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Reducing the Dimensionality of Linear Quadratic Control Problems

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Author Info
Ronald J. Balvers () (West Virginia University, USA)
Douglas W. Mitchell (West Virginia University, USA)

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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.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-043/2.

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Date of creation: 11 Apr 2001
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Handle: RePEc:dgr:uvatin:20010043

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Linear-quadratic control Riccati equation Riccati reduction Kalman filtering Intertemporal optimization

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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  1. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September. [Downloadable!] (restricted)
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  4. Mitchell, Douglas W., 2000. "An analytic Riccati solution for two-target discrete-time control," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 615-622, April. [Downloadable!] (restricted)
  5. Paul A. Ruud, 2000. "natural rate of unemployment data," Instructional Stata datasets for econometrics nairu, Boston College Department of Economics. [Downloadable!]
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  7. Ronald J. Balvers & Yangru Wu, 2004. "Momentum and Mean Reversion Across National Equity Markets," Working Papers 04-11, Department of Economics, West Virginia University. [Downloadable!]
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  8. Ehlgen, Jurgen, 1999. "A Nonrecursive Solution Method for the Linear-Quadratic Optimal Control Problem with a Singular Transition Matrix," Computational Economics, Springer, vol. 13(1), pages 17-23, February. [Downloadable!]
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  11. Amman, Hans M. & Neudecker, Heinz, 1997. "Numerical solutions of the algebraic matrix Riccati equation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 363-369. [Downloadable!] (restricted)
  12. Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994. "Mechanics of forming and estimating dynamic linear economies," Staff Report 182, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  13. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252. [Downloadable!] (restricted)
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Cited by:
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  1. Mehari Mekonnen Akalu, 2002. "Measuring and Ranking Value Drivers," Tinbergen Institute Discussion Papers 02-043/2, Tinbergen Institute. [Downloadable!]
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