On Minimum-Dispersion Control of Nonlinear Diffusion Processes

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 calle...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Chertovskih, Roman, Pogodaev, Nikolay, Staritsyn, Maxim, A Pedro Aguiar
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 13.05.2024
Subjects:
Cost analysis
Differential equations
Fokker-Planck equation
Mathematical analysis
Monte Carlo simulation
Nonlinear control
Optimal control
Steering
Stochastic processes
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.2405.07676