Event-triggered control under Poisson events: the role of sporadicity*

We consider an event-triggered control loop in which the intervals between consecutive events are exponentially distributed. Events cause state jumps following a given distribution and may result from multiple sources. This framework can capture scenarios in which events are sporadic (low rate Poisson processes) or frequent (in the limit Wiener processes). We propose an event-triggered control strategy which guarantees a better transmission rate vs performance trade-off than periodic control and which is optimal when events are sporadic, although approaching the periodic control trade-off when events are frequent. Performance is measured by an average cost. We also propose a different strategy by which transmissions are triggered when a special estimation error norm exceeds a threshold. For the latter strategy, we provide lower and upper bounds for the transmission rate and performance. We discuss the applicability of the results in queuing systems, control of plants disturbed by Wiener processes, and networked control.