English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A characterization and numerical scheme to control problem governed by a three-dimensional (3D) time-dependent Fokker–Planck (FP) equation is presented. We formulate a control formulation that controls the drift of the stochastic (FP) process. In this way, the probability density function attains a specific configuration. Moreover, a FP control strategy for collective motion is investigated and first-order optimality conditions are presented. On staggered grids, the Chang–Cooper discretization scheme that ensures the positivity, second-order accuracy, and conservativeness to the FP equation is employed to the discretized state (respectively adjoint) system. Furthermore, a line search strategy is applied to update the control variable. Results of numerical experiments show the efficiency of the proposed numerical scheme to stochastic (FP) control problems.

Numerical solution to 3D bilinear Fokker–Planck control problem