Foundations of Value of Information: A Semantic Metric for Networked Control Systems Tasks

TL;DR

This paper introduces a semantic metric called the value of information for networked control systems, quantifies its relationship with control performance, and establishes conditions for optimal information exchange.

Contribution

It formulates a causal tradeoff between packet rate and regulation cost, characterizes the value of information, and proves the global optimality of the equilibrium strategy.

Findings

Value of information depends on state estimate discrepancy.

Optimal communication occurs when the value of information is nonnegative.

The equilibrium strategy is globally optimal.

Abstract

In this chapter, we present our recent invention, i.e., the notion of the value of information$\unicode{x2014}$a semantic metric that is fundamental for networked control systems tasks. We begin our analysis by formulating a causal tradeoff between the packet rate and the regulation cost, with an encoder and a decoder as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this tradeoff. More precisely, we characterize an equilibrium, and quantify the value of information there as the variation in a value function with respect to a piece of sensory measurement that can be communicated from the encoder to the decoder at each time. We prove that, in feedback control of a dynamical process over a noiseless channel, the value of information is a function of the discrepancy between the state estimates at the encoder and the decoder, and that a data packet containing a sensory measurement at each time should be exchanged only if the value of information at that time is nonnegative. Finally, we prove that the characterized equilibrium is in fact globally optimal.