Reducing the Dimensionality of Linear Quadratic Control Problems

Ronald Balvers and Douglas W. Mitchell
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Douglas W. Mitchell: West Virginia University, USA

No 01-043/2, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Linear-quadratic control; Riccati equation; Riccati reduction; Kalman filtering; Intertemporal optimization (search for similar items in EconPapers)
JEL-codes: C61 C63 D83 (search for similar items in EconPapers)
Date: 2001-04-11
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Related works:
Journal Article: Reducing the dimensionality of linear quadratic control problems (2007)
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