A Max-plus Finite Element Method for Solving Finite Horizon Deterministic Optimal Control Problems

@inproceedings{Gaubert2008AMF,
  title={A Max-plus Finite Element Method for Solving Finite Horizon Deterministic Optimal Control Problems},
  author={St{\'e}phane Gaubert},
  year={2008}
}
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 √ ∆t + ∆x(∆t), for a subclass of problems in dimension 1. We compare our method with a max-plus based… CONTINUE READING
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