Output Feedback Event-Triggered Control

Abstract

Event-triggered control has been proposed as an alternative implementation to conventional time-triggered approach in order to reduce the amount of transmissions. The idea is to adapt transmissions to the state of the plant such that the loop is closed only when it is needed according to the stability or/and the performance requirements. Most of the existing event-triggered control strategies assume that the full state measurement is available. Unfortunately, this assumption is often not satisfied in practice. There is therefore a strong need for appropriate tools in the context of output feedback control. Most existing works on this topic focus on linear systems. The objective of this chapter is to first summarize our recent results on the case where the plant dynamics is nonlinear. The approach we follow is emulation as we first design a stabilizing output feedback law in the absence of sampling; then we consider the network and we synthesize the event-triggering condition. The latter combines techniques from event-triggered and time-triggered control. The results are then proved to be applicable to linear time-invariant (LTI) systems as a particular case. We then use these results as a starting point to elaborate a co-design method, which allows us to jointly construct the feedback law and the triggering condition for LTI systems where the problem is formulated in terms of linear matrix inequalities (LMI). We then exploit the flexibility of the method to maximize the guaranteed minimum amount of time between two transmissions. The results are illustrated on physical and numerical examples.