  A linear non-modal mechanism for transient amplification of perturbation
energy is known to trigger sub-critical transition to turbulence in many shear
flows. Feedback control strategies for minimizing this transient energy growth
can be formulated as convex optimization problems based on linear matrix
inequalities. Unfortunately, solving the requisite linear matrix inequality
problem can be computationally prohibitive within the context of
high-dimensional fluid flows. In this work, we investigate the utility of
control-oriented reduced-order models to facilitate the design of feedback flow
control strategies that minimize the maximum transient energy growth. An output
projection onto proper orthogonal decomposition modes is used to faithfully
capture the system energy. Subsequently, a balanced truncation is performed to
reduce the state dimension, while preserving the system's input-output
properties. The model reduction and control approaches are studied within the
context of a linearized channel flow with blowing and suction actuation at the
walls. Controller synthesis for this linearized channel flow system becomes
tractable through the use of the proposed control-oriented reduced-order
models. Further, the resulting controllers are found to reduce the maximum
transient energy growth compared with more conventional linear quadratic
optimal control strategies.
