  In this chapter, we present our recent invention, i.e., the notion of the
value of information$\unicode{x2014}$a semantic metric that is fundamental for
networked control systems tasks. We begin our analysis by formulating a causal
tradeoff between the packet rate and the regulation cost, with an encoder and a
decoder as two distributed decision makers, and show that the valuation of
information is conceivable and quantifiable grounded on this tradeoff. More
precisely, we characterize an equilibrium, and quantify the value of
information there as the variation in a value function with respect to a piece
of sensory measurement that can be communicated from the encoder to the decoder
at each time. We prove that, in feedback control of a dynamical process over a
noiseless channel, the value of information is a function of the discrepancy
between the state estimates at the encoder and the decoder, and that a data
packet containing a sensory measurement at each time should be exchanged only
if the value of information at that time is nonnegative. Finally, we prove that
the characterized equilibrium is in fact globally optimal.
