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arXiv · 2407.13045

Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation for Optimal Control Problems with Uncertainty

M. Soledad Aronna·Michele Palladino·Oscar Sierra
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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.

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M. Soledad Aronna, Michele Palladino, Oscar Sierra. 2024-07-17. Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation for Optimal Control Problems with Uncertainty. https://arxiv.org/abs/2407.13045

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