Optimal control of infinite dimensional systems with parametric uncertainty

The authors are concerned with the optimal feedback control of a class of infinite-dimensional systems with parametric uncertainty. The uncertainty is modeled by a random variable taking values in a compact set in a Euclidean space. The problem is to find an optimal (with respect to a quadratic index) Hilbert-Schmidt feedback operator that does not depend on the uncertainty set on the initial conditions, subject to the uncertainty evolution equation. The authors review the uncertain optimal control problem and illustrate it by means of numerical examples. The results demonstrate the applicability of the proposed method and its success in dealing with uncertainty