Finite dimensional optimal control of Poiseuille flow

In this paper we consider linear stabilization of plane, Poiseuille flow us ing linear quadratic Gaussian optimal control theory. It is shown that we m ay significantly increase the dissipation rate of perturbation energy, whil e reducing the required control energy, as compared with that reported usin g simple, integral compensator control schemes. Poiseuille flow is describe d by the infinite dimensional Navier-Stokes equations. Because it is imposs ible to implement infinite dimensional controllers, we implement high hut f inite order controllers. We show that this procedure in theory can lead to destabilization of unmodeled dynamics. We then show that this may be avoide d using distributed control or, dually, distributed sensing. A problem in h igh plant order linear quadratic Gaussian controller design is numerical in stability in the synthesis equations, We show a linear quadratic Gaussian d esign that uses an extremely low-order plant model. This low-order controll er produces results essentially equivalent to the high-order controller.