  In this paper, we consider a chain of distributed systems governed by a
degenerate parabolic equation, which satisfies a weak H\"{o}rmander type
condition, with a control distributed over an open subdomain. In particular, we
consider two 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 overall system close to a given reference
trajectory on a finite, compact time intervals. We introduce the following
framework. First, we partition the control subdomain into two disjoint open
subdomains that are compatible with the strategy subspaces of the {\it leader}
and that of the {\it follower}, respectively. Then, using the notion of
Stackelberg's optimization (which is a hierarchical optimization framework), we
provide a new result on the existence of optimal strategies for such an
optimization problem -- where the {\it follower} (which corresponds to the
second criterion) is required to respond optimally, in the sense of {\it
best-response correspondence} to the strategy of the {\it leader} (that is
associated to the controllability-type criterion) so as to achieve the overall
objectives. Finally, we remark on the implication of our result in assessing
the influence of the reachable target set on the optimal strategy of the {\it
follower} in relation to the direction of {\it leader-follower} and {\it
follower-leader} information flows.

Optimization and Control