Abstract:
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
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.
Also, the influence on bounds on the control are investigated. Numerical results
for swarming models in the mean-field setting are given. |