LQG control over lossy TCP-like networks with probabilistic packet acknowledgements

This paper focuses on control applications over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network. Sensor, control and acknowledgement packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time Linear Quadratic Gaussian (LQG) optimal control problem is considered. We can show how the partial loss of acknowledgements makes the optimal control law a nonlinear function of the information set. For the special case of complete state observation we can compute the optimal controller and show that the stability range increases monotonically with the arrival rate of the acknowledgement packets.