Distributed Control of Descriptor Networks: A Convex Procedure for Augmented Sparsity

TL;DR

This paper introduces a convex, iterative method for designing distributed controllers in descriptor networks that ensures $ ext{H}_ extinfty$ performance and promotes sparsity in controller structure, even with improper transfer functions.

Contribution

It presents a novel convex optimization framework for distributed control of descriptor networks with sparsity constraints, guaranteeing convergence and robustness.

Findings

Guaranteed convergence of the proposed iterative procedure.

Ability to obtain sparse control laws not directly supported by the nominal model.

Framework applicable to networks with improper transfer functions.

Abstract

For networks of systems, with possibly improper transfer function matrices, we present a design framework which enables $\mathcal{H}_\infty$ control, while imposing sparsity constraints on the controller's coprime factors. We propose a convex and iterative optimization procedure with guaranteed convergence to obtain distributed controllers. By exploiting the robustness-oriented nature of our proposed approach, we provide the means to obtain sparse representations of our control laws that may not be directly supported by the network's nominal model.