Feedback reconstruction techniques for optimal control problems on a tree structure

TL;DR

This paper enhances tree-structured dynamic programming methods for optimal control by introducing a scattered data interpolation technique to refine feedback control, improving accuracy without extensive grid computation.

Contribution

It extends existing tree structure algorithms by incorporating scattered data interpolation for better feedback control reconstruction in optimal control problems.

Findings

Improved control accuracy with finer control sets.

Effective value function reconstruction for non-tree nodes.

Numerical example demonstrating method effectiveness.

Abstract

The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes the value function avoiding the construction of a space grid and the need for interpolation techniques using a discrete set of controls. However, the computation of the control is strictly linked to control set chosen in the computation of the tree. Here, we extend and complete the method selecting a finer control set in the computation of the feedback. This requires to use an interpolation method for scattered data which allows us to reconstruct the value function for nodes not belonging to the tree. The effectiveness of the method is shown via a numerical example.