Insensitizing Controls for Stochastic Kuramoto–Sivashinsky Equation

ABSTRACT In this paper, we consider the existence of insensitizing controls for the controlled linear stochastic Kuramoto–Sivashinsky equation. We reduce the insensitizing control problem to an equivalent null‐control problem of a coupled forward‐backward linear stochastic Kuramoto–Sivashinsky system. This can be done by proving a suitable observability inequality for the associated adjoint system to the extended coupled system, and we establish this by means of a proper Carleman estimate. Then, the null controllability of the concerned coupled system is proved via classical duality arguments between controllability and observability.