Some ingredients on event-triggered control for some partial differential equations
Résumé
Event-triggered control devises event-triggering mechanisms leading to only seldom control updates. In event-triggered control, two objectives are (1) emulation, whereby the controller is a priori predesigned and only the event-triggering rules have to be designed and (2) co-design, where the joint design of the control law and the event-triggering conditions has to be performed. Control systems are connected to generic digital communication networks for implementation, transmission, coding, or decoding. Therefore, event-triggered control strategies have been developed to cope with communication, energy consumption, and computation constraints. The talk is within this scope when dealing with some partial differential equations. Indeed, this talk proposes condition to carry out the global exponential stability of the wave equation under an event-triggering mechanism that updates a damping source term. The damping is distributed in the whole space but sampled in time. The well-posedness of the closed-loop event-triggered control system is considered. The talk mainly focuses on the avoidance of Zeno behavior provided that the initial data are more regular. The interest of the results is drawn through some numerical simulations.