Value of Information in Feedback Control: Quantification

• 成果类型: Article
• 署名作者: Soleymani, Touraj; Baras, John S.; Hirche, Sandra
• 署名单位: Royal Institute of Technology; University System of Maryland; University of Maryland College Park; Technical University of Munich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3113472
• 发表日期: 2022
• 页码: 3730-3737
• 关键词: Decision policies; Nash equilibria; networked control systems; rate-regulation tradeoff; semantic communications; semantic metrics; value of information

摘要

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 VoI(k) 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, VoI(k) 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 VoI(k) is nonnegative. Moreover, we discuss that VoI(k) can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.