Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation for Optimal Control Problems with Uncertainty
Optimization and Control
2024-07-19 v1
Abstract
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and appear in the dynamics, in the terminal cost and in the initial condition, which yield an infinite-dimensional formulation. By stating the problem as an evolution equation in a Hilbert space, we show that the value function is the unique lower semi-continuous proximal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Our approach relies on invariance properties and the dynamic programming principle.
Cite
@article{arxiv.2407.13045,
title = {Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation for Optimal Control Problems with Uncertainty},
author = {M. Soledad Aronna and Michele Palladino and Oscar Sierra},
journal= {arXiv preprint arXiv:2407.13045},
year = {2024}
}