Some Properties of Composed Identification-and-Control Maps

A problem in the identification for control of distributed parameter systems is considered. Some data determine the unknown parameters; then parameters, together with new controls, yield an output. With reference to the one and two dimensional, time independent heat equations, the properties of the composed data-to-output map are studied, which consists of an inverse problem (identification of conductivity from interior measurements) followed by a direct (control) problem. Some new conditions for the uniqueness of conductivity and the corresponding stability estimates for the composed map are provided.