Distributed Robust Set-Invariance for Interconnected Linear Systems

TL;DR

This paper develops distributed control policies for interconnected linear systems with disturbances, ensuring safety constraints are met, and determines the minimal communication structure needed for such invariance.

Contribution

It introduces a linear programming approach for optimal distributed control and identifies the sparsest communication graph for invariance.

Findings

Linear program computes optimal distributed control policies.

Minimal communication graph for invariance identified.

Applicable to safety-critical networked systems.

Abstract

We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invariance-inducing control policy. Illustrative examples, including one on platooning, are presented.