On Minimum-Dispersion Control of Nonlinear Diffusion Processes
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915555095609344 |
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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 | This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient of our approach is the theoretical foundation called $\infty$-order variational analysis. This framework consists in establishing an exact representation of the increment ($\infty$-order variation) of the objective functional using the duality, implied by the transformation of the nonlinear stochastic control problem to a linear deterministic control of the Fokker-Planck equation. The resulting formula for the cost increment analytically represents a "law-feedback" control for the diffusion process. This control mechanism enables us to learn time-dependent coefficients for a predefined Markovian control structure using Monte Carlo simulations with a modest population of samples. Numerical experiments prove the vitality of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Minimum-Dispersion Control of Nonlinear Diffusion Processes Chertovskih, Roman Pogodaev, Nikolay Staritsyn, Maxim Aguiar, A. Pedro Optimization and Control This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient of our approach is the theoretical foundation called $\infty$-order variational analysis. This framework consists in establishing an exact representation of the increment ($\infty$-order variation) of the objective functional using the duality, implied by the transformation of the nonlinear stochastic control problem to a linear deterministic control of the Fokker-Planck equation. The resulting formula for the cost increment analytically represents a "law-feedback" control for the diffusion process. This control mechanism enables us to learn time-dependent coefficients for a predefined Markovian control structure using Monte Carlo simulations with a modest population of samples. Numerical experiments prove the vitality of our approach. |
| title | On Minimum-Dispersion Control of Nonlinear Diffusion Processes |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2405.07676 |