Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures

TL;DR

This paper introduces a unified framework for verifying convexity in distributed control problems with arbitrary information structures, enabling efficient control policy computation under complex communication and safety constraints.

Contribution

It generalizes quadratic invariance to arbitrary information structures, providing a binary matrix test for convexity in distributed control with polytopic constraints.

Findings

The proposed test certifies convexity for any information structure.

Framework accommodates time-varying communication networks.

Includes polytopic state and input constraints naturally.

Abstract

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this technical note, we focus on the requirement that the control policy is distributed, in the sense that it can only be based on partial information about the history of the outputs. It is well-known that when a condition denoted as Quadratic Invariance (QI) holds, the optimal distributed control policy can be computed in a tractable way. Our goal is to unify and generalize the class of information structures over which quadratic invariance is equivalent to a test over finitely many binary matrices. The test we propose certifies convexity of the output-feedback distributed control problem in finite-horizon given any arbitrarily defined information structure, including the case of time varying communication networks and forgetting mechanisms. Furthermore, the framework we consider allows for including polytopic constraints on the states and the inputs in a natural way, without affecting convexity.