Some results on Model Predictive Control for the Fokker-Planck equation

Abstract : A Model Predictive Control scheme is applied to track the solution of a Fokker-Planck equation over a fixed time horizon. We analyse the dependence of the total cost functional on several parameters of the algorithm, in particular on the prediction horizon, on the regularization parameter, and on the sampling time. Comparison among different numerical simulations show valuable improvements by properly tuning the scheme's parameters. Our numerical study is complemented by a theoretical controllability analysis explaining the superior performance of controls with time and space dependence.