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

Touraj Soleymani, John S. Baras, Siyi Wang, Sandra Hirche, Karl H. Johansson

TL;DR

The work analyzes the consistency of the Value of Information (VoI) as a semantic metric in networked control tasks subject to packet loss and fixed delays. It formulates a causal trade-off between communication rate and estimation error for a partially observable Gauss-Markov process and proves the existence of a globally optimal policy profile: a symmetric VoI-based scheduling rule and a non-Gaussian estimator, with the scheduling depending on 3d-1 source/channel variables. The results extend to feedback control, where a separation principle yields a certainty-equivalent controller that uses the derived estimation policy, illustrating how VoI-guided transmissions adapt to both estimation error and channel conditions. Collectively, the findings provide principled design guidance for remote monitoring and control over lossy, delayed networks, linking information-theoretic notions with control performance.

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.

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

TL;DR

The work analyzes the consistency of the Value of Information (VoI) as a semantic metric in networked control tasks subject to packet loss and fixed delays. It formulates a causal trade-off between communication rate and estimation error for a partially observable Gauss-Markov process and proves the existence of a globally optimal policy profile: a symmetric VoI-based scheduling rule and a non-Gaussian estimator, with the scheduling depending on 3d-1 source/channel variables. The results extend to feedback control, where a separation principle yields a certainty-equivalent controller that uses the derived estimation policy, illustrating how VoI-guided transmissions adapt to both estimation error and channel conditions. Collectively, the findings provide principled design guidance for remote monitoring and control over lossy, delayed networks, linking information-theoretic notions with control performance.

Abstract

In this chapter, we study the consistency of the value of informationa semantic metric that claims to determine the right piece of information in networked control systems tasksin 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 variables related to the source and the channel, where 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.
Paper Structure (8 sections, 6 theorems, 19 equations, 2 figures)

This paper contains 8 sections, 6 theorems, 19 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Literature Survey
  3. Contributions and Organization
  4. A Tradeoff in the Lossy and Delayed Communication Regime
  5. Characterization of an Optimal Solution
  6. Transition from State Estimation to Feedback Control
  7. Numerical Example
  8. Conclusions

Key Result

lemma 1

Without loss of optimality, at each time $k$, one can adopt $\check{x}(k) = \mathop{\mathrm{\mathsf{E}}}\nolimits[x(k) | \mathcal{I}(k)]$ as the message that can be transmitted by the encoder, and $\hat{x}(k) = \mathop{\mathrm{\mathsf{E}}}\nolimits[x(k) | \mathcal{J}(k)]$ as the state estimate that

Figures (2)

  • Figure 1: Mean square error and packet transmission trajectories under the optimal policy profile. The total mean square error is $0.0536$, and the total number of packet transmissions is $46$, out of which $11$ were lost. The solid lines represent successful deliveries, and the dotted lines represent packet losses.
  • Figure 2: Mean square error and packet transmission trajectories under a periodic policy profile. The total mean square error is $0.0610$, and the total number of packet transmissions is $48$, out of which $10$ were lost. The solid lines represent successful deliveries, and the dotted lines represent packet losses.

Theorems & Definitions (13)

  • remark 1
  • lemma 1: erasure2023
  • lemma 2: stoccontrol
  • lemma 3: erasure2023
  • remark 2
  • definition 1: Value function
  • definition 2: Value of Information
  • theorem 1: erasure2023
  • remark 3
  • lemma 4: stoccontrol
  • ...and 3 more