Optimal linear LQG control over lossy networks without packet acknowledgment

This paper is concerned with 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 and control 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. It is known that in the scenario described above, and for protocols for which there is no acknowledgment of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear. However, the simplicity of a linear sub-optimal solution is attractive for a variety of applications. Accordingly, this paper characterizes the optimal linear static controller and compares its performance to the case when there is acknowledgment of delivery of packets (e.g. TCP-like protocols).