  We consider the optimal control problem of steering an agent population to a
desired distribution over an infinite horizon. This is an optimal transport
problem over a dynamical system, which is challenging due to its high
computational cost. In this paper, we propose Sinkhorn MPC, which is a
dynamical transport algorithm combining model predictive control and the
so-called Sinkhorn algorithm. The notable feature of the proposed method is
that it achieves cost-effective transport in real time by performing control
and transport planning simultaneously. In particular, for linear systems with
an energy cost, we reveal the fundamental properties of Sinkhorn MPC such as
ultimate boundedness and asymptotic stability.
