The infinite-dimensional Riccati equation

AbstractThe infinite-dimensional versions of the linear quadratic cost control problem and of the linear filtering problem lead to an infinite-dimensional Riccati equation with unbounded operators. Existence and uniqueness theorems for mild solutions of this Riccati equation are established using a sequential approach based on approximating controllers for the linear quadratic cost control problem. By using a semigroup and evolution equation approach, the results are valid for a large class of unbounded operators and, hence, are applicable to many linear infinite-dimensional control systems