Mathematics – Optimization and Control
Scientific paper
2005-09-12
Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), S
Mathematics
Optimization and Control
13 pages, 2 figures
Scientific paper
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.
Akian Marianne
Gaubert Stephane
Lakhoua Asma
No associations
LandOfFree
The max-plus finite element method for optimal control problems: further approximation results does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The max-plus finite element method for optimal control problems: further approximation results, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The max-plus finite element method for optimal control problems: further approximation results will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1924