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 InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 31 (2007)
Issue (Month): 1 (January)
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Other versions of this item:
- Ronald J. Balvers & Douglas W. Mitchell, 2001. "Reducing the Dimensionality of Linear Quadratic Control Problems," Tinbergen Institute Discussion Papers 01-043/2, Tinbergen Institute.
- 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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