A Simple Model for the Interference Between Event-Based Control Loops Using a Shared Medium

In English Traditionally, control loops are closed using periodic
sensing and actuation. When communication resources
are scarce, however, much may be gained from transmitting
only when something important has happened in the loop.
This paper presents a simple model of the interference between
event-based control loops caused by sharing a common medium,
based on the coupled dynamics of a Markov chain representing
the state of the medium, and the processes modeled as integrators
disturbed by white noise. The model is simple enough
to derive the stationary state distribution at low computational
cost using mostly standard linear time-invariant system theory
(applied in the spatial dimension), while capturing important
aspects of the problem. Control laws are optimized to minimize
state variance using the limited communication resources. The
results are compared to the less restrictive but unrealistic case
of aperiodic control, and to simulations of the system without
simplifications.