  In this work, we focus on the design of optimal controllers that must comply
with an information structure. State-of-the-art approaches do so based on the
H2 or Hinfty norm to minimize the expected or worst-case cost in the presence
of stochastic or adversarial disturbances. Large-scale systems often experience
a combination of stochastic and deterministic disruptions (e.g., sensor
failures, environmental fluctuations) that spread across the system and are
difficult to model precisely, leading to sub-optimal closed-loop behaviors.
Hence, we propose improving performance for these scenarios by minimizing the
regret with respect to an ideal policy that complies with less stringent
sensor-information constraints. This endows our controller with the ability to
approach the improved behavior of a more informed policy, which would detect
and counteract heterogeneous and localized disturbances more promptly.
Specifically, we derive convex relaxations of the resulting regret minimization
problem that are compatible with any desired controller sparsity, while we
reveal a renewed role of the Quadratic Invariance (QI) condition in designing
informative benchmarks to measure regret. Last, we validate our proposed method
through numerical simulations on controlling a multi-agent distributed system,
comparing its performance with traditional H2 and Hinfty policies.
