Error estimates for a tree structure algorithm solving finite horizon control problems
Abstract
In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this approach suffers of the "curse of dimensionality" and this limitation has reduced its practical in real world applications. Here we analyze a dynamic programming algorithm based on a tree structure. The tree is built by the time discrete dynamics avoiding in this way the use of a fixed space grid which is the bottleneck for high-dimensional problems, this also drops the projection on the grid in the approximation of the value function. We present some error estimates for a first order approximation based on the tree-structure algorithm. Moreover, we analyze a pruning technique for the tree to reduce the complexity and minimize the computational effort. Finally, we present some numerical tests.
Cite
@article{arxiv.1812.11194,
title = {Error estimates for a tree structure algorithm solving finite horizon control problems},
author = {Luca Saluzzi and Alessandro Alla and Maurizio Falcone},
journal= {arXiv preprint arXiv:1812.11194},
year = {2022}
}