Optimal Local and Remote Controllers with Unreliable Uplink Channels

TL;DR

This paper develops explicit optimal control strategies for a networked control system with multiple plants and controllers, accounting for unreliable uplink communication channels, using a novel dynamic programming approach.

Contribution

It introduces a dynamic programming framework for decentralized control with unreliable uplinks, providing explicit optimal strategies despite non-partial nestedness.

Findings

Controllers compute common state estimates from shared information.

Optimal actions are linear in local states and common estimates.

Numerical experiments validate the effectiveness of the strategies.

Abstract

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 obtained from the communication network. The remote controller's action is linear in the common state estimates, and the action of each local controller is linear in both the actual state of its co-located plant and the common state estimates. We illustrate our results with numerical experiments using randomly generated models.