Optimal inverse LQG control for certain ode and PDE stationary processes

Following work carried out earlier on linear-quadratic optimal control for linear finite dimensional stationary systems we report, in this article, on extension of some of those results to certain infinite dimensional systems; in particular a class of PDE systems of elliptic type. These systems are studied in the now familiar framework developed by J. L. Lions and E. Magenes, specialized to a subclass of such systems important in a variety of applications. As an extended example this paper studies an optimal redistribution problem in a groundwater flow system governed by Darcy’s equation, presenting both analytic and computational work related to such problems.