Nonlinear controller design for a class of parabolic-hyperbolic systems

Mohamed Boutayeb (1) , Mohamed Ghattassi (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This contribution concerns the problem of nite di- mensional control for a class of systems described by nonlinear hyperbolic-parabolic coupled partial dierential equations (PDE's). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary dierential equation (ODE) system that accu- rately describes the dynamics of the dominant (slow) modes of the PDE system. After, we introduce a useful nonlinear controller to assure stabilization under convex sucient conditions. At last, we give a numerical example showing the eectiveness of the proposed controller and some comments illustrate this approach.

Mots clés: Radiative transfer equation; Nonlinear heat equation; Galerkin method; Linear Matrix Inequalities (LMIs).

Domaines: Automatique / Robotique

Mohamed Boutayeb, Mohamed Ghattassi. Nonlinear controller design for a class of parabolic-hyperbolic systems. Journal of Nonlinear Systems and Applications, 2016, 5 (1), pp.15-20. ⟨hal-01321528⟩