Distributed Robust Control for Systems with Structured Uncertainties

TL;DR

This paper introduces D-Phi iteration, a novel distributed control algorithm that enhances robustness in systems with structured uncertainties, combining SLS parametrization with robust control criteria, and demonstrating improved stability margins in simulations.

Contribution

It presents the first distributed, localized algorithm for structured robust control with complexity depending only on local neighborhoods.

Findings

Achieves good nominal performance in simulations.

Significantly increases robust stability margin over LQR.

Algorithm complexity is independent of global system size.

Abstract

We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm complexity depends only on the size of local neighborhoods and is independent of global system size. We additionally characterize the suitability of different robustness criteria for distributed and localized computation.