D.S. Bernstein

University of Michigan, Ann Arbor, Michigan, United States

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Publications (656)467.49 Total impact

  • Asad A. Ali · Jesse B. Hoagg · Magnus Mossberg · Dennis S. Bernstein ·
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    ABSTRACT: A sliding-window variable-regularization recursive-least-squares algorithm is derived, and its convergence properties, computational complexity, and numerical stability are analyzed. The algorithm operates on a finite data window and allows for time-varying regularization in the weighting and the difference between estimates. Numerical examples are provided to compare the performance of this technique with the least mean squares and affine projection algorithms. Copyright © 2015 John Wiley & Sons, Ltd.
    International Journal of Adaptive Control and Signal Processing 10/2015; DOI:10.1002/acs.2634 · 1.35 Impact Factor
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    Khaled F. Aljanaideh · Dennis S. Bernstein ·
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    ABSTRACT: A transmissibility is a relationship between signals of the same type, where the input and the output of the transmissibility are outputs of the underlying system. Transmissibility estimates are traditionally obtained using frequency-domain methods, which are based on the assumption that the input and output signals are stationary, and thus initial conditions and transient effects are ignored. In this paper we develop a time-domain framework for SISO and MIMO transmissibilities that accounts for nonzero initial conditions for both force-driven and displacement-driven structures. We show that transmissibilities in force-driven and displacement-driven structures are equal when the locations of the forces and prescribed displacements are identical. We present three examples to illustrate this equality.
    Journal of Sound and Vibration 07/2015; 347. DOI:10.1016/j.jsv.2015.01.018 · 1.81 Impact Factor
  • Ankit Goel · Antia Xie · Karthik Duraisamy · Dennis S. Bernstein ·
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    ABSTRACT: We use retrospective cost adaptive control (RCAC) to control the thrust generated by a scramjet. A quasi-one-dimensional version of the mass, momentum, and energy conservation equations of compressible fluid flow with heat release is used to model the physics of the scramjet. First, we study the dynamic behavior of the scramjet model. Then, we apply system identification techniques to fit a linear model to the data generated by the scramjet model to investigate the dependence of scramjet dynamics on the Mach number. Finally, we use RCAC to maintain the commanded thrust in the presence of a disturbance in the Mach number.
    American Control Conference, Chicago, IL; 07/2015
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    Xin Zhou · Tulga Ersal · Jeffrey L Stein · Dennis S Bernstein ·
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    ABSTRACT: Previous work framed the battery State of Health (SoH) monitoring problem as an inaccessible subsystem identification problem and conceived an approach to monitor SoH via side reaction current density estimation when State of Charge (SoC) is perfectly known. In practice, however, SoC is only estimated, and even an SoC estimation error of less than 1% can significantly undermine the accuracy of the SoH estimation. In this paper, the development of a new inaccessible subsystem identification technique, called the Two Step Filter, is presented in a linear setting to estimate the SoC error and SoH variable simultaneously and hence allow for SoH monitoring even under SoC estimation errors. The potential of the Two Step Filter is demonstrated on a linearized battery model example. The result shows that the filter can successfully track the side reaction current density despite the presence of an SoC estimation error of 1%.
    American Control Conference, Chicago, IL; 07/2015
  • Asad A. Ali · Ankit Goel · Aaron J. Ridley · Dennis S. Bernstein ·

    Journal of Aerospace Information Systems 05/2015; DOI:10.2514/1.I010286
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    Khaled F. Aljanaideh · Dennis S. Bernstein ·

    Journal of Guidance Control and Dynamics 04/2015; 38(8):1-4. DOI:10.2514/1.G001125 · 1.29 Impact Factor
  • Anna Prach · Ozan Tekinalp · Dennis S. Bernstein ·
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    ABSTRACT: One of the foundational principles of optimal control theory is that optimal control laws are propagated backward in time. For linear-quadratic control, this means that the solution of the Riccati equation must be obtained from backward integration from a final-time condition. These features are a direct consequence of the transversality conditions of optimal control, which imply that a free final state corresponds to a fixed final adjoint state [1], [2]. In addition, the principle of dynamic programming and the associated Hamilton-Jacobi-Bellman equation is an inherently backward-propagating methodology [3].
    IEEE control systems 04/2015; 35(2):78-93. DOI:10.1109/MCS.2014.2385252 · 2.09 Impact Factor
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    Khaled F. Aljanaideh · Dennis S. Bernstein ·
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    ABSTRACT: In some applications, multiple measurements are available, but the driving input that gives rise to those outputs may be unknown. This raises the question as to whether it is possible to model the response of a subset of sensors based on the response of the remaining sensors without knowledge of the driving input. To address this issue, we develop time-domain sensor-to-sensor models that account for nonzero initial conditions. The sensor-to-sensor model is in the form of a transmissibility operator that is a rational function of the differentiation operator. The development is carried out for both SISO and MIMO transmissibility operators. These time-domain sensor-to-sensor models can be used for diagnostics and output prediction.
    Automatica 03/2015; 53. DOI:10.1016/j.automatica.2015.01.004 · 3.02 Impact Factor
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    M.A. Janaideh · D.S. Bernstein ·
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    ABSTRACT: We numerically investigate the sense in which an adaptive control law achieves internal model control of Hammerstein plants with Prandtl-Ishlinskii hysteresis. We apply retrospective cost adaptive control (RCAC) to a command-following problem for uncertain Hammerstein systems with hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. Describing functions are used to determine whether the adaptive controller inverts the plant at the exogenous frequencies.
    Proceedings of the IEEE Conference on Decision and Control 02/2015; 2015:545-550. DOI:10.1109/CDC.2014.7039438
  • E. Dogan Sumer · Dennis S. Bernstein ·
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    ABSTRACT: We consider adaptive control of non-square plants, that is, plants that have an unequal number of inputs and outputs. In particular, we focus on retrospective cost adaptive control (RCAC), which is a direct, discrete-time adaptive control algorithm that is applicable to stabilisation, command following, disturbance rejection, and model reference control problems. Previous studies on RCAC have focused on control of square plants. In the square case, RCAC requires knowledge of the first non-zero Markov parameter and the non-minimum-phase (NMP) transmission zeros of the plant, if any. No additional information about the plant or the exogenous signals need be known. The goal of the present paper is to consider RCAC for non-square plants. Unlike the square case, we show that the assumption that the non-square plant is minimum phase does not guarantee closed-loop stability and signal boundedness. The main purpose of this paper is to establish the existence of time-invariant input and output subspaces corresponding to the adaptive controller. In particular, we show that RCAC implicitly squares down non-square plants through pre-/post-compensation of the non-square plant with a constant matrix. We show that, for wide plants, the control input generated by RCAC lies in a time-invariant ‘input subspace’, which is equivalent to pre-compensating the plant with a constant matrix. On the other hand, for tall plants, we show that the controller update is driven by the output of the plant post-compensated with a constant matrix. Accordingly, in either case, signal boundedness properties of the closed-loop system are determined by the transmission zeros of the squared system, which we call the ‘subspace zeros’. To deal with NMP subspace zeros, we introduce a robustness modification, which prevents RCAC from cancelling the NMP subspace zeros.
    International Journal of Control 02/2015; 88(2). DOI:10.1080/00207179.2014.951690 · 1.65 Impact Factor
  • A.G. Burrell · A. Goel · A.J. Ridley · D. S. Bernstein ·
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    ABSTRACT: Many physics-based models are used to study and monitor the terrestrial upper atmosphere. Each of these models has internal parameterizations that introduce bias if they are not tuned for a specific set of run conditions. This study uses Retrospective Cost Model Refinement (RCMR) to remove internal model bias in the Global Ionosphere Thermosphere Model (GITM) through parameter estimation. RCMR is a low-cost method that uses the error between truth data and a biased estimate to improve the biased model. Neutral mass density measurements are used to estimate an appropriate photoelectron heating efficiency, which is shown to drive the modeled thermosphere closer to the real thermosphere. Observations from the Challenging Mini-Payload (CHAMP) satellite taken under active and quiet solar conditions show that RCMR successfully drives the GITM thermospheric mass density to the observed values, removing model bias and appropriately accounting for missing physical processes in the thermospheric heating through the photoelectron heating efficiency.
    Journal of Atmospheric and Solar-Terrestrial Physics 01/2015; 124. DOI:10.1016/j.jastp.2015.01.004 · 1.47 Impact Factor
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    ABSTRACT: We compare four spacecraft attitude control laws that require no prior modeling of the spacecraft mass distribution. All four control laws are based on rotation matrices, which provide a singularity-free attitude representation and unwinding-free operation without discontinuous switching. We apply these control laws to motion-to-rest and motion-to-spin maneuvers. Simulation results are given to illustrate the robustness of the control laws to uncertainty in the spacecraft inertia. For motion-to-rest maneuvers about a principal axis with bounded torque, we compare the settling time of the inertia-free control laws with the time-optimal bang-bang control law operating under known inertia. We also investigate closed-loop performance in the presence of attitude-dependent torque disturbances, actuator nonlinearities, sensor noise, and actuator bias.
    Advances in Estimation, Navigation, and Spacecraft Control, Edited by Daniel Choukroun, Yaakov Oshman, Julie Thienel, Moshe Idan, 01/2015: chapter A Comparison of Nonlinear PI and PID Inertia-free Spacecraft Attitude Control Laws: pages 517-541; Springer Berlin Heidelberg., ISBN: 978-3-662-44784-0
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    Shicong Dai · Taeyoung Lee · Dennis S Bernstein ·
