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A numerical scheme to solve Fokker–Planck control collective-motion problem

Author

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  • Butt, M.M.
  • Roy, S.

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.

Suggested Citation

  • Butt, M.M. & Roy, S., 2024. "A numerical scheme to solve Fokker–Planck control collective-motion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1056-1071.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:1056-1071
    DOI: 10.1016/j.matcom.2023.10.005
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