Reducing the Dimensionality of Linear Quadratic Control Problems Article uri icon

  •  
  • Overview
  •  
  • Research
  •  
  • View All
  •  

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.

publication date

  • April 11, 2001