Observability of parabolic systems with scanning sensors

The observability of the linear parabolic system is studied with observations provided by a pointwise moving sensor. It is assumed that an output is corrupted by a disturbance, unknown but a priori bounded. This uncertainty leads to a set-valued setting of the observability problem. A method is presented for the construction of trajectories for sensors that are able to ensure continuous observability at final time regardless of the spatial dimensionality of the system in question