Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one-dimensional 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. We show that although the second case provides better simulations, this POD basis is in-suited for control problems. We provide a discussion of both the linear quadratic regulator (LQR) problem, and the linear quadratic Gaussian (LQG) problem. (C) 2001 Elsevier Science Ltd. All rights reserved.
proper orthogonal decomposition feedback control heat equation principal component analysis karhunen-loeve expansion