Lqg Control with Missing Observation and Control Packets

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. For protocols where packets are acknowledged at the receiver (e.g. TCP type protocols), the separation principle holds. Moreover, 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 and lower bounds on the cost functional, and stochastically characterizing their convergence properties in the infinite horizon. More interestingly, it turns out that when there is no feedback on whether a control packet has been delivered or not(e.g. UDP type protocols), the LQG optimal controller is in general nonlinear. A special case when the optimal controller is indeed linear is shown.