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

TL;DR

This paper investigates how packet loss and delay affect the value of information in networked control systems, proposing optimal policies for scheduling and estimation to improve system performance.

Contribution

It introduces a symmetric threshold scheduling policy and a non-Gaussian linear estimation policy, establishing structural results and an optimal control policy under lossy and delayed communication.

Findings

Existence of an optimal threshold-based scheduling policy

Structural characterization of the estimation policy

Development of an optimal control policy using the separation principle

Abstract

In this chapter, we study the consistency of the value of information$\unicode{x2014}$a semantic metric that claims to determine the right piece of information in networked control systems tasks$\unicode{x2014}$in 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.