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

Roman Chertovskih; Nikolay Pogodaev; Maxim Staritsyn; A. Pedro Aguiar

doi:10.1109/lcsys.2024.3410632

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arXiv · 2403.01945

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

Roman Chertovskih·Nikolay Pogodaev·Maxim Staritsyn·A. Pedro Aguiar

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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.

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Roman Chertovskih, Nikolay Pogodaev, Maxim Staritsyn, A. Pedro Aguiar. 2024-03-04. Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution. https://doi.org/10.1109/lcsys.2024.3410632

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