Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Relation between Value and Age of Information in Feedback Control

Touraj Soleymani, John S. Baras, Karl H. Johansson

TL;DR

This chapter investigates the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system and establishes the mathematical relation between the value of information and the age of information.

Abstract

In this chapter, we investigate the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system. In particular, we quantify the value of information based on the variation in a value function, and discuss the structural properties of this metric. Through our analysis, we establish the mathematical relation between the value of information and the age of information. We prove that the value of information is in general a function of an estimation discrepancy that depends on the age of information and the primitive variables. In addition, we prove that there exists a condition under which the value of information becomes completely expressible in terms of the age of information. Nonetheless, we show that this condition is not achievable without a degradation in the performance of the system.

Relation between Value and Age of Information in Feedback Control

TL;DR

This chapter investigates the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system and establishes the mathematical relation between the value of information and the age of information.

Abstract

In this chapter, we investigate the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system. In particular, we quantify the value of information based on the variation in a value function, and discuss the structural properties of this metric. Through our analysis, we establish the mathematical relation between the value of information and the age of information. We prove that the value of information is in general a function of an estimation discrepancy that depends on the age of information and the primitive variables. In addition, we prove that there exists a condition under which the value of information becomes completely expressible in terms of the age of information. Nonetheless, we show that this condition is not achievable without a degradation in the performance of the system.
Paper Structure (5 sections, 10 theorems, 45 equations, 3 figures)

This paper contains 5 sections, 10 theorems, 45 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Main Results
  4. Numerical Example
  5. Conclusion

Key Result

lemma 1

The conditional mean $\mathop{\mathrm{\mathsf{E}}}\nolimits[x_k | \mathcal{I}^e_k]$ is the minimum mean-square-error estimator at the event trigger, and satisfies for $k \in \mathcal{K}$.

Figures (3)

  • Figure 1: The estimation error norm trajectories at the controller and at the event trigger.
  • Figure 2: The age of information trajectories at the controller and at the event trigger.
  • Figure 3: The value of information (scaled by $1/N$) and transmission event trajectories.

Theorems & Definitions (22)

  • definition 1
  • lemma 1
  • proof
  • lemma 2
  • proof
  • lemma 3
  • proof
  • lemma 4
  • proof
  • lemma 5
  • ...and 12 more