Singular functions are fundamental properties that capture the spatial nature of distributed parameter systems (DPS). This paper presents a framework for the dynamic identification of singular functions of an unknown DPS. The input to a DPS can be spatially distributed or applied at the boundary. Previous work [Gay and Ray, Chemical Engineering Science 50 (10) (1995) 1519-1539] considered the former. The current effort is more concerned with the case of boundary inputs. The concept of boundary topos is also introduced. Both singular functions and boundary topos can be identified through simple boundary input response tests and provide alternate bases for a pseudo-modal control scheme. Thus, this work also provides a systematic means for identification and control of distributed parameter systems through the use of boundary inputs alone. Examples of self-adjoint and non-self-adjoint systems are considered to demonstrate the efficacy of the identification and control schemes.