Reducing the dimensionality of linear quadratic control problems

In linear-quadratic control (LQC) problems with singularities in the control cost and/or the transition matrices, 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.