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  • 1.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Simulated Maximum Likelihood Method for Estimation of Stochastic Wiener Systems2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, 3060-3065 p., 7798727Conference paper (Refereed)
    Abstract [en]

    This paper introduces a simulation-based method for maximum likelihood estimation of stochastic Wienersystems. It is well known that the likelihood function ofthe observed outputs for the general class of stochasticWiener systems is analytically intractable. However, when the distributions of the process disturbance and the measurement noise are available, the likelihood can be approximated byrunning a Monte-Carlo simulation on the model. We suggest the use of Laplace importance sampling techniques for the likelihood approximation. The algorithm is tested on a simple first order linear example which is excited only by the process disturbance. Further, we demonstrate the algorithm on an FIR system with cubic nonlinearity. The performance of the algorithm is compared to the maximum likelihood method and other recent techniques.

  • 2.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    On Re-Weighting, Regularization Selection, and Transient in Nuclear Norm Based Identification2015Conference paper (Refereed)
    Abstract [en]

    In this contribution, we consider the classical problem of estimating an Output Error model given a set of input-output measurements. First, we develop a regularization method based on the re-weighted nuclear norm heuristic. We show that the re-weighting improves the estimate in terms of better fit. Second, we suggest an implementation method that helps in eliminating the regularization parameters from the problem by introducing a constant based on a validation criterion. Finally, we develop a method for considering the effect of the transient when the initial conditions are unknown. A simple numerical example is used to demonstrate the proposed method in comparison to classical and another recent method based on the nuclear norm heuristic.

  • 3.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH Royal Institute of Technology.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models2017In: The 20th IFAC World Congress, Elsevier, 2017, Vol. 50, 14058-14063 p.Conference paper (Refereed)
    Abstract [en]

    Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimator. These methods, albeit asymptotically optimal, are computationally expensive. In this contribution, we present a simulation-based pseudo likelihood estimator for nonlinear stochastic models. It relies only on the first two moments of the model, which are easy to approximate using Monte-Carlo simulations on the model. The resulting estimator is consistent and asymptotically normal. We show that the pseudo maximum likelihood estimator, based on a multivariate normal family, solves a prediction error minimization problem using a parameterized norm and an implicit linear predictor. In the light of this interpretation, we compare with the predictor defined by an ensemble Kalman filter. Although not identical, simulations indicate a close relationship. The performance of the simulated pseudo maximum likelihood method is illustrated in three examples. They include a challenging state-space model of dimension 100 with one output and 2 unknown parameters, as well as an application-motivated model with 5 states, 2 outputs and 5 unknown parameters.

  • 4.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 4, 632-637 p.Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.

  • 5. Akcay, H.
    et al.
    Hjalmarsson, Håkan
    Department of Electrical Engineering, Linköping University.
    Ljung, Lennart
    Department of Electrical Engineering, Linköping University.
    On the choice of norms in system identification1996In: IEEE Transactions on Automatic Control, ISSN 00189286 (ISSN), Vol. 41, no 9, 1367-1372 p.Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.

  • 6.
    Akçay, H.
    et al.
    Linköping University.
    Hjalmarsson, Håkan
    Linköping University.
    The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise1994In: 10th IFAC Symposium on System Identification, 1994, Vol. 2, 85-90 p.Conference paper (Refereed)
  • 7.
    Akçay, H.
    et al.
    Linköping University.
    Hjalmarsson, Håkan
    Linköping University.
    The least-squares identification of FIR systems subject to worst-case noise1994In: System & Control Letters, Vol. 23, 329-338 p.Article in journal (Refereed)
  • 8.
    Akçay, H.
    et al.
    Linköping University.
    Hjalmarsson, Håkan
    Linköping University.
    Ljung, Lennart
    Department of Electrical Engineering, Linköping University.
    On the choice of norms i system identification1994In: 10th IFAC Symposium on System Identification, 1994, Vol. 2, 103-108 p.Conference paper (Refereed)
  • 9.
    Alberer, Daniel
    et al.
    Johannes Kepler University.
    Hjalmarsson, HåkanKTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.del Re, LuigiJohannes Kepler University.
    Identification for Automotive Systems2012Collection (editor) (Refereed)
  • 10.
    Alberer, Daniel
    et al.
    Johannes Kepler University.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    del Re, Luigi
    Johannes Kepler University.
    System Identification for Automotive Systems: Opportunities and Challenges2012In: Identification for Automotive Systems / [ed] Daniel Alberer, Håkan Hjalmarsson, Luigi del Re, Springer London, 2012, 1-10 p.Chapter in book (Refereed)
    Abstract [en]

