Reducing the Dimensionality of Linear Quadratic Control Problems
AbstractIn 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 InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-043/2.
Date of creation: 11 Apr 2001
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Web page: http://www.tinbergen.nl
Linear-quadratic control; Riccati equation; Riccati reduction; Kalman filtering; Intertemporal optimization;
Other versions of this item:
- 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.
- 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, and Information
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