Adaptive Grid Refinement for Optimal Feedback Control
Abstract
This paper introduces an algorithmic approach for adaptive grid refinement for solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) to obtain the optimal feedback control. Traditional grid generation methods often face challenges associated with state-space dimensionality, solution regularity, and large variations in the solution. Whereas fixed grid generation methods may fail to capture the intricate details of the optimal solution, our methodology addresses this challenge by dynamically refining the grid used to solve the HJB equation, thereby optimizing computational resource usage while targeting improved solution accuracy. The reinforcement learning (RL)-based approach presented in this study seeks to reduce the node population while constructing a grid with higher node density in regions with large discretization error.
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BibTeX
@misc{golpashin2026adaptive,
title = {{Adaptive Grid Refinement for Optimal Feedback Control}},
author = {Alen E. Golpashin and Matthew T. Clark and Bruce A. Conway},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29368},
eprint = {2610.29368},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29368},
}
RIS
TY - UNPB
TI - Adaptive Grid Refinement for Optimal Feedback Control
AU - Alen E. Golpashin
AU - Matthew T. Clark
AU - Bruce A. Conway
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29368
UR - https://arxiv.org/abs/2610.29368
AB - This paper introduces an algorithmic approach for adaptive grid refinement for solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) to obtain the optimal feedback control. Traditional grid generation methods often face challenges associated with state-space dimensionality, solution regularity, and large variations in the solution. Whereas fixed grid generation methods may fail to capture the intricate details of the optimal solution, our methodology addresses this challenge by dynamically refining the grid used to solve the HJB equation, thereby optimizing computational resource usage while targeting improved solution accuracy. The reinforcement learning (RL)-based approach presented in this study seeks to reduce the node population while constructing a grid with higher node density in regions with large discretization error.
ER -