A new integral boundary control for de Saint-Venant Partial Differential Equations

Valérie dos Santos Martins (1) , C.-Z Xu (2) , V Andrieu

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 LAGEP - Laboratoire d'automatique et de génie des procédés

The paper deals with output feedback regulation of exponentially stable systems by an integral controller. We have recently proposed an appropriate Lyapunov functional to prove exponential stability of the closed-loop system. The approach is dedicated in this paper to hyperbolic systems and especially to the de Saint-Venant equations giving explicitly the gains to ensure an exponentially stabilized integral controller: the parameters expression is deduced directly of the Lyapunov functional based on the Forwarding approach. Numerical simulations illustrate this approach.

Mots clés: de Saint-Venant equations; Hyperbolic PDE; Lyapunov; Forwarding; Integral controller

Domaines: Equations aux dérivées partielles [math.AP]; Automatique / Robotique

Valérie dos Santos Martins, C.-Z Xu, V Andrieu. A new integral boundary control for de Saint-Venant Partial Differential Equations. MTNS 2020, Aug 2020, Cambridge, United Kingdom. ⟨hal-02880656⟩