Performance Analysis of Event-Triggered Control Systems with A Probabilistic Triggering Mechanism: The Scalar Case

Abstract

This paper considers a linear stochastic control system whose feedback loop is closed over (possibly low-power wireless) communication channels. A probabilistic event-based scheduling rule is adopted to transmit measurements from the sensor to the controller. The controller only computes a new control command whenever a sensor packet arrives at the controller. The event-triggered strategy proposed in this paper aims at providing significant reductions in the usage of both the sensor-to-controller and controller-to-actuator channels. Within this setup, we investigate dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system. We also provide analytic expressions that quantify the trade-off between the communication cost and the control performance of such event-triggered control systems. This trade-off is demonstrated quantitatively via a numerical example.