  Recent works in the domain of networked control systems have demonstrated
that the joint design of medium access control strategies and control
strategies for the closed-loop system is beneficial. However, several metrics
introduced so far fail in either appropriately representing the network
requirements or in capturing how valuable the data is. In this paper we propose
a distributed value of information (dVoI) metric for the joint design of
control and schedulers for medium access in a multi-loop system and multi-hop
network. We start by providing conditions under certainty equivalent controller
is optimal. Then we reformulate the joint control and communication problem as
a Bellman-like equation. The corresponding dynamic programming problem is
solved in a distributed fashion by the proposed VoI-based scheduling policies
for the multi-loop multi-hop networked control system, which outperforms the
well-known time-triggered periodic sampling policies. Additionally we show that
the dVoI-based scheduling policies are independent of each other, both
loop-wise and hop-wise. At last, we illustrate the results with a numerical
example.
