Adaptive Stabilization of the Kuramoto-Sivashinsky Equation Subject to Intermittent Sensing

We study in this paper the one-dimensional Kuramoto-Sivashinsky equation (KS), subject to intermittent sensing. Namely, we measure the state on a sub-interval of the spatial domain during certain intervals of time, and we measure the state on the remaining sub-interval of space during the remaining intervals of time. As a result, we assign an active control at the boundaries of the spatial domain, and we set a zero boundary condition at the junction of the two spatial sub-intervals. Under the assumption that the destabilizing coefficient is unknown, we design adaptive boundary controllers that guarantee global exponential stability (GES) of the trivial solution in the L-2 norm. Numerical simulations are performed to illustrate our results.