Reducing the dimensionality of linear quadratic control problems
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.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
- 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.
- 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.
- Claar, Victor V, 2002.
"Is the NAIRU More Useful in Forecasting Inflation than the Natural Rate of Unemployment?,"
14257, University Library of Munich, Germany.
- 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.
- J. Bradford De Long & Lawrence H. Summers, 1985.
"Is Increased Price Flexibility Stabilizing?,"
NBER Working Papers
1686, National Bureau of Economic Research, Inc.
- Binder, M. & Pesaran, H., 1996.
"Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation,"
Cambridge Working Papers in Economics
9619, Faculty of Economics, University of Cambridge.
- Michael Binder & M. Hashem Pesaran, 1997. "GAUSS and Matlab codes for Multivariate Linear Rational Expectations Models: Characterization of the Nature of the Solutions and Their Fully Recursive Computation," QM&RBC Codes 73, Quantitative Macroeconomics & Real Business Cycles.
- 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.
- 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.
- 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.
- Volker W. 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.).
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:31:y:2007:i:1:p:141-159. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.