Robust boundary control for the Kuramoto-Sivashinsky equation

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 [BTZ], 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. This approach is also applicable as well to other equations with a structure similar to that of the Kuramoto-Sivashinsky equation. Details will be given elsewhere, as well as an application to a data assimilation problem.