Professor Bernstein's interest include identification, estimation, and control for aerospace applications. His research has focused on active noise and vibration control, as well as attitude control for space applications. His current interests are in the theory and application of nonlinear system identification, large-scale state estimation for data assimilation, and adaptive control. He is directorof the Noise, Vibration, and Motion Control Laboratory, which includes instrumentation and testbeds for control applications. A 6-degree-of-freedom electric shaker table under all-digital control is used for vibration and motion control applications. Facilities are available for implementing and testing algorithms for active noise and vibration control. Current research is focusing on adaptive command following and disturbance rejection algorithms for systems with uncertain dynamics and unknown disturbance spectra. He is co-director (with Ilya Kolmanovsky) of the Attitude Dynamics and Control Laboratory. In this laboratory, a triaxial air bearing is used to develop and implement adaptive control algorithms for spacecraft applications. He was Editor-in-Chief of the IEEE Control Systems Magazine from 2003 to 2011.
Prof. Bernstein has authored more than 200 journal papers and 350 conference papers. He is the author of Matrix Mathematics, which is published by Princeton University Press. (A review of Matrix Mathematics can be downloaded from:http://www.siam.org/news/news.php?id=125) Matrix Mathematics - Errata and Addenda