Boundary Observers for Linear and Quasi-linear Hyperbolic Systems with Application to Flow Control

Felipe Castillo Buenaventura (1) , Emmanuel Witrant (1) , Christophe Prieur (2) , Luc Dugard (1)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

In this paper we consider the problem of boundary observer design for one-dimensional fi rst order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some su fficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We consider static as well as dynamic boundary controls for the boundary observer design. The main results are illustrated on the model of an inviscid incompressible flow.

Mots clés: in finite dimensional observer; Boundary observers; hyperbolic systems; in finite dimensional observer.

Domaines: Automatique / Robotique

Felipe Castillo Buenaventura, Emmanuel Witrant, Christophe Prieur, Luc Dugard. Boundary Observers for Linear and Quasi-linear Hyperbolic Systems with Application to Flow Control. Automatica, 2013, 49 (11), pp.3180-3188. ⟨10.1016/j.automatica.2013.07.027⟩. ⟨hal-00841207⟩