  We consider the problem of optimal swarm tracking which can be formulated as
a tracking problem for distributions in the Wasserstein metric. Optimal control
solutions to this problem are non-causal and require knowing the
time-trajectory of the distribution to be tracked in advance. We propose a
scheme where these non-causal solutions can be used together with a predictive
model for the reference to achieve causal tracking control of a priori-unknown
references. We develop the resulting model-predictive control scheme in the
simple case where the reference is predicted to be constant-in-time. A
computational algorithm based on particle methods and discrete optimal mass
transport is presented, and numerical simulations are provided for various
classes of reference signals. The results demonstrate that the proposed control
algorithm achieves reasonable performance even when using simple predictive
models.
