problems. [Research Report] RR-5163, INRIA. 2004. ⟨inria-00071426⟩

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