paper

Value of Information in Feedback Control: Quantification

arXiv:1812.07534 · doi:10.1109/TAC.2021.3113472

Abstract

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 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 . We prove that, for a multi-dimensional Gauss-Markov process, 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 should be transmitted to the controller only if is nonnegative. Moreover, we discuss that can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.

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