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- Title
Non-linear robust boundary control of the Kuramoto–Sivashinsky equation.
- Authors
SAKTHIVEL, RATHINASAMY; ITO, HIROSHI
- 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∞.
- Subjects
EQUATIONS; ROBUST control; SCALING laws (Statistical physics); NONLINEAR boundary value problems; LYAPUNOV functions; DIFFERENTIAL equations
- Publication
IMA Journal of Mathematical Control & Information, 2007, Vol 24, Issue 1, p47
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnl009