Some New Analytic and Computational Results for Operator Riccati Equations

The operator Riccati equation associated with a distributed parameter quadratic cost-linear dynamics control process is considered. Making use of ideas from transport theory, a derivation of a generalized version of the X-Y functions of radiative transfer is given, and it is seen that, under commonly occurring conditions, the new equations may be easier to numerically resolve than the original Riccati equation. In particular, the new equations express directly the optimal gain function. The analytic results are illustrated by a numerical example of heat regulation on a rod.