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Reducing the Dimensionality of Linear Quadratic Control Problems

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  • Ronald J. Balvers

    ()
    (West Virginia University, USA)

  • Douglas W. Mitchell

    (West Virginia University, USA)

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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Bibliographic 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

Related research

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

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  1. Balvers, Ronald J & Cosimano, Thomas F, 1994. "Inflation Variability and Gradualist Monetary Policy," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 721-38, October.
  2. Binder, Michael & Pesaran, Hashem, 2000. "Solution of finite-horizon multivariate linear rational expectations models and sparse linear systems," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 325-346, March.
  3. 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.
  4. 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.
  5. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  6. Paul A. Ruud, 2000. "natural rate of unemployment data," Instructional Stata datasets for econometrics nairu, Boston College Department of Economics.
  7. Ehlgen, Jurgen, 1999. "A Nonrecursive Solution Method for the Linear-Quadratic Optimal Control Problem with a Singular Transition Matrix," Computational Economics, Society for Computational Economics, vol. 13(1), pages 17-23, February.
  8. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March Cit.
  9. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
  10. Volker Wieland, 1996. "Learning by doing and the value of optimal experimentation," Finance and Economics Discussion Series 96-5, Board of Governors of the Federal Reserve System (U.S.).
  11. 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.
  12. Balvers, Ronald J. & Wu, Yangru, 2006. "Momentum and mean reversion across national equity markets," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 24-48, January.
  13. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  14. Pesaran, M. H. & Binder, M., 1997. "Solution of Multivariate Linear Rational Expectations Models and Large Sparse Linear Systems," Cambridge Working Papers in Economics 9708, Faculty of Economics, University of Cambridge.
  15. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  16. J. Bradford De Long & Lawrence H. Summers, 1987. "Is Increased Price Flexibility Stabilizing?," NBER Working Papers 1686, National Bureau of Economic Research, Inc.
  17. Zadrozny, Peter A., 1998. "An eigenvalue method of undetermined coefficients for solving linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1353-1373, August.
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Cited by:
  1. Mehari Mekonnen Akalu, 2002. "Measuring and Ranking Value Drivers," Tinbergen Institute Discussion Papers 02-043/2, Tinbergen Institute.

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