L 2-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker–Planck Equation

This paper presents the first results for the stability analysis of Model Predictive Control schemes applied to the Fokker–Planck equation for tracking probability density functions. The analysis is carried out for linear dynamics and Gaussian distributions, where the distance to the desired reference is measured in the L2-norm. We present results for general such systems with and without control penalization. Refined results are given for the special case of the Ornstein–Uhlenbeck process. Some of the results establish stability for the shortest possible (discrete time) optimization horizon N = 2. © 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.