Event-based control of linear hyperbolic systems of conservation laws

Nicolás Espitia (1) , Antoine Girard (2) , Nicolas Marchand (1) , Christophe Prieur (1)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 L2S - Laboratoire des signaux et systèmes

In this article, we introduce event-based boundary controls for 1-dimensional linear hyperbolic systems of conservation laws. Inspired by event-triggered controls developed for finite-dimensional systems, an extension to the infinite dimensional case by means of Lyapunov techniques, is studied. The main contribution of the paper lies in the definition of two event-triggering conditions, by which global exponential stability and well-posedness of the system under investigation is achieved. Some numerical simulations are performed for the control of a system describing traffic flow on a roundabout.

Mots clés: Linear hyperbolic systems; Lyapunov techniques; Triggering conditions; Piecewise continuous functions

Domaines: Automatique / Robotique; Automatique

Nicolás Espitia, Antoine Girard, Nicolas Marchand, Christophe Prieur. Event-based control of linear hyperbolic systems of conservation laws. Automatica, 2016, 70, pp.275-287. ⟨10.1016/j.automatica.2016.04.009⟩. ⟨hal-01309671⟩