Consistency of Value of Information: Effects of Packet Loss and Time Delay in Networked Control Systems Tasks

In this chapter, we study the consistency of the value of informationx2014a semantic metric that claims to determine the right piece of information in networked control systems tasksx2014in a lossy and delayed communication regime. Our analysis begins with a focus on state estimation, and subsequently extends to feedback control. To that end, we make a causal tradeoff between the packet rate and the mean square error. Associated with this tradeoff, we demonstrate the existence of an optimal policy profile, comprising a symmetric threshold scheduling policy based on the value of information for the encoder and a non-Gaussian linear estimation policy for the decoder. Our structural results assert that the scheduling policy is expressible in terms of $3d-1$ variables related to the source and the channel, where d is the time delay, and that the estimation policy incorporates no residual related to signaling. We then construct an optimal control policy by exploiting the separation principle.