  We consider a decentralized networked control system (DNCS) consisting of a
remote controller and a collection of linear plants, each associated with a
local controller. Each local controller directly observes the state of its
co-located plant and can inform the remote controller of the plant's state
through an unreliable uplink channel. The downlink channels from the remote
controller to local controllers were assumed to be perfect. The objective of
the local controllers and the remote controller is to cooperatively minimize
the infinite horizon time average of expected quadratic cost. The finite
horizon version of this problem was solved in our prior work [2]. The optimal
strategies in the finite horizon case were shown to be characterized by coupled
Riccati recursions. In this paper, we show that if the link failure
probabilities are below certain critical thresholds, then the coupled Riccati
recursions of the finite horizon solution reach a steady state and the
corresponding decentralized strategies are optimal. Above these thresholds, we
show that no strategy can achieve finite cost. We exploit a connection between
our DNCS Riccati recursions and the coupled Riccati recursions of an auxiliary
Markov jump linear system to obtain our results. Our main results in Theorems 1
and 2 explicitly identify the critical thresholds for the link failure
probabilities and the optimal decentralized control strategies when all link
failure probabilities are below their thresholds.
