117
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Two-level method for a time-independent Fokker–Planck control problem

Pages 1542-1560 | Received 22 Mar 2020, Accepted 08 Sep 2020, Published online: 29 Sep 2020
 

Abstract

A time-independent Fokker–Planck (FP) control problem and a two-level numerical method are presented. We aim to formulate a control problem that controls the drift of the stochastic process so that the probability density function (PDF) attains a specific steady-state configuration. First-order optimality conditions, which characterize the solution of the control problem, are discretized by the Chang-Cooper (CC) scheme. For positivity and conservativeness of a PDF in the stationary FP control formulation and discretization, we take advantage of CC-scheme. We investigate a two-grid method with coarsening by a factor-of-three strategy. It is found that the coarsening by a factor-of-three strategy simplifies the inter-grid transfer operators and hence the computations. We present several numerical experiments to show the effectiveness of the proposed two-level framework to solve Fokker–Planck or stochastic models control problems with and without control-constrained.

MSC (2010) CLASSIFICATIONS:

Acknowledgements

The author is thankful to the anonymous referees for their careful reading and useful comments that help to improve the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,129.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.