A max-plus finite element method for solving finite horizon deterministic optimal control problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2004
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| _version_ | 1866914099762298880 |
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| author | Akian, Marianne Gaubert, Stephane Lakhoua, Asma |
| author_facet | Akian, Marianne Gaubert, Stephane Lakhoua, Asma |
| contents | 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 $(Δt)^{1/2}+Δx(Δt)^{-1}$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0404184 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | A max-plus finite element method for solving finite horizon deterministic optimal control problems Akian, Marianne Gaubert, Stephane Lakhoua, Asma Optimization and Control Numerical Analysis 49L20 (Primary); 65M60, 06A15, 12K10 (Secondary) 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 $(Δt)^{1/2}+Δx(Δt)^{-1}$, 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. |
| title | A max-plus finite element method for solving finite horizon deterministic optimal control problems |
| topic | Optimization and Control Numerical Analysis 49L20 (Primary); 65M60, 06A15, 12K10 (Secondary) |
| url | https://arxiv.org/abs/math/0404184 |