# The max-plus finite element method for optimal control problems: further approximation results

Abstract : We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of projectors on max-plus semimodules. We prove here a convergence result, in arbitrary dimension, showing that for a subclass of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$, where $\delta$ and $\Delta x$ are the time and space steps respectively. We also show how the max-plus analogues of the mass and stiffness matrices can be computed by convex optimization, even when the global problem is non convex. We illustrate the method by numerical examples in dimension 2.
Document type :
Conference papers
Domain :

https://hal.inria.fr/inria-00000965
Contributor : Marianne Akian <>
Submitted on : Friday, January 6, 2006 - 3:48:37 PM
Last modification on : Wednesday, May 30, 2018 - 10:04:18 AM

### Identifiers

• HAL Id : inria-00000965, version 1

### Citation

Marianne Akian, Stéphane Gaubert, Asma Lakhoua. The max-plus finite element method for optimal control problems: further approximation results. 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Dec 2005, Seville, Spain. ⟨inria-00000965⟩

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