Feedback flow control for transient energy growth minimization using convex-optimization techniques

The sub-critical transition of channel flow from a laminar to turbulent regime results from large transient energy growth (TEG) of disturbances. TEG can be minimized using previously formulated convex-optimization-based feedback control laws, requiring the solution to a standard linear matrix inequality (LMI) problem; however, methods for solving the associated LMI problem suffer from the curse of dimensionality, making controller synthesis intractable for high-dimensional fluid flows. In this talk, we develop reduced-order models to facilitate LMI-based controller synthesis in the context of a linearized channel flow with wall-normal blowing and suction actuators. The talk will focus on lessons learned, addressing fundamental modeling and design challenges. Performance and robustness trade-offs are examined and compared with other common optimal flow control strategies.