  In this article the robust Stackelberg controllability (RSC) problem is
studied for a nonlinear fourth-order parabolic equation, namely, the
Kuramoto-Sivashinsky equation. When three external sources are acting into the
system, the RSC problem consists essentially in combining two subproblems: the
first one is a saddle point problem among two sources. Such an sources are
called the "follower control" and its associated "disturbance signal". This
procedure corresponds to a robust control problem. The second one is a
hierarchic control problem (Stackelberg strategy), which involves the third
force, so-called leader control. The RSC problem establishes a simultaneous
game for these forces in the sense that, the leader control has as objective to
verify a controllability property, while the follower control and perturbation
solve a robust control problem. In this paper the leader control obeys to the
exact controllability to the trajectories. Additionally, iterative algorithms
to approximate the robust control problem as well as the robust Stackelberg
strategy for the nonlinear Kuramoto-Sivashinsky equation are developed and
implemented.
