Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution
Optimization and Control
2024-09-23 v1
Abstract
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a novel concept of local optimality surpassing Pontryagin's minimum, originally crafted for deterministic optimal ensemble control problems. A key practical outcome is a rapidly converging numerical algorithm, which proves its feasibility for problems involving Markovian and open-loop strategies.
Cite
@article{arxiv.2403.01945,
title = {Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution},
author = {Roman Chertovskih and Nikolay Pogodaev and Maxim Staritsyn and A. Pedro Aguiar},
journal= {arXiv preprint arXiv:2403.01945},
year = {2024}
}