  In a crowd model based on leader-follower interactions, where positions of
the leaders are viewed as the control input, up-to-date solutions rely on
knowledge of the agents' coordinates. In practice, it is more realistic to
exploit knowledge of statistical properties of the group of agents, rather than
their exact positions. In order to shape the crowd, we study thus the problem
of controlling the moments instead, since it is well known that shape can be
determined by moments. An optimal control for the moments tracking problem is
obtained by solving a modified Hamilton-Jacobi-Bellman (HJB) equation, which
only uses the moments and leaders' states as feedback. The optimal solution can
be solved fast enough for on-line implementations.
