Event-triggered control of Korteweg-de Vries equation under averaged measurements

Wen Kang (1) , Lucie Baudouin (2) , Emilia Fridman (3)

1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, China
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 Department of Electrical Engineering

This work addresses distributed event-triggered control law of 1-D nonlinear Korteweg-de Vries (KdV) equation posed on a bounded domain. Such a system, in a continuous framework, is exponentially stabilizable by a linear state feedback as a source term. Here we consider the situation where the feedback is sampled in time and piecewise averaged in space, and an event-triggering mechanism is designed to maintain stability of this infinite dimensional system. Both well-posedness of the closed-loop system and avoiding the Zeno behaviour issues are addressed. Sufficient LMI-based conditions are constructed to guarantee the regional exponential stability. A numerical example illustrates the efficiency of the method.

Mots clés: LMIs; Korteweg-de Vries equation; event-trigger; LMI

Domaines: Optimisation et contrôle [math.OC]; Automatique

Wen Kang, Lucie Baudouin, Emilia Fridman. Event-triggered control of Korteweg-de Vries equation under averaged measurements. Automatica, 2021, 123, pp.109315. ⟨10.1016/j.automatica.2020.109315⟩. ⟨hal-02459827v2⟩