Dynamic reconstruction of unbounded controls in a parabolic equation (Q1033584)

Linear infinite-dimensional continuous time control systems with constant parameters are considered. It is assumed that the systems are defined in Hilbert spaces and the control values are taken also from Hilbert spaces. The state differential equation is parabolic type and the controls are unbounded. Using methods and theorems taken directly from the theory of linear operators and optimal control theory, the reconstruction of unbounded controls is discussed. Sufficient conditions for reconstruction are formulated and proved. The special case of parabolic type state equations with memory is also investigated with the aid of integral equation. Finally it should be pointed out that the problem discussed in the paper belongs to the class of so-called inverse problems of estimating unknown characteristics on the basis of measurements. The paper contains also several remarks, comments and relationships to the results existing in the literature.