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  • 101.
    Verhaegen, Michel
    et al.
    Delft University of Technology, Netherlands.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    N2SID: Nuclear norm subspace identification of innovation models2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 72, p. 57-63Article in journal (Refereed)
    Abstract [en]

    The identification of multivariable state space models in innovation form is solved in a subspace identification framework using convex nuclear norm optimization. The convex optimization approach allows to include constraints on the unknown matrices in the data-equation characterizing subspace identification methods, such as the lower triangular block-Toeplitz of weighting matrices constructed from the Markov parameters of the unknown observer. The classical use of instrumental variables to remove the influence of the innovation term on the data equation in subspace identification is avoided. The avoidance of the instrumental variable projection step has the potential to improve the accuracy of the estimated model predictions, especially for short data length sequences. (C) 2016 Elsevier Ltd. All rights reserved.

  • 102.
    Wahlberg, Bo
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    The Effects of Rapid Sampling in System Identification1990In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 26, no 1, p. 167-170Article in journal (Refereed)
    Abstract [en]

    This paper deals with the effects of rapid sampling in system identification. In continuous time, noise models of non-zero relative degree imply that one has to differentiate the measured data to find the prediction error parameter estimate. This problem can be avoided by using noise models of relative degree zero or by introducing prefilters. The corresponding difficulty for the discrete time case is less obvious. However, by linking the discrete time and continuous time parameter estimation problem, we show that the same problem arises for rapid sampled systems.

  • 103.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kao, Chung-Yao
    University of Melbourne, Australia.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Cutting Plane Method for Solving KYP-SDPs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 2, p. 418-429Article in journal (Refereed)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. To this end structure exploiting algorithms have been proposed, based on the dual formulation. In this paper a cutting plane algorithm is proposed. In a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension.

  • 104.
    Wan, Yiming
    et al.
    Delft University of Technology, Netherlands.
    Keviczky, Tamas
    Delft University of Technology, Netherlands.
    Verhaegen, Michel
    Delft University of Technology, Netherlands.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Data-driven robust receding horizon fault estimation2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 71, p. 210-221Article in journal (Refereed)
    Abstract [en]

    This paper presents a data-driven receding horizon fault estimation method for additive actuator and sensor faults in unknown linear time-invariant systems, with enhanced robustness to stochastic identification errors. State-of-the-art methods construct fault estimators with identified state-space models or Markov parameters, without compensating for identification errors. Motivated by this limitation, we first propose a receding horizon fault estimator parameterized by predictor Markov parameters. This estimator provides (asymptotically) unbiased fault estimates as long as the subsystem from faults to outputs has no unstable transmission zeros. When the identified Markov parameters are used to construct the above fault estimator, stochastic identification errors appear as model uncertainty multiplied with unknown fault signals and online system inputs/outputs (I/O). Based on this fault estimation error analysis, we formulate a mixed-norm problem for the offline robust design that regards online I/O data as unknown. An alternative online mixed-norm problem is also proposed that can further reduce estimation errors at the cost of increased computational burden. Based on a geometrical interpretation of the two proposed mixed-norm problems, systematic methods to tune the user-defined parameters therein are given to achieve desired performance trade-offs. Simulation examples illustrate the benefits of our proposed methods compared to recent literature. (C) 2016 Elsevier Ltd. All rights reserved.

  • 105.
    Wang, Jiandong
    et al.
    Peking University, China.
    Zhang, Qinghua
    INRIA, France.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Revisiting Hammerstein System Identification through the Two-Stage Algorithm for Bilinear Parameter Estimation2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 11, p. 2627-2633Article in journal (Refereed)
    Abstract [en]

    The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.

  • 106.
    Wernholt, Erik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Moberg, Stig
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Gray-Box Identification Using Local Models Applied to Industrial Robots2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 4, p. 650-660Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the problem of estimating unknown parameters in nonlinear gray-box models that may be multivariable, nonlinear, unstable, and resonant at the same time. A straightforward use of time-domain predication-error methods for this type of problem easily ends up in a large and numerically stiff optimization problem. We therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem. The procedure is based on the estimation of the nonparametric frequency response function (FRF) in a number of operating points. The nonlinear gray-box model is linearized in the same operating points, resulting in parametric FRFs. The optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric FRFs. The procedure is illustrated by estimating elasticity parameters in a six-axes industrial robot. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control.

