Extending the linear quadratic Gaussian/loop transfer recovery technique to a class of distributed parameter systems

Sufficient conditions for extending the linear quadratic Gaussian/loop-transfer recovery technique to a class of distributed parameter systems are presented. Two different approaches are considered in developing the conditions. The goal is to fully extend the technique to a class of infinite-dimensional regulator problems which utilize a Kalman filter. It is not known whether or not the sufficient conditions are satisfied by the entire class of problems considered. The difficulties encountered in trying to prove that the sufficient conditions are satisfied are discussed, and an approximation based on the work of H.T. Bank and K. Kunisch (1984) is presented