Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics

Mahmoud Abdelrahim (1) , Romain Postoyan (1) , Jamal Daafouz (1, 2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 IUF - Institut universitaire de France

We study event-triggered control based on a reduced or simplified model of the plant's dynamics. In particular, we address two time-scale systems and we investigate whether it is possible to synthesize a stabilizing event-triggered controller based only on an approximate model of the slow dynamics given by singular perturbation theory, when the fast one is stable. We highlight specific challenges which arise with the event-triggered implementation: the state of the fast model experiences jumps at transmissions which induces non-trivial difficulties for the stability analysis and the Zeno phenomenon may occur due to the fact that we neglect the fast dynamics. We describe the overall problem as a hybrid singularly perturbed system. We first provide a necessary condition on the triggering condition to avoid the Zeno phenomenon. Afterwards, we propose two solutions which respectively use a dead-zone and a clock variable and which ensure different asymptotic stability properties. The existence of a minimum inter-transmission interval is guaranteed. Our results are illustrated by a physical example.

Mots clés: Event-triggered control; singularly perturbed systems; hybrid systems

Domaines: Automatique / Robotique

Mahmoud Abdelrahim, Romain Postoyan, Jamal Daafouz. Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics. 9th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2013, Sep 2013, Toulouse, France. pp.347-352. ⟨hal-00875666⟩