Dennis S. Bernstein | Faculty
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 director of 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.
University of Michigan
PhD Computer, Information and Control Engineering '82
MSE Computer, Information and Control Engineering '79
ScB Applied Mathematics '77
POSITIONS HELD AT U-M
- Professor, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan, 1997-present
- Associate Professor, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan, 1991-97
Linear and nonlinear systems, identification, optimal, robust and adaptive control.
- Performance of Aircraft and Spacecraft, AE245
- Flight Mechanics, AE345
- Control of Structures and Fluids, AE579
- Linear Control Systems, AE580
- Analytical Dynamics, AE540
- Data Analysis and System Identification, AE566
- Trajectory Optimization, AE575
- Fellow of IEEE
- Honorary Doctorate, University of Glasgow, 2006
- A. A. Ali, J. B. Hoagg, M. Mossberg, and D. S. Bernstein, “On the Stability and Convergence of a Sliding-Window Variable-Regularization Recursive-Least-Squares Algorithm,” Int. J. Adaptive Contr. Sig. Proc., pp. 715--735, 2016.
- V. Chellaboina, S. P. Bhat, W. M. Haddad, and D. S. Bernstein, "Modeling and Analysis of Mass-Action Kinetics: Nonnegativity, realizability, reducibility, and semistability,'' IEEE Contr. Sys. Mag., Vol. 29, pp. 60-78, August 2009.
- A. Sanyal, A. Fosbury, N. Chaturvedi, and D. S. Bernstein, "Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization,'' AIAA J. Guid. Contr. Dyn., Vol. 32, pp. 1167-1178, 2009.
- S. P. Bhat and D. S. Bernstein, "Average-Preserving Symmetries and Energy Equipartition in
Linear Hamiltonian Systems,'' Math. Contr. Sig. Sys., Vol. 21, pp. 127--146, 2009.
- M. A. Santillo and D. S. Bernstein, "Adaptive Control Based on Retrospective Cost Optimization,'' AIAA J. Guid. Contr. Dyn., Vol. 33, pp. 289--304, 2010.
- H. Palanthandalam-Madapusi, T. Van Pelt, and D. S. Bernstein, "Parameter Consistency and Quadratically Constrained Errors-in-Variables Least-Squares Identification,'' Int. J. Contr., Vol. 83, pp. 862--877, 2010.
- S. P. Bhat and D. S. Bernstein, "Arc-Length-Based Lyapunov Tests for Convergence and Stability with Applications to Systems Having a Continuum of Equilibria, ''Math. Contr. Sig. Sys., Vol. 22, pp. 156--184, 2010.
- O. M. Baksalary, D. S. Bernstein, and G. Trenkler, "On the Equality between Rank and Trace
of an Idempotent Matrix,'' Applied Mathematics and Computation, Vol. 217, pp. 4076--4080, 2010.
- J. Yan, J. B. Hoagg, R. E. Hindman, and D. S. Bernstein, "Longitudinal Aircraft Dynamics and the Instantaneous Acceleration Center of Rotation: The Case of the Vanishing Zeros,''IEEE Contr. Sys. Mag., Vol. 30, pp. 68--92, 2011.
- A. M. D'Amato, A. J. Ridley, and D. S. Bernstein, "Retrospective-Cost-Based Adaptive Model Refinement for the Ionosphere and Thermosphere,''Statistical Analysis and Data Mining, Vol. 4, pp. 446--458, 2011.
- M. H. Holzel and D. S. Bernstein, "From Polynomial Matrices to Markov Parameters and Back: Theory and Numerical Algorithms, ''Lin. Alg. Appl., Vol. 437, pp. 783--808, 2012.
- J. B. Hoagg and D. S. Bernstein, "Retrospective Cost Model Reference Adaptive Control for Nonminimum-Phase Systems,'' AIAA J. Guid. Contr. Dyn., Vol. 35, pp. 1767--1786, 2012.
- A. Weiss, I. Kolmanovsky, D. S. Bernstein, and A. Sanyal, "Inertia-Free Spacecraft Attitude Control Using Reaction Wheels,''AIAA J. Guid. Contr. Dyn., Vol. 36, pp. 1425--1439, 2013.
- A. V. Morozov, A. J. Ridley, D. S. Bernstein, N. Collins, T. J. Hoar, and J. L. Anderson "Data Assimilation and Driver Estimation for the Global Ionosphere–Thermosphere Model Using the Ensemble Adjustment Kalman Filter,'' J. Atmospheric and Solar-Terrestrial Physics, Vol. 104, pp. 126--136, 2013.
- J. Yan and D. S. Bernstein, "Minimal Modeling Retrospective Cost Adaptive Control of Uncertain Hammerstein Systems Using Auxiliary Nonlinearities,'' Int. J. Contr., Vol. 87, pp. 483--505, 2014.
The second edition of Matrix Mathematics was published in July 2009. This edition is a significantly expanded version of the original edition. For further information, read Matrix Mathematics: Theory, Facts, and Formulas (Second Edition)