 A numerical scheme to solve Fokker–Planck control collective-motion problemM.M. Butt and S. Roy Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 1056-1071 Abstract: A numerical scheme to solve the optimal control problem, governed by Fokker–Planck (FP) equation, is presented. In particular, a bilinear optimal control framework is considered for the evolution of the probability density function (PDF), corresponding to collective (stochastic) motion. A FP optimality system is described and a Chang–Cooper (CC) discretization scheme is employed on staggered grids to numerically solve this optimality system. This CC scheme preserves non-negativity, conservation and second-order accuracy to the PDF. Analysis of the forward time Chang–Cooper (FT-CC) scheme is provided. For the time discretization, we use the Euler first-order time differencing scheme. Furthermore, a gradient update procedure combined with a projection step is investigated to solve the optimal control problem. Numerical results validate the proposed staggered-grid FT-CC scheme for the proposed control framework in stochastic motion. Keywords: Fokker–Planck equation; PDE-constrained optimization; Stochastic models; Chang–Cooper scheme (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:1056-1071 DOI: 10.1016/j.matcom.2023.10.005 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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