Model Predictive Control for the Fokker-Planck equation : analysis and structural insight

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Fleig, Arthur ; Grüne, Lars:
Model Predictive Control for the Fokker-Planck equation : analysis and structural insight.
In: University of Minnesota (ed.): 22nd International Symposium on Mathematical Theory of Networks and Systems : July 12-15, 2016 (MTNS 2016, Proceedings). - Minneapolis, Minnesota , 2016 . - pp. 689-690
ISBN 978-1-5323-1385-5

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For the control of ensembles governed by controlled stochastic differential equations we follow the approach to control the corresponding probability density function. To this end, we propose to use Model Predictive Control (MPC) for the Fokker-Planck equation. In this talk we start by describing the basic setup and illustrating the approach by numerical examples. Then, we provide first results on the analysis of the stability and performance of the MPC approach. Finally, we discuss the structure of the controller resulting from the MPC approach, particularly its dependence on space, time and on the probability density function of the ensemble under consideration.