Robust Distributed Control Beyond Quadratic Invariance

TL;DR

This paper introduces a new tractable optimization framework for distributed control that handles various information structures, providing optimal or near-optimal solutions with performance guarantees, especially when quadratic invariance does not hold.

Contribution

It proposes a novel decomposition-based approach to design controllers under complex information constraints, extending control design beyond quadratic invariance conditions.

Findings

The method yields globally optimal controllers when QI holds.

It provides feasible solutions and upper bounds on costs when QI does not hold.

Application to autonomous vehicle platooning demonstrates improved performance guarantees.

Abstract

The problem of robust distributed control arises in several large-scale systems, such as transportation networks and power grid systems. In many practical scenarios controllers might not have enough information to make globally optimal decisions in a tractable way. We propose a novel class of tractable optimization problems whose solution is a controller complying with any specified information structure. The approach we suggest is based on decomposing intractable information constraints into two subspace constraints in the disturbance feedback domain. We discuss how to perform the decomposition in an optimized way. The resulting control policy is globally optimal when a condition known as Quadratic Invariance (QI) holds, whereas it is feasible and it provides a provable upper bound on the minimum cost when QI does not hold. Finally, we show that our method can lead to improved performance guarantees with respect to previous approaches, by applying the developed techniques to the platooning of autonomous vehicles.