On the trade-off between control performance and communication cost for event-triggered control over lossy networks

This paper develops a theoretical framework for quantifying the trade-off between communication cost and control performance in event-triggered control over lossy networks. We consider a system where the communication between the controller and actuator is dictated by a threshold-based event-triggering algorithm, and develop a Markov-chain model that describes the attempted and successful transmissions of control messages over the lossy communication channel. A feature of our model is that it considers retransmissions of unsuccessful messages and that it accounts for the delay associated with such retransmissions. A systematic framework for analyzing the trade-off between the communication rate and control performance and for optimal tuning of the event threshold emanates by combining this model with an analytical model of the closed-loop performance. Numerical examples demonstrate the effectiveness of the proposed framework.