    Without control many essential targets of the automotive industry could not be achieved. As control relies directly or indirectly on models and model quality directly influences the control performance, especially in feedforward structures as widely used in the automotive world, good models are needed. Good first principle models would be the first choice, and their determination is frequently difficult or even impossible. Against this background methods and tools developed by the system identification community could be used to obtain fast and reliably models, but a large gap seems to exist: neither these methods are sufficiently well known in the automotive community, nor enough attention is paid by the system identification community to the needs of the automotive industry. This introduction summarizes the state of the art and highlights possible critical issues for a future cooperation as they arose from an ACCM Workshop on Identification for Automotive Systems recently held in Linz, Austria.

  • 11.
    Annergren, Mariette
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Larsson, Christian A.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bombois, Xavier
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Application-Oriented Input Design in System Identification Optimal input design for control2017In: IEEE CONTROL SYSTEMS MAGAZINE, ISSN 1066-033X, Vol. 37, no 2, 31-56 p.Article in journal (Refereed)
  • 12.
    Auvert, Marine
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Hjalmarsson, Håkan
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Johansson, Karl H.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Karlsson, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    On Router Control for Congestion Avoidance2002Conference paper (Refereed)
    Abstract [en]

    This short paper deals with active queue management for computer networks. The goal is to develop control mechanisms for routers in heterogeneous networks that reduce traffic fluctuations. The proposed control strategy operates with local information (such as estimated arrival rates) and actively use the buffers to smooth traffic, and thus it avoids the buildup and propagation of traffic bursts.

  • 13.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bombois, Xavier
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mixed H-2 and H-Infinity$ Input Design for Multivariable Systems2006In: 14th IFAC Symposium on System Identification, 2006, 1335-1340 p.Conference paper (Refereed)
    Abstract [en]

    In this contribution a new procedure for input design for identification of linear multivariable systems is proposed. The goal is to minimize the input power used in the system identification experiment. The quality constraint on the estimated model is formulated in H∞. The input design problem is converted to linear matrix inequalities by a separation of graphs theorem. For illustration, the proposed method is applied on a chemical distillation column and the result shows that it is optimal to amplify the low gain direction of the plant.

  • 14.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bombois, Xavier
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for control of multivariable systems: Controller validation and experiment design via LMIs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 12, 3070-3078 p.Article in journal (Refereed)
    Abstract [en]

    This paper presents a new controller validation method for linear multivariable time-invariant models. Classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature. Our controller validation criterion computes an upper bound for the worst case performance, measured in terms of the H-infinity-norm of a weighted closed loop transfer matrix, achieved by a given controller over all plants in such uncertainty sets. This upper bound on the worst case performance is computed via an LMI-based optimization problem and is deduced via the separation of graph framework. Our main technical contribution is to derive, within that framework, a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from PE identification of MIMO systems. The proposed approach also allows for iterative experiment design. The results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system.

  • 15.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Enqvist, Martin
    Linköping University.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Gain estimation for Hammerstein systems2006In: IFAC Proceedings Volumes (IFAC-PapersOnline) / [ed] Brett Ninness, Håkan Hjalmarsson, 2006Conference paper (Refereed)
    Abstract [en]

    In this paper, we discuss and compare three different approaches for L2- gain estimation of Hammerstein systems. The objective is to find the input signal that maximizes the gain. A fundamental difference between two of the approaches is the class, or structure, of the input signals. The first approach involves describing functions and therefore the class of input signals is sinusoids. In this case we assume that we have a model of the system and we search for the amplitude and frequency that give the largest gain. In the second approach, no structure on the input signal is assumed in advance and the system does not have to be modelled first. The maximizing input is found using an iterative procedure called power iterations. In the last approach, a new iterative procedure tailored for memoryless nonlinearities is used to find the maximizing input for the unmodelled nonlinear part of the Hammerstein system. The approaches are illustrated by numerical examples.

