Event-triggered Controllers using Contraction Analysis

Brigitte Bidégaray-Fesquet (1) , Nacim Meslem (2) , Fairouz Zobiri (3)

1 EDP - Equations aux Dérivées Partielles
2 GIPSA-MODUS - GIPSA - Modelling and Optimal Decision for Uncertain Systems
3 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven

In this paper, we introduce an event-triggered control method that relies on contraction analysis. Contraction analysis considers stability with respect to a nominal trajectory rather than an equilibrium point. If two neighboring trajectories of a system are located in a contraction region, they will tend to each other and to a nominal trajectory. In the event-triggered control algorithm that we introduce, we suggest to update the control law whenever the system trajectory is about to leave the contraction region. We show that such a scheduling of the control law guarantees system stability, and we show that a minimum inter-event time exists between consecutive updates of the control law. We also show how to place the system trajectory in a contraction region and discuss the conditions of existence of the required transformation to perform that.

Mots clés: LTV systems, Nonlinear systems, Stability analysis, Event-based control, Contraction theory

Domaines: Automatique / Robotique

Brigitte Bidégaray-Fesquet, Nacim Meslem, Fairouz Zobiri. Event-triggered Controllers using Contraction Analysis. 2022. ⟨hal-03862017v1⟩