Value of Information in Minimum-Rate LQG Control

This study concerns fundamental limitations in control of mobile cyber-physical systems. In these systems, communication between a node and its base station due to limited power of the node is asymmetrical in terms of bandwidth and signal-to-noise ratio. The framework we develop in this paper is for partially observed linear quadratic Gaussian (LQG) control over communication networks in which the forward channel transporting measurements is modeled by a zero-delay packet-deletion channel and the feedback channel transporting control inputs is assumed ideal. Making use of dynamic programming, we characterize the optimal control and the optimal sampling policies that achieve the minimum data rate required for a guaranteed level of control performance. In particular, we prove that in the presence of eventdriven sampling the adopted filter is optimal and the separation principle between control and estimation holds. We show that the optimal control policy is a certainty equivalent policy and the optimal sampling policy is a threshold policy expressed in terms of the value of information. Furthermore, we prove that the value of information is a quadratic function of the innovation.