Optimal LQG Control over Lossy Packet Networks

This paper is concerned with control applications over lossy data networks. Sensor data is transmitted to a estimation-control unit over a network, and control commands are issued to subsystems over the same network. Sensor and control packets may be lost or delayed. This is modeled by allowing that sensor and control packets are successfully received with certain probabilities. In this context, the discrete-time Linear Quadratic Gaussian (LQG) optimal control problem is considered. The objective of this paper is to understand the system-theoretic implications of using unreliable networks for control and estimation. It is shown that for protocols where successful transmissions of packets are acknowledged at the receiver (e.g. TCP-like protocols), the separation principle holds. For these protocols, the optimal LQG control is a linear function of the estimated state. Further, there exists a critical probability for the successful delivery of packets, below which the optimal controller fails to stabilize the system. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear.