Proper orthogonal decomposition for reduced basis feedback controllers forparabolic equations

In this paper, we present a discussion of the proper orthogonal decompositi on (POD) as applied to simulation and feedback control of the one-dimension al heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the finite element basis of linear B-splines. Next, we additionally include time snapshots. W e show that although the second case provides better simulations, this POD basis is in-suited for control problems. We provide a discussion of both th e linear quadratic regulator (LQR) problem, and the linear quadratic Gaussi an (LQG) problem. (C) 2001 Elsevier Science Ltd. All rights reserved.