Summary: Robust control theory, a generalization of optimal control theory, has been proposed as an effective technique when control algorithms are sensitive to a broad class of external disturbances. In [T. R. Bewley
, R. Teman
and M. Ziane
, Physica D 138, No. 3-4, 360-392 (2000; Zbl 0981.76026
)], a general framework for the robust control of the Navier-Stokes equations in finite time horizon was developed. In this article the robust boundary control for the Kuramoto-Sivashinsky equation is considered in the same spirit: a robust boundary control problem is formulated, and the existence and uniqueness for the robust control problem are proved. A data assimilation problem corresponding to the Kuramoto-Sivashinsky equation is considered, existence and uniqueness of solution are derived. This approach is also applicable as well to other equations with a structure similar to that of the Kuramoto-Sivashinsky equation.