ABSTRACT
Abstract We define the notion of a stable abstract Volterra operator, and show that it can be realized as the input-output map of a stable well-posed linear system. We then formulate a quadratic cost minimization problem involving such an abstract Volterra operator, and derive the Wiener-Hopf equation satisfied by the optimal solution. This equation is solved within the setting of a well-posed linear system with the projection method based on a Wiener-Hopf factorization. Under an extra regularity assumption it is possible to derive an algebraic Riccati equation satisfied by the optimal cost operator.
