Coupling estimation and control for a two dimensional Burgers type equation

Buchot, Jean-Marie; Raymond, Jean-Pierre; Tiago, Jorge

ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 535-560.

The aim of this paper is to study the boundary feedback stabilization of a two dimensional Burgers type equation with a Dirichlet boundary control and boundary measurements. Thus we have to deal with highly unbounded control and observation operators. We study the well posedness of the infinite dimensional system obtained by coupling a linear estimator with a linear feedback control law for the corresponding linearized parabolic system in a neighborhood of an unstable stationary solution. We prove the local stabilization of the system obtained by applying to the nonlinear equation the linear feedback control coupled with the linear compensator. Numerical experiments confirm the theoretical results.

Classification : 93B52, 93C20, 93E10
Mots clés : Burgers equation, feedback law, estimation, boundary control, compensator, boundary measurements, semilinear parabolic equations

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