  • 16.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Identification and control: Joint input design and H infinity state feedback with ellipsoidal parametric uncertainty2005In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005, 6454-6459 p.Conference paper (Refereed)
    Abstract [en]

    One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a sufficient condition for the existence of a H-infinity state feedback controller for the multi-input/single-output case which accomodates for ellipsoidal parametric uncertainty. The condition takes the form of a linear matrix inequality whose solution also provides a set of valid feedback gains. The model class considered corresponds to systems with known poles but uncertain zero locations. A second important contribution of the paper is to integrate the input design problem in system identification with this control synthesis method. This means that given H-infinity specifications on the closed loop transfer function are translated into the requirements on the input signal spectrum used to identify the process so that the ellipsoidal model uncertainty resulting from model identification using this input spectrum will be shaped such that the control specifications are satisfied for all models in the uncertainty set and hence guaranteed for the true system. The procedures are illustrated on a numerical example.

  • 17.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 2, 543-551 p.Article in journal (Refereed)
    Abstract [en]

    One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a joint robust state feedback control/input design procedure which guarantees stability and prescribed closed-loop performance using models identified from experimental data. This means that given H-infinity specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process. The condition takes the form of a linear matrix inequality.

  • 18.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Jansson, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications of mixed H2 and H∞ input design in identification2005In: / [ed] Pavel Zítek, 2005, Vol. 16, 458-463 p.Conference paper (Refereed)
    Abstract [en]

    The objective of this contribution is to quantify benefits of optimal input design compared to the use of standard identification input signals, e.g. PRBS signals for some common, and important, application areas of system identification. Two benchmark problems taken from process control and control of flexible mechanical structures are considered. We present results both when the design is based on knowledge of the true system (in general the optimal design depends on the system itself) and for a practical two step procedure when an initial model estimate is used in the design instead of the true system. The results show that there is a substantial reduction in experiment time and input excitation level. A discussion on the sensitivity of the optimal input design to model estimates is provided.

  • 19.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Jansson, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    A control perspective on optimal input design in system identification2006In: Forever Ljung in System Identification / [ed] Torkel Glad and Gustaf Hendeby, Lund: Studentlitteratur, 2006, 197-220 p.Chapter in book (Other academic)
  • 20.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mosskull, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Validation of stability for an induction machine drive using power iterations2005In: Proceedings of the 16th IFAC World Congress, 2005, Prague, 2005, Vol. 16, 892-897 p.Conference paper (Refereed)
    Abstract [en]

    This work is an extension of the paper (Mosskull et al., 2003), in which the modelling, identification and stability of an nonlinear induction machine drive is studied. The validation of the stability margins of the system is refined by an improved estimate of the induced L2 loop gain of the system. This is done with a procedure called power iterations where input sequences suitable for estimating the gain are generated iteratively through experiments on the system. The power iterations result in higher gain estimates compared to the experiments previously presented. This implies that more accurate estimates are obtained as, in general, only lower bounds can be obtained as estimates for the gain. The new gain estimates are well below one, which suggests that the feedback system is stable. The experiments are performed on an industrial hardware/software simulation platform. in this paper we also discuss the power iterations from a more general point of view. The usefulness of the method for gain estimation of nonlinear systems is illustrated through simulation examples. The basic principles of the method are provided.

