Optimal control via asynchronous communications 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, and its outputs are sent to the actuators via communication channels that produce random transmission times and may lose messages. Various signals may incur independent delays and arrive at the destination point out of order. Under certain assumptions, a recursive minimum variance state estimator is proposed. A finite horizon linear-quadratic optimal control problem is solved.