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.

Feedback reconstruction techniques for optimal control problems on a tree structure

Saluzzi, Luca
2022

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.
2022
Settore MAT/08 - Analisi Numerica
8th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2022
Oslo, Norvegia
2022
World Congress in Computational Mechanics and ECCOMAS Congress
Scipedia S.L.
Dynamic Programming Principle; Feedback reconstruction; Hamilton-Jacobi-Bellman; Optimal Control
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/131688
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