Optimal Local and Remote Controllers with Unreliable Communication

We consider a decentralized optimal control problem for a linear plant controlled by two controllers, a local controller and a remote controller. The local controller directly observes the state of the plant and can inform the remote controller of the plant state through a packet-drop channel. We assume that the remote controller is able to send acknowledgments to the local controller to signal the successful receipt of transmitted packets. The objective of the two controllers 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 LQG problem, we obtain explicit optimal strategies for the two controllers. In the optimal strategies, both controllers compute a common estimate of the plant state based on the common information. The remote controller's action is linear in the common estimated state, and the local controller's action is linear in both the actual state and the common estimated state.