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Reducing the dimensionality of linear quadratic control problems

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

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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Suggested Citation

  • 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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    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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