We introduce a new problem, the Online Selective Anomaly Detection (OSAD), to model a specific scenario emerging from research in sleep science. Scientists have segmented sleep into several stages and stage two is characterized by two patterns (or anomalies) in the EEG time series recorded on sleep subjects. These two patterns are sleep spindle (SS) and K-complex. The OSAD problem was introduced to design a residual system, where all anomalies (known and unknown) are detected but the system only triggers an alarm when non-SS anomalies appear. The solution of the OSAD problem required us to combine techniques from both data mining and control theory. Experiments on data from real subjects attest to the effectiveness of our approach.