LQG computer control via communication channels with irregular transmission times

We study a linear discrete-time partially observed system perturbed by white noises. The observations are transmitted to the controller via communication channels that provide random transmission retardation. Various measurement signals and even various parts of a given sensor output may incur independent delays. Furthermore the messages transferred over the channels may be lost or corrupted. Under certain assumptions, a recursive minimum variance state estimator is proposed. A finite horizon linear-quadratic optimal control problem is solved. We also find a solution for the problem of minimizing the average cost per unit time over the infinite planning horizon. A concept of observability via the irregular communication channels is also introduced and investigated.