Error estimates for a tree structure algorithm solving finite horizon control problems

Understand

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.