New Insights into Kuramoto-Sivashinsky methods part2(Machine Learning 2024) | by Monodeep Mukherjee | Jun, 2024

Adaptive Boundary Administration of the Kuramoto-Sivashinsky Equation Beneath Intermittent Sensing

Authors: Mohamed Camil Belhadjoudja, Mohamed Maghenem, Emmanuel Witrant, Christophe Prieur

Abstract: We analysis on this paper boundary stabilization, inside the L2 sense, of the one-dimensional Kuramoto-Sivashinsky equation subject to intermittent sensing. We assume that we measure the state of this spatio-temporal equation on a given spatial subdomain all through positive intervals of time, whereas we measure the state on the remaining spatial subdomain all through the remaining intervals of time. Consequently, we assign a recommendations laws on the boundary of the spatial space and drive to zero the price of the state on the junction of the two subdomains. All by way of the analysis, the destabilizing coefficient is assumed to be space-dependent and bounded nevertheless unknown. Adaptive boundary controllers are designed beneath utterly totally different assumptions on the forcing time interval. Notably, when the forcing time interval is null, we guarantee worldwide exponential stability of the origin. Furthermore, when the forcing time interval is bounded and admits a recognized greater positive, we guarantee input-to-state stability, and solely worldwide uniform closing boundedness is assured when the upper positive is unknown. Numerical simulations are carried out for instance our outcomes