Reduced order feedback synthesis for viscous incompressible flows

We discuss the application of the reduced basis method for the simulation a nd control of unsteady viscous flows governed by the incompressible Navier- Stokes equations. We describe how to use this method in terms of the constr uction of a lower-order compensator design. Our approach includes a constru ction method of the optimal state feedback law for finite-dimensional nonli near regulator problems. The method is applied to construct a feedback law for the reduced order control model of the Navier-Stokes equations, and the n we apply our feedback law to the original control system. Our method is d emonstrated on a control problem formulated in a channel Row using a bounda ry velocity control. We also show how these ideas can be extended to contro l problems governed by partial differential equations. Numerical results ar e reported for the open and closed loop controls, and a compensator design is proposed to complete the closed loop dynamics. (C) 2001 Elsevier Science Ltd. All rights reserved.