Journal Article

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

Rathinasamy Sakthivel and Hiroshi Ito

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 1, pages 47-55
Published in print March 2007 | ISSN: 0265-0754
Published online March 2007 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnl009
Non-linear robust boundary control of the Kuramoto–Sivashinsky equation

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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.

Keywords: Kuramoto–Sivashinsky equation; robust global stabilization; spatially dependent scaling; non-linear boundary control; Lyapunov function

Journal Article.  0 words. 

Subjects: Mathematics

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