  The paper introduces a Data-driven Hierarchical Control (DHC) structure to
improve performance of systems operating under the effect of system and/or
environment uncertainty. The proposed hierarchical approach consists of two
parts: 1) A data-driven model identification component to learn a linear
approximation between reference signals given to an existing lower-level
controller and uncertain time-varying plant outputs. 2) A higher-level
controller component that utilizes the identified approximation and wraps
around the existing controller for the system to handle modeling errors and
environment uncertainties during system deployment.
  We derive loose and tight bounds for the identified approximation's
sensitivity to noisy data. Further, we show that adding the higher-level
controller maintains the original system's stability. A benefit of the proposed
approach is that it requires only a small amount of observations on states and
inputs, and it thus works online; that feature makes our approach appealing to
robotics applications where real-time operation is critical. The efficacy of
the DHC structure is demonstrated in simulation and is validated experimentally
using aerial robots with approximately-known mass and moment of inertia
parameters and that operate under the influence of ground effect.
