Robust control of 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 t o a broad class of external disturbances. In [6], a general framework for t he robust control of the Navier-Stokes equations in finite time horizon was developed. In this article the robust boundary control for the Kuramoto-Si vashinsky equation is considered in the same spirit: a robust boundary cont rol problem is formulated, and the existence and uniqueness for the robust control problem are proved. A data assimilation problem corresponding to th e Kuramoto-Sivashinsky equation is considered, existence and uniqueness of solution are derived. This approach is also applicable as well to other equ ations with a structure similar to that of the Kuramoto-Sivashinsky equatio n.