Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution

Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution

IEEE Control Systems Letters, vol. 8, pp. 1469-1474, 2024 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 nov...

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Bibliographic Details
Main Authors: Chertovskih, Roman, Pogodaev, Nikolay, Staritsyn, Maxim, Aguiar, A. Pedro
Format: Journal Article
Language:English
Published: 04-03-2024
Subjects:
Mathematics - Optimization and Control
Online Access:Get full text
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Summary:IEEE Control Systems Letters, vol. 8, pp. 1469-1474, 2024 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.
DOI:10.48550/arxiv.2403.01945