Optimal Local and Remote Controllers with Unreliable Uplink Channels

We consider a networked control system 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. We assume that the downlink channels from the remote controller to local controllers are perfect. The objective of the local controllers and the remote controller is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested problem, we obtain explicit optimal strategies for all controllers. In the optimal strategies, all controllers compute common estimates of the states of the plants based on the common information from the communication network. The remote controller’s action is linear in the common estimated states, and the action of each local controller is linear in both the actual state of its co-located plant and the common estimated states. We illustrate our results with a platoon control problem for autonomous vehicles.