A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part I: formulation

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 paper (Part I), a numerically tractable feedback control strategy is formulated 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 laminar boundary-layer flow. A companion paper (Part II) presents numerical simulations which verify the effectiveness of the present approach. (C) 2003 Elsevier B.V. All rights reserved.