Event-triggered control

The rise of digital communication networks and embedded computing platforms offer many advantages for controller implementation (ease of installation and maintenance, lower costs, etc.). On the other hand, this type of implementation raises new challenges for automatic control, as the available computing and/or communication resources are subject to restrictions, and can be shared with tasks other than control. The classic approach of periodically updating the controller and communicating with sensors and actuators is generally unsuitable in this context. Indeed, to be effective, the sampling period must be selected small enough to cope with the worst case. This leads to frequent transmissions and computations, which can exceed available capacities. What is more, calculations and communications take place even when they are not necessary. If, for example, the objective is to bring the system state to an equilibrium point, and this is reached, then there is no need to update the controller and communicate (in the absence of disturbance). A periodic implementation, on the other hand, will blindly continue to generate transmissions and computations at the same frequency, thereby wasting available resources.

It is therefore necessary to envision new paradigms for implementing control laws in this context. An alternative has emerged over the past two decades: event-driven sampling (or transmission) control, commonly referred to as "event-triggered control". This paradigm involves adapting communications between the system and its controller, and the updating of the latter, according to the needs of the system, rather than the time elapsed since the last transmission, as is the case with periodic sampling. In this way, data is transmitted to the controller (and/or actuators) only when it is necessary for the closed-loop system to meet the set objective. More precisely, data transmission and controller execution are triggered when the current measured data become significantly different from the last reported. The question then becomes what is meant by "significantly different". This is formalized in the form of a criterion that typically depends on the current and last transmitted data. The challenge is then to define this criterion in such a way as to satisfy the control objective while guaranteeing the existence of a strictly positive minimum time between two transmissions, a prerequisite for any implementation.

The aim of this article is to present the main techniques in this field. For the sake of pedagogy, we will concentrate on the problem of stabilizing an operating point (the origin) of a linear system by event-triggered state feedback control. Nevertheless, the techniques presented and the methodological challenges they raise are at the heart of most of the methods...