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Reducing the Dimensionality of Linear Quadratic Control Problems

Author

Listed:
  • Ronald J. Balvers

    (West Virginia University, USA)

  • Douglas W. Mitchell

    (West Virginia University, USA)

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.

Suggested Citation

  • Ronald J. Balvers & Douglas W. Mitchell, 2001. "Reducing the Dimensionality of Linear Quadratic Control Problems," Tinbergen Institute Discussion Papers 01-043/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010043
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    References listed on IDEAS

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    More about this item

    Keywords

    Linear-quadratic control; Riccati equation; Riccati reduction; Kalman filtering; Intertemporal optimization;
    All these keywords.

    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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