Optimal control with unreliable communication: the TCP case

The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We consider the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon our previous results on estimation with unreliable communication, the paper shows the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower hounds on the cost functional.