Non-linear robust boundary control of the Kuramoto-Sivashinsky equation

Abstract

This paper considers the problem of robust global stabilization of the Kuramoto–Sivashinsky equation subject to Neumann and Dirichlet boundary conditions. The aim is to derive non-linear robust boundary control laws which make the system robustly globally asymptotically stable in spite of uncertainty in both the instability parameter and the anti-diffusion parameter. A unique approach this paper introduces for achieving the required robustness is spatially dependent scaling of uncertain elements in Lyapunov-based stabilization. An important advantage of this approach is flexibility to obtain robust control laws with small control effort. The control laws can be implemented as Dirichlet-like boundary control as well as Neumann-like boundary control. Furthermore, it is shown that they guarantee the stability and boundedness in terms of both L2 and L∞.