Event-based boundary control of a linear 2x2 hyperbolic system via backstepping approach

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 paper, we introduce an event-based boundary control for a 2 × 2 coupled linear hyperbolic system. We use a well established backstepping controller which stabilizes the system along with a dynamic triggering condition which determines when the controller must be updated. The main contributions rely on the definition of an event-based controller under which global exponential stability of the system is achieved and furthermore, the existence of a minimal dwell-time between two triggering times is guaranteed. The well-posedness of the system under the event-based controller is stated. A simulation example is presented to illustrate the results.

Mots clés: Linear hyperbolic systems; dynamic triggering condition; Backstepping control design; event-based control

Domaines: Automatique; Mathématiques [math]

Nicolás Espitia, Antoine Girard, Nicolas Marchand, Christophe Prieur. Event-based boundary control of a linear 2x2 hyperbolic system via backstepping approach . IEEE Transactions on Automatic Control, 2018, 63 (8), pp. 2686 - 2693. ⟨10.1109/TAC.2017.2774011⟩. ⟨hal-01592643⟩