  In this paper, we consider a hierarchical control problem with model
uncertainty. Specifically, we consider the following objectives that we would
like to accomplish. The first one being of a controllability-type that consists
of guaranteeing the terminal state to reach a target set starting from an
initial condition, while the second one is keeping the state trajectory of the
system close to a given reference trajectory over a finite time interval. We
introduce the following framework. First, we partition the control subdomain
into two disjoint open subdomains, with smooth boundaries, that are compatible
with the strategy subspaces of the {\it leader} (which is responsible for the
controllability-type criterion) and that of the {\it follower} (which is
associated with the second criterion), respectively. Moreover, we account at
the optimization stage for model uncertainty by allowing the {\it leader} to
choose its control strategy based on a class of alternative models about the
system, whereas the {\it follower} makes use of an approximate model about the
system. Using the notion of Stackelberg's optimization, we provide conditions
on the existence of optimal control strategies for such a hierarchical control
problem, under which the {\it follower} is required to respond optimally to the
strategy of the {\it leader} so as to achieve the overall objectives. Apart
from the issue of modeling and uncertainty, this paper is a companion to our
previous work.
