Distributed Robust Control for Systems with Structured Uncertainties

We present D-Φ 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 ${\mathcal{L}_1},{\mathcal{L}_\infty }$, and ν 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.