Adaptive Identification of a Linear Unstable Parabolic System with Boundary Sensing and Actuation

The paper deals with identifiability analysis and on-line identification of a parabolic system with boundary sensing and actuation. When open-loop stable, the plant proves to be identifiable whenever it is excited by a constant boundary input. An adaptive identifier of the system is then constructed to estimate an unknown plant parameter on-line. If the plant is not necessarily stable the closed-loop identification of the unknown parameter is still feasible. An adaptive identifier, constructed in this case, forms a part of an adaptive controller, stabilizing the system. The identifier is shown to yield a true parameter estimate if the closed-loop system is additionally excited by a constant input