Title data
Fleig, Arthur ; Grüne, Lars:
Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the FokkerPlanck Equation.
Bayreuth
,
2016
.  6 S.
PDF
2016_fleiggruene_minstabhorizonmpcfp.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (363kB) 
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract
In a series of papers by Annunziato and Borzì, Model Predictive Control of the FokkerPlanck equation has been established as a numerically feasible way for controlling stochastic processes via their probability density functions. Numerical simulations suggest that the resulting controller yields an asymptotically stable closed loop system for optimization horizons looking only one time step into the future. In this paper we provide a formal proof of this fact for the FokkerPlanck equation corresponding to the controlled OrnsteinUhlenbeck process using an L² cost and control functions which are constant in space. The key step of the proof consists in the verification of an exponential controllability property with respect to the stage cost. Numerical simulations are provided to illustrate our results.