We present a novel computational framework for density control in
high-dimensional state spaces. The considered dynamical system consists of a
large number of indistinguishable agents whose behaviors can be collectively
modeled as a time-evolving probability distribution. The goal is to steer the
agents from an initial distribution to reach (or approximate) a given target
distribution within a fixed time horizon at minimum cost. To tackle this
problem, we propose to model the drift as a nonlinear reduced-order model, such
as a deep network, and enforce the matching to the target distribution at
terminal time either strictly or approximately using the Wasserstein metric.
The resulting saddle-point problem can be solved by an effective numerical
algorithm that leverages the excellent representation power of deep networks
and fast automatic differentiation for this challenging high-dimensional
control problem. A variety of numerical experiments were conducted to
demonstrate the performance of our method.Comment: 8 pages, 4 figures. Accepted for IEEE Conference on Decision and
Control 202