Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910614976200704 |
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| author | Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro |
| author_facet | Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_01945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro Optimization and Control 49K20, 49J45, 93C20 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. |
| title | Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution |
| topic | Optimization and Control 49K20, 49J45, 93C20 |
| url | https://arxiv.org/abs/2403.01945 |