arXiv subjects

Oscar Sierra

Publications and source records attributed to Oscar Sierra.

2 recordsLinked to original sources

arXiv2025

Singular Arcs on Average Optimal Control-Affine Problems

In this paper we address optimal control problems in which the system parameters follow a probability distribution, and the optimization is based on average performance. These problems, known as Riemann-Stieltjes optimal control or optimal ensemble control problems, involve uncertainties that influence system dynamics. Focusing on control-affine systems, we apply the Pontryagin Maximum Principle to characterize singular arcs in a feedback form. To demonstrate the practical relevance of our approach, we apply it to the sterile insect technique, a biological pest control method. Numerical simulations confirm the effectiveness of our framework in addressing control problems under uncertainty.

math.OC↗

arXiv2024

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

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.

math.OC↗