Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation

Motivated by the successful implementation of Pseudo-spectral (PS) methods in optimal control problems (OCP), a new technique is introduced to control the probability density function (PDF) of the state of the 1-D system described by a stochastic differential equation (SDE). In this paper, the Fokke...

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Autores principales:	Ali Namadchian, Mehdi Ramezani
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2019
Materias:	pseudo-spectral optimal control fokker planck equation stochastic process genetic algorithm legendre pseudo-spectral method Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/9b26829ace5547098c1cf72767facfcf
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spelling	oai:doaj.org-article:9b26829ace5547098c1cf72767facfcf2021-11-04T15:51:56ZPseudo-spectral optimal control of stochastic processes using Fokker Planck equation2331-191610.1080/23311916.2019.1691804https://doaj.org/article/9b26829ace5547098c1cf72767facfcf2019-01-01T00:00:00Zhttp://dx.doi.org/10.1080/23311916.2019.1691804https://doaj.org/toc/2331-1916Motivated by the successful implementation of Pseudo-spectral (PS) methods in optimal control problems (OCP), a new technique is introduced to control the probability density function (PDF) of the state of the 1-D system described by a stochastic differential equation (SDE). In this paper, the Fokker Planck equation (FPE) is used to model the time evolution of the PDF of the stochastic process. Using FPE instead of SDE, changes the problem of stochastic optimal control to a deterministic one. FPE is a parabolic PDE. Solving an OCP with PDE constraint is computationally a difficult task. We use two strategies to efficiently solve this OCP problem: firstly, we use PS methods in order to transform the OCP to a non-linear programming (NLP) with fewer discretization points but higher order of accuracy, and secondly, we utilize Genetic algorithm (GA) to solve this large-scale NLP in a more efficient approach than gradient-based optimization methods. The simulation results based on Monte-Carlo simulations prove the performance of the proposed method.Ali NamadchianMehdi RamezaniTaylor & Francis Grouparticlepseudo-spectral optimal controlfokker planck equationstochastic processgenetic algorithmlegendre pseudo-spectral methodEngineering (General). Civil engineering (General)TA1-2040ENCogent Engineering, Vol 6, Iss 1 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	pseudo-spectral optimal control fokker planck equation stochastic process genetic algorithm legendre pseudo-spectral method Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	pseudo-spectral optimal control fokker planck equation stochastic process genetic algorithm legendre pseudo-spectral method Engineering (General). Civil engineering (General) TA1-2040 Ali Namadchian Mehdi Ramezani Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
description	Motivated by the successful implementation of Pseudo-spectral (PS) methods in optimal control problems (OCP), a new technique is introduced to control the probability density function (PDF) of the state of the 1-D system described by a stochastic differential equation (SDE). In this paper, the Fokker Planck equation (FPE) is used to model the time evolution of the PDF of the stochastic process. Using FPE instead of SDE, changes the problem of stochastic optimal control to a deterministic one. FPE is a parabolic PDE. Solving an OCP with PDE constraint is computationally a difficult task. We use two strategies to efficiently solve this OCP problem: firstly, we use PS methods in order to transform the OCP to a non-linear programming (NLP) with fewer discretization points but higher order of accuracy, and secondly, we utilize Genetic algorithm (GA) to solve this large-scale NLP in a more efficient approach than gradient-based optimization methods. The simulation results based on Monte-Carlo simulations prove the performance of the proposed method.
format	article
author	Ali Namadchian Mehdi Ramezani
author_facet	Ali Namadchian Mehdi Ramezani
author_sort	Ali Namadchian
title	Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
title_short	Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
title_full	Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
title_fullStr	Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
title_full_unstemmed	Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
title_sort	pseudo-spectral optimal control of stochastic processes using fokker planck equation
publisher	Taylor & Francis Group
publishDate	2019
url	https://doaj.org/article/9b26829ace5547098c1cf72767facfcf
work_keys_str_mv	AT alinamadchian pseudospectraloptimalcontrolofstochasticprocessesusingfokkerplanckequation AT mehdiramezani pseudospectraloptimalcontrolofstochasticprocessesusingfokkerplanckequation
_version_	1718444666184007680

Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation

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