Cyber attacks and extreme events can cause severe consequences to the grid that require immediate response. Conventional remedial action schemes (RAS) use offline calculations to determine corrective control actions to deploy for a predetermined set of credible contingencies. Yet, cyber attacks cannot be sufficiently represented in a look-up table approach; such contingencies are highly dynamic and unpredictable. Online RAS with real-time calculation of corrective controls provides the most suitable and effective response. To achieve rapid computation and reduce the search space to only the most effective candidate control(s), the analytic corrective control selection method using clustering and factorisation techniques is developed based on controllability analysis. The resulting critical controls comprise a minimum set that is most effective in reducing the violations in the stressed areas of the system. While this study focuses on generators as the critical control mechanism, this methodology is broadly applicable to any corrective control for which a sensitivity matrix in relation to the violated components can be derived. The algorithm is evaluated with the IEEE 24-bus and IEEE 118-bus systems under compromised generator outage scenarios, and the identified critical control set is shown to be highly effective for reducing violations and improving RAS computation time.