Value of Information in Feedback Control: Quantification

• Published in: IEEE transactions on automatic control Vol. 67; no. 7; pp. 3730 - 3737
• Main Authors: Soleymani, Touraj, Baras, John S., Hirche, Sandra
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Controllers; Cost accounting; Cost benefit analysis; Costs; Decision making; Decision policies; Decision policy; Economic and social effects; Estimation; Feedback control; Game theory; Gaussian process; Markov processes; Nash equilibria; Network control; Networked control systems; Optimal control; Optimal controls; Process control; Quadratic equations; rate-regulation trade-off; rate-regulation tradeoff; Regulation; Semantic communication; semantic communications; semantic metrics; Semantics; Sensory information; Stochastic systems; Trade off; Tradeoffs; value of information
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2021.3113472

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 trade-off 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 trade-off. In particular, we characterize an equilibrium in the rate-regulation trade-off, and quantify the value of information <inline-formula><tex-math notation="LaTeX">{\rm{VoI}}_k</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>. We prove that, for a multi-dimensional Gauss--Markov process, <inline-formula><tex-math notation="LaTeX">{\rm{VoI}}_k</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> should be transmitted to the controller only if <inline-formula><tex-math notation="LaTeX">{\rm{VoI}}_k</tex-math></inline-formula> is nonnegative. Moreover, we discuss that <inline-formula><tex-math notation="LaTeX">{\rm{VoI}}_k</tex-math></inline-formula> can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.