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Title
Control strategies for the FokkerPlanck equation
AuthorBreiten, Tobias ; Kunisch, Karl ; Pfeiffer, Laurent
Published in
ESAIM: Control, Optimisation and Calculus of Variations, 2017, Vol. ume 23, Issue Number 4, page 1543-1553
PublishedEDP Sciences, 2017
LanguageEnglish
Document typeJournal Article
Keywords (EN)FokkerPlanck equation / bilinear control systems / Lyapunov functions / Riccati equation / Lyapunov equation
Project-/ReportnumberERC advanced Grant 668998 (OCLOC)
URNurn:nbn:at:at-ubg:3-5187 Persistent Identifier (URN)
DOI10.1051/cocv/2016064 
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 The work is publicly available
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Abstract (English)

Using a projection-based decoupling of the FokkerPlanck 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.

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