Robust control of the Kuramoto-Sivashinsky equation

Authors
Citation
Cb. Hu et R. Temam, Robust control of the Kuramoto-Sivashinsky equation, DYN CONT B, 8(3), 2001, pp. 315-338
Citations number
25
Categorie Soggetti
Engineering Mathematics
Journal title
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS
ISSN journal
12013390 → ACNP
Volume
8
Issue
3
Year of publication
2001
Pages
315 - 338
Database
ISI
SICI code
1201-3390(200109)8:3<315:RCOTKE>2.0.ZU;2-I
Abstract
Robust control theory, a generalization of optimal control theory, has been proposed as an effective technique when control algorithms are sensitive t o a broad class of external disturbances. In [6], a general framework for t he robust control of the Navier-Stokes equations in finite time horizon was developed. In this article the robust boundary control for the Kuramoto-Si vashinsky equation is considered in the same spirit: a robust boundary cont rol problem is formulated, and the existence and uniqueness for the robust control problem are proved. A data assimilation problem corresponding to th e Kuramoto-Sivashinsky equation is considered, existence and uniqueness of solution are derived. This approach is also applicable as well to other equ ations with a structure similar to that of the Kuramoto-Sivashinsky equatio n.