Results of numerical and experimental studies on monitoring and control for optical elements of an electric discharge KrF laser by the method of density-based spatial clustering of applications with noises (DBSCAN) are presented. Different methods of processing digital signals obtained using a position-sensitive detector controlling the position of the optical axis of the laser system are considered. A numerical model of optical system stability is developed based on the DBSCAN method with an additional inclusion of digital signal processing with the use of the cumulative moving average. A technique for correction of controlled mirrors with an accuracy of 60 ± 10 μrad for their return to normal position is proposed and implemented; the alignment time does not exceed 5 min.