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, L-infinity, and nu robust
control. We show in simulation that this algorithm achieves near-optimal
nominal performance (within 12% of the LQR controller) while doubling or
tripling the stability margin (depending on the stability criterion) 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, and
discuss open questions on the topic of distributed robust control.Comment: Submitted to CDC 202