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

@misc{citeulike:1607280, 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 \$(\Delta t)^{1/2}+\Delta x(\Delta 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.}, archivePrefix = {arXiv}, author = {Akian, Marianne and Gaubert, Stephane and Lakhoua, Asma}, citeulike-article-id = {1607280}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0404184}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0404184}, day = {8}, eprint = {math/0404184}, keywords = {finite-element, hamilton-jacobi, numeric, tropical}, month = {Apr}, posted-at = {2007-08-30 14:23:17}, priority = {2}, title = {A max-plus finite element method for solving finite horizon deterministic optimal control problems}, url = {http://arxiv.org/abs/math/0404184}, year = {2004} }

TY - ELEC ID - citeulike:1607280 L3 - citeulike-article-id:1607280 N2 - 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 $(\Delta t)^{1/2}+\Delta x(\Delta t)^{-1}$, 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. TI - A max-plus finite element method for solving finite horizon deterministic optimal control problems KW - finite-element KW - hamilton-jacobi KW - numeric KW - tropical AU - Akian, Marianne AU - Gaubert, Stephane AU - Lakhoua, Asma PY - 2004/Apr/08/ UR - http://arxiv.org/abs/math/0404184 ER -