  The rate-regulation tradeoff, defined between two objective functions, one
penalizing the packet rate and one the regulation cost, can express the
fundamental performance bound of networked control systems. However, the
characterization of the set of globally optimal solutions in this tradeoff for
multi-dimensional Gauss-Markov processes has been an open problem. In the
present article, we characterize a policy profile that belongs to this set
without imposing any restrictions on the information structure or the policy
structure. We prove that such a policy profile consists of a symmetric
threshold triggering policy based on the value of information and a
certainty-equivalent control policy based on a non-Gaussian linear estimator.
These policies are deterministic and can be designed separately. Besides, we
provide a global optimality analysis for the value of information
$\text{VoI}_k$, a semantic metric that emerges from the rate-regulation
tradeoff as the difference between the benefit and the cost of a data packet.
We prove that it is globally optimal that a data packet containing sensory
information at time $k$ be transmitted to the controller only if $\text{VoI}_k$
becomes nonnegative. These results have important implications in the areas of
communication and control.