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    ABSTRACT: We design an adaptive controller for a quadrotor UAV transporting a point-mass payload connected by a flexible cable modeled as serially-connected rigid links. The mass of the payload is uncertain. The objective is to transport the payload to a desired position while aligning the links along the vertical direction from an arbitrary initial condition. A fixed-gain nonlinear proportional-derivative controller is presented to achieve the desired performance for a nominal payload mass, and a retrospective cost adaptive controller is used to compensate for the payload mass uncertainty.
    Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, Los Angeles, CA; 12/2014
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    Ahmad Ansari · Ming-Jui Yu · Dennis S Bernstein ·
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    ABSTRACT: The flight envelope of an aircraft consists of the constant trim states that the aircraft can attain, given in terms of airspeed, turn rate, and flight path angle. Flight trajectories typically consist of a sequence of trim commands with intermediate transitions. While the flight envelope of an aircraft is determined beforehand, it may change under off-nominal conditions due to damage or actuator failure. The goal of this paper is to investigate the ability of an adaptive control law to reach new trim states in the case where the flight envelope is totally unknown. Within simulation, this approach provides an alternative technique for mapping the flight envelope. For an aircraft in flight, this approach can be used to reach new trim states under envelope uncertainty, as may occur during off-nominal flight conditions.
    53rd IEEE Conference on Decision and Control, Los Angeles, California, USA; 12/2014
  • Anna Prach · Ozan Tekinalp · Dennis Bernstein ·
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    ABSTRACT: Pseudo-linear models of nonlinear systems use either a state-dependent coefficient or the Jacobian of the vector field to facilitate the use of Riccati techniques. In this paper we use the state-dependent Riccati equation (SDRE) and the forward propagating Riccati equation (FPRE) with pseudo-linear models to construct nonlinear observer-based compensators for output-feedback control of nonlinear discrete-time systems. While attractive due to their simplicity and potentially wide applicability, these techniques remain largely heuristic. The goal of this paper is thus to present numerical experiments to assess the performance of these 'faux' Riccati techniques on representative nonlinear systems. The goal is to compare the performance of SDRE and FPRE when used with either a state-dependent coefficient or the Jacobian of the vector field. Stabilization and performance are considered, along with integral control for step command following.
    53rd Conference on Decision and Control, Los Angeles, CA; 12/2014
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    Khaled F. Aljanaideh · James Richard Forbes · D.S. Bernstein ·
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    ABSTRACT: Control textbooks sometimes give the impression that amplification and phase shift are properties confined to asymptotically stable systems. For example, [1, p. 400] states that "Any system with a pole in the RHP is unstable; hence it would be impossible to determine its frequency response experimentally because the system would never reach a steady-state sinusoidal response for a sinusoidal input." This statement is correct in reference to an unstable plant operating in open loop but does not consider the case of an unstable plant operating inside a stabilized closed loop.
    IEEE control systems 12/2014; 34(6):86-141. DOI:10.1109/MCS.2014.2350591 · 2.09 Impact Factor
  • Matthew S. Hölzel · Dennis S. Bernstein ·
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    ABSTRACT: We present an elimination theory-based method for solving equality-constrained multivariable polynomial least-squares problems in system identification. While most algorithms in elimination theory rely upon Groebner bases and symbolic multivariable polynomial division algorithms, we present an algorithm which is based on computing the nullspace of a large sparse matrix and the zeros of a scalar, univariate polynomial.
    Automatica 10/2014; 50(2014-12-12). DOI:10.1016/j.automatica.2014.10.039 · 3.02 Impact Factor
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    Xin Zhou · Tulga Ersal · Jeffrey L Stein · Dennis S Bernstein ·
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    ABSTRACT: This paper introduces a method to estimate battery state of health (SoH) via health-relevant electrochemical features. Battery state of health estimation is a critical part of battery management because it allows for balancing the trade-off between maximizing performance and minimizing degradation. In this paper, a health-relevant electrochemical feature, the side reaction current density, is used as the indicator of battery SoH. An estimation algorithm is required due to the unavailability of the side reaction current density via noninvasive methods. In this paper, Retrospective-Cost Subsystem Identification (RCSI) is used to estimate the side reaction current density via identification of an unknown battery health subsystem that generates the side reaction current density. Simulation results are provided for constant current charge and discharge cycles with different C rates. A current profile for an electric vehicle (EV) going through Urban Dynamometer Driving Schedule (UDDS) cycles is also used as the excitation signal during estimation. The simulations show promising results in battery health dynamic identification and side reaction current density estimation with RCSI.
    ASME Dynamic Systems and Control Conference, San Antonio, TX; 10/2014
  • Marc Camblor · Gerardo Cruz · Sergio Esteban · Fred A. Leve · Dennis S. Bernstein ·
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    ABSTRACT: We present a numerical investigation of the performance of retrospective cost adaptive control (RCAC) for spacecraft attitude control using control-moment-gyroscopes (CMG). The setup consists of three orthogonally mounted CMG's that are velocity commanded without the use of a steering law. RCAC is applied in a decentralized architecture; each CMG is commanded by an independent RCAC control laws. This architecture simplifies the required modeling information and treats the axis-coupling effects as unmodeled disturbances. A rotation-matrix parameterization of attitude is used to implement a dynamic compensator with state feedback. The adaptive controller is able to complete various slew and spin maneuvers using limited information about the mass-distribution of the spacecraft.
    American Control Conference (ACC), 2014, Portland, OR, USA; 06/2014
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    Mohammad Al Janaideh · Dennis S. Bernstein ·
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    ABSTRACT: We investigate a NARMAX controller structure involving hysteretic nonlinearities. A weighted combination of backlash nonlinearities constitutes a Prandtl-Ishlinskii hysteresis model. The rationale for using a Prandtl-Ishlinskii NARMAX (PIN) controller is due to the fact that the describing function of a backlash nonlinearity has both gain and phase shift. By combining backlash nonlinearities into a NARMAX control law it is reasonable to expect that arbitrary gain and phase shift can be attained by adaptively updated controller coefficients.
    2014 American Control Conference - ACC 2014; 06/2014

