Geodesic
Control strategies for the Fokker−Planck equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 741-763

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Using a projection-based decoupling of the Fokker−Planck equation, control strategies that allow to speed up the convergence to the stationary distribution are investigated. By means of an operator theoretic framework for a bilinear control system, two different feedback control laws are proposed. Projected Riccati and Lyapunov equations are derived and properties of the associated solutions are given. The well-posedness of the closed loop systems is shown and local and global stabilization results, respectively, are obtained. An essential tool in the construction of the controls is the choice of appropriate control shape functions. Results for a two dimensional double well potential illustrate the theoretical findings in a numerical setup.

DOI : 10.1051/cocv/2017046
Classification : 35Q35, 49J20, 93D05, 93D15
Keywords: Fokker−Planck equation, bilinear control systems, Lyapunov functions, Riccati equation, Lyapunov equation

Breiten, Tobias 1 ; Kunisch, Karl 1 ; Pfeiffer, Laurent 1

1 
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     title = {Control strategies for the {Fokker\ensuremath{-}Planck} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {741--763},
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Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent. Control strategies for the Fokker−Planck equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 741-763. doi: 10.1051/cocv/2017046

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