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Reducing the dimensionality of linear quadratic control problems


  • Balvers, Ronald J.
  • Mitchell, Douglas W.


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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  • Balvers, Ronald J. & Mitchell, Douglas W., 2007. "Reducing the dimensionality of linear quadratic control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 141-159, January.
  • Handle: RePEc:eee:dyncon:v:31:y:2007:i:1:p:141-159

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    References listed on IDEAS

    1. 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 1015-1026, November.
    2. De Long, James Bradford & Summers, Lawrence H, 1986. "Is Increased Price Flexibility Stabilizing?," American Economic Review, American Economic Association, vol. 76(5), pages 1031-1044, December.
    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. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
    5. Victor Claar, 2006. "Is the NAIRU more useful in forecasting inflation than the natural rate of unemployment?," Applied Economics, Taylor & Francis Journals, vol. 38(18), pages 2179-2189.
    6. 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.
    7. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    8. 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.
    9. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    10. Ehlgen, Jurgen, 1999. "A Nonrecursive Solution Method for the Linear-Quadratic Optimal Control Problem with a Singular Transition Matrix," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 17-23, February.
    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.
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    13. Ronald J. Balvers & Thomas F. Cosimano, 1994. "Inflation Variability and Gradualist Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 721-738.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness


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