A noncausal strategy for feedback control of spatially-parabolic flow systems

We present a noncausal framework for model-based feedback stabilization of a large class of spatially-developing boundary-layer flow systems. The systems considered are (approximately) parabolic in the spatial coordinate x. This facilitates the application of a range of established feedback control theories which are based on the solution of differential Riccati equations which march over a finite horizon in x (rather than marching in t, as customary). However, unlike systems which are parabolic in time, there is no causality constraint for the feedback control of systems which are parabolic in space; that is, downstream information may be used to update the controls upstream. Thus, a particular actuator may be used to neutralize the effects of a disturbance which actually enters the system downstream of the actuator location. In the present study, a feedback control strategy is proposed which takes advantage of this special capability of feedback control rules in the spatially-parabolic setting in order to minimize a globally-defined cost function in an effort to maintain the flow laminar. Numerical results which verify the effectiveness of this approach is presented.