Turbulent drag reduction by feedback: a Wiener-filtering approach

In an attempt to devise control laws for reducing drag in turbulent wall ows, modern control theory has recently been employed for the design of linear controllers [1], state estimators [2], and compensators [3; 4]. These approaches led to encouraging results, revealing the potential of linear control in targeting significant dynamics in wall turbulence [5]. All the aforementioned works, however, rely on an approximate statespace representation of the system dynamics, obtained by linearization of the governing equations about a base ow profile. The state-space formulation reduces the compensator design problem to the solution of two matrix Riccati equations, a procedure that becomes computationally cumbersome for high-dimensional systems. Effects of nonlinearities and modeling errors are accounted for by introducing state and measurement noises with known (approximately modeled) statistics.