  • 107.
    Wills, Adrian
    et al.
    University of Newcastle, Australia .
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ninness, Brett
    University of Newcastle, Australia .
    Identification of Hammerstein-Wiener Models2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 1, p. 70-81Article in journal (Refereed)
    Abstract [en]

    This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

  • 108.
    Yu, Chengpu
    et al.
    Beijing Inst Technol, Peoples R China.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Verhaegen, Michel
    Delft Univ Technol, Netherlands.
    Identification of structured state-space models2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 90, p. 54-61Article in journal (Refereed)
    Abstract [en]

    Identification of structured state-space (gray-box) model is popular for modeling physical and network systems. Due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for successful applications. In this paper, the non-convex gray-box identification problem is reformulated as a structured low-rank matrix factorization problem by exploiting the rank and structured properties of a block Hankel matrix constructed by the system impulse response. To address the low-rank optimization problem, it is first transformed into a difference-of-convex (DC) formulation and then solved using the sequentially convex relaxation method. Compared with the classical gray-box identification methods like the prediction-error method (PEM), the new approach turns out to be more robust against converging to non-global minima, as supported by a simulation study. The developed identification can either be directly used for gray-box identification or provide an initial parameter estimate for the PEM. (C) 2018 Elsevier Ltd. All rights reserved.

  • 109.
    Yuan, Zhen-Dong
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Uprejudiced Optimal Open Loop Input Design for Identification of Transfer Functions1985In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 21, no 6, p. 697-708Article in journal (Refereed)
    Abstract [en]

    The problem to estimate transfer functions of linear systems is considered. The quality of the resulting estimate depends, among other things, on the input used during the identification experiment. We measure the quality using a quadratic norm in the frequency domain. The problem to determine optimal inputs, i.e. inputs that minimize the chosen norm, subject to constrained input variance, has long been studied. We point out that such procedures may involve a prejudice (that the system is to be found in a certain model set) that may have some surprising effects. We discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set. We also calculate explicit expressions for the resulting “unprejudiced” optimal inputs. These expressions relate the signal-to-noise ratio (as a function of frequency) to the chosen weighting function in the quadratic norm. We also point out the role of the employed noise model for the design.

  • 110.
    Zhang, Qinghua
    et al.
    Inria IFSTTAR, France.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    From structurally independent local LTI models to LPV model*2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 84, p. 232-235Article in journal (Refereed)
    Abstract [en]

    The local approach to linear parameter varying (LPV) system identification consists in interpolating individually estimated local linear time invariant (LTI) models corresponding to fixed values of the scheduling variable. It is shown in this paper that, without any global structural assumption of the considered LPV system, individually estimated local state-space LTI models do not contain sufficient information for determining similarity transformations making them coherent. It is possible to estimate these similarity transformations from input-output data under appropriate excitation conditions. (C) 2017 Published by Elsevier Ltd.

  • 111.
    Åslund, Jan
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Vehicular Systems.
    Frisk, Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Vehicular Systems.
    An observer for non-linear differential-algebraic systems2006In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 42, no 6, p. 959-965Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider design of observers for non-linear models containing both dynamic and algebraic equations, so-called differential-algebraic equations (DAE), of index 1. The observer is formulated as a DAE that, by construction, has index 1. The main results of the paper include conditions that ensure local stability of the observer error dynamics. Design methodology is presented and illustrated using a small simulation study. © 2006 Elsevier Ltd. All rights reserved.

  • 112.
    Åslund, Jan
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Jung, Daniel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Asymptotic behavior of a fault diagnosis performance measure for linear systems2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 106, p. 143-149Article in journal (Refereed)
    Abstract [en]

    Fault detection and fault isolation performance of a model based diagnosis system mainly depends on the level of model uncertainty and the time allowed for detection. The longer time for detection that can be accepted, the more certain detection can be achieved and the main objective of this paper is to show how the window length relates to a diagnosis performance measure. A key result is an explicit expression for asymptotic performance with respect to window length and it is shown that there exists a linear asymptote as the window length tends to infinity. The gradient of the asymptote is a system property that can be used in the evaluation of diagnosis performance when designing a system. A key property of the approach is that the model of the system is analyzed directly, which makes the approach independent of detection filter design. (C) 2019 Elsevier Ltd. All rights reserved.

    The full text will be freely available from 2021-05-17 11:36
  • 113.
    Åström, Karl Johan
    et al.
    Lund Institute of Technology, Sweden.
    Borisson, U
    Gränges Data, Sweden.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wittenmark, Björn
    Lund Institute of Technology.
    Theory and Applications of Self Tuning Regulators1977In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 13, no 5, p. 457-476Article in journal (Refereed)
    Abstract [en]

    This paper reviews work on self-tuning regulators. The regulator algorithms, their theory and industrial applications are reviewed. The paper is expository—the major ideas are covered but detailed analysis is given elsewhere.

  • 114.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Smidl, Vaclav
    Institute of Information Theory and Automation, Czech Republic.
    Saha, Saikat
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lundquist, Christian
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Marginalized Adaptive Particle Filtering for Nonlinear Models with Unknown Time-Varying Noise Parameters2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1566-1575Article in journal (Refereed)
    Abstract [en]

    Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback-Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.

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