Publication Stats

11k Citations
467.49 Total Impact Points


  • 1993-2015
    • University of Michigan
      • Department of Aerospace Engineering
      Ann Arbor, Michigan, United States
  • 1992-2013
    • Concordia University–Ann Arbor
      Ann Arbor, Michigan, United States
    • Arizona State University
      • Department of Mechanical Engineering
      Phoenix, Arizona, United States
  • 2011
    • University of Bologna
      Bolonia, Emilia-Romagna, Italy
  • 2009
    • Palo Alto Research Center
      Palo Alto, California, United States
    • The American Institute of Aeronautics and Astronautics
      Reston, Virginia, United States
    • Indian Institute of Technology Madras
      Chennai, Tamil Nādu, India
  • 2008
    • Syracuse University
      • Department of Mechanical and Aerospace Engineering
      Syracuse, NY, United States
  • 1999-2003
    • Indian Institute of Technology Ropar
      Rūpar, Punjab, India
  • 2000
    • Honeywell
      Morristown, New Jersey, United States
  • 1994-1999
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, GA, United States
  • 1995
    • Butler University
      Indianapolis, Indiana, United States
  • 1992-1994
    • Virginia Polytechnic Institute and State University
      • Department of Computer Science
      Blacksburg, VA, United States
  • 1989-1994
    • Florida Institute of Technology
      • Department of Mechanical and Aerospace Engineering
      Melbourne, FL, United States
  • 1984-1992
    • Harris Corporation
      Melbourne, Florida, United States
  • 1983-1992
    • Massachusetts Institute of Technology
      • Department of Aeronautics and Astronautics
      Cambridge, MA, United States