1Foundations of Control and Estimation over Lossy Networks

Abstract — When data are transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network, both observation and control packets may be lost or delayed. This process can be modeled by assigning probabilities to successfully receive packets. Determin-ing the impact of this uncertainty on the feedback-loop requires a generalization of classical control theory. This paper presents the foundations of such new theory. Motivations and overview of the efforts of different research groups are described first. Then, novel contributions of the authors are presented. These include showing threshold behav-iors which are governed by the uncertainty parameters of the communication network: for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g. TCP-like protocols), there exists critical probabilities for the successful delivery of packets, below which the optimal controller fails to stabilize the system. Furthermore, for these protocols, the separation principle holds and the optimal LQG control is a linear function of the estimated state. 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. I