Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2001-04-11
Number: 01-043/2
Author-Name: Ronald J. Balvers
Author-Email: rbalvers@wvu.edu
Author-Workplace-Name: West Virginia University, USA
Author-Name: Douglas W. Mitchell
Author-Workplace-Name: West Virginia University, USA
Title: Reducing the Dimensionality of Linear Quadratic Control Problems
Abstract: In linear-quadratic control (LQC) problems with singular control cost matrix and/or singular transition matrix, we derive a reduction of the dimension of the Riccati matrix, simplifying iteration and solution. Employing a novel transformation, we show that, under a certain rank condition, the matrix of optimal feedback coefficients is linear in the reduced Riccati matrix. For a substantive class of problems, our technique permits scalar iteration, leading to simple analytical solution. By duality the technique can also be applied to Kalman filtering problems with a singular measurement error covariance matrix.
Classification-JEL: C61; C63; D83
Keywords: Linear-quadratic control; Riccati equation; Riccati reduction; Kalman filtering; Intertemporal optimization
File-Url: https://papers.tinbergen.nl/01043.pdf
File-Format: application/pdf
File-Size: 242999 bytes
Handle: RePEc:tin:wpaper:20010043