In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given.
Performance bounds for the mean-field limit of constrained dynamics / Herty, Michael; Zanella, Mattia. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 37:4(2017), pp. 2023-2043.
|Titolo:||Performance bounds for the mean-field limit of constrained dynamics|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.3934/dcds.2017086|
|Appare nelle tipologie:||1.1 Articolo in rivista|