Average Communication Rate for Networked Event-Triggered Stochastic Control Systems

Quantifying the average communication rate (ACR) of a networked event-triggered stochastic control system (NET-SCS) with deterministic thresholds is a challenging problem due to the non-stationary nature of the system's stochastic processes. For such a system, a closed-loop effect emerges due to the interdependence between the system variable and the trigger of communication. This effect, commonly referred to as \textit{side information} by related work, distorts the stochastic distribution of the system variables and makes the ACR computation non-trivial. Previous work in this area used to over-simplify the computation by ignoring the side information and misusing a Gaussian distribution, which leads to approximated results. This paper proposes both analytical and numerical approaches to predict the exact ACR for a NET-SCS using a recursive model. Furthermore, we use theoretical analysis and a numerical study to qualitatively evaluate the deviation gap of the conventional approach that ignores the side information. The accuracy of our proposed method, alongside its comparison with the simplified results of the conventional approach, is validated by experimental studies. Our work is promising to benefit the efficient resource planning of networked control systems with limited communication resources by providing accurate ACR computation.