A simple model for the interference between event-based control loops using a shared medium

Traditionally, control loops are closed using periodic sensing and actuation. When communication resources are scarce, much may be gained by instead transmitting only when something important has happened in the loop. However, there are no known closed form solutions to this kind of control problem. This paper presents a simple model of the interference between event-based control loops caused by sharing a common medium, based on approximating the behavior of all loops except one foreground loop. The stationary state distribution can be computed at low computational cost using mostly standard linear time-invariant system theory (applied in the spatial dimension). Control laws are optimized to minimize state variance using the limited communication resources. Comparison to Monte Carlo simulations of a full model shows the simple model to be remarkably accurate. The model is applied to investigate how the performance of N control loops sharing a common Carrier Sense Multiple Access channel approaches the ideal case of aperiodic control as the number of loops grows.