Threshold optimization of event-triggered multi-loop control systems

This paper considers multiple linear stochastic control systems whose feedback loops are closed over a shared communication medium. A threshold-based event-triggering rule is used to transmit control commands from the controllers to the actuators, and network access is arbitrated using a static priority mechanism. Under these conditions, we study dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system as a function of the event-thresholds of the individual loops. Also, we present analytical expressions that quantify the trade-off between the communication cost and the control performance of such event-triggered control systems. Using a multi-dimensional exhaustive search method, we determine the set of event thresholds that attains the minimal expected linear-quadratic loss of the closed-loop systems. Simulation studies highlight the trade-off between the communication and control cost.