# Value of Information in Feedback Control: Quantification

arXiv: https://arxiv.org/abs/1812.07534 · HTML: https://mlsanity.com/paper/1812.07534/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 6 of 6)

- [Task-Oriented Communication Design at Scale](https://mlsanity.com/paper/2305.08481/) (2023)
- [InterQ: A DQN Framework for Optimal Intermittent Control](https://mlsanity.com/paper/2504.09035/) (2025)
- [World Model-Enabled Causal Digital Twins for Semantic Communications in Physical AI Systems](https://mlsanity.com/paper/2605.16547/) (2026)
- [VoI-Driven Joint Optimization of Control and Communication in Vehicular Digital Twin Network](https://mlsanity.com/paper/2505.07892/) (2025)
- [The Silence that Speaks: Neural Estimation via Communication Gaps](https://mlsanity.com/paper/2512.01056/) (2025)
- [When Does Test-Time Physical Diagnosis Pay? A Frozen Policy Buys Evidence It Never Reads](https://mlsanity.com/paper/2609.22299/) (2026)

## Abstract (arXiv)

Although transmission of a data packet containing sensory information in a networked control system improves the quality of regulation, it has indeed a price from the communication perspective. It is, therefore, rational that such a data packet be transmitted only if it is valuable in the sense of a cost-benefit analysis. Yet, the fact is that little is known so far about this valuation of information and its connection with traditional event-triggered communication. In the present article, we study this intrinsic property of networked control systems by formulating a rate-regulation tradeoff between the packet rate and the regulation cost with an event trigger and a controller as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this tradeoff. In particular, we characterize an equilibrium in the rate-regulation tradeoff, and quantify the value of information VoIk there as the variation in a so-called value function with respect to a piece of sensory information that can be communicated to the controller at each time k. We prove that, for a multi-dimensional Gauss-Markov process, VoIk is a symmetric function of the discrepancy between the state estimates at the event trigger and the controller, and that a data packet containing sensory information at time k should be transmitted to the controller only if VoIk is nonnegative. Moreover, we discuss that VoIk can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.