  • 21.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Barkhagen, Mathias
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Data-driven methods for L2-gain estimation2009In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2009, Vol. 15, no PART 1, 1597-1602 p.Conference paper (Refereed)
    Abstract [en]

    In this paper we present and discuss some data-driven methods for estimation of the L2-gain of dynamical systems. Partial results on convergence and statistical properties are provided. The methods are based on multiple experiments on the system. The main idea is to directly estimate the maximizing input signal by using iterative experiments on the true system. We study such a data-driven method based on a stochastic gradient method. We show that this method is very closely related to the so-called power iteration method based on the power method in numerical analysis. Furthermore, it is shown that this method is applicable for linear systems with noisy measurements. We will also study L2-gain estimation of Hammerstein systems. The stochastic gradient method and the power iteration method are evaluated and compared in simulation examples. © 2009 IFAC.

  • 22. Bombois, Xavier
    et al.
    den Dekker, Arjan J.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Van den Hof, Paul M. J.
    Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging2011In: Proceedings of the 18th IFAC World Congress, 2011, 9953-9958 p.Conference paper (Refereed)
    Abstract [en]

    Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H0. The alternative hypothesis H1 is the hypothesis that is accepted when H0 is rejected. In hypothesis testing, the probability of deciding H1 when in fact H0 is true is known as the false alarm rate, whereas the probability of deciding H1when in fact H1is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).

  • 23.
    Bombois, Xavier
    et al.
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal input design for robust H2 deconvolution filtering2009In: 15th IFAC Symposium on System Identification, SYSID 2009, 2009, Vol. 15, no PART 1, 934-939 p.Conference paper (Refereed)
    Abstract [en]

    Deconvolution filtering where the system and noise dynamics are obtained by parametric system identification is considered. Consistent with standard identification methods, ellipsoidal uncertainty in the estimated parameters is considered. Three problems are considered: 1) Computation of the worst case H2 performance of a given deconvolution filter in this uncertainty set. 2) Design of a filter which minimizes the worst case H2 performance in this uncertainty set. 3) Input design for the identification experiment, subject to a limited input power budget, such that the filter in 2) gives the smallest possible worst-case H2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to 1) and 2) while the third problem can be treated via iterating between two convex optimization problems.

  • 24.
    Bombois, Xavier
    et al.
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for robust H-2 deconvolution filtering2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 3, 577-584 p.Article in journal (Refereed)
    Abstract [en]

    This paper addresses robust deconvolution filtering when the system and noise dynamics are obtained by parametric system identification. Consistent with standard identification methods, the uncertainty in the estimated parameters is represented by an ellipsoidal uncertainty region. Three problems are considered: (1) computation of the worst case H-2 performance of a given deconvolution filter in this uncertainty set; (2) design of a filter which minimizes the worst case H-2 performance in this uncertainty set; (3) input design for the identification experiment, subject to a limited input power budget, such that the filter in (2) gives the smallest possible worst case H-2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to (1) and (2) while the third problem can be treated via iterating between two convex optimization problems.

  • 25.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Aravkin, A. Y.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Pillonetto, G.
    Outlier robust system identification: A Bayesian kernel-based approach2014In: IFAC Proceedings Volumes (IFAC-PapersOnline), IFAC Papers Online, 2014, 1073-1078 p.Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.

  • 26.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the variance of identified SIMO systems with spatially correlated output noise2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, 2636-2641 p.Conference paper (Refereed)
    Abstract [en]

    In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.

  • 27.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Aravkin, A.Y.
    Pillonetto, G.
    Outlier robust kernel-based system identification using l1-Laplace techniques2015In: 2015 54th IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers (IEEE), 2015, 2109-2114 p.Conference paper (Refereed)
    Abstract [en]

    Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.

  • 28. Bottegal, Giulio
    et al.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pillonetto, Gianluigi
    A new kernel-based approach to system identification with quantized output data2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 85, 145-152 p.Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data. (C) 2017 Elsevier Ltd. All rights reserved.

  • 29.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pillonetto, G.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bayesian kernel-based system identification with quantized output data2015In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 48, no 28, 455-460 p.Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.

  • 30.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Risuleo, Riccardo Sven
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Blind system identification using kernel-based methods2015Conference paper (Refereed)
    Abstract [en]

    We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has been recently introduced for system identification purposes and depends on an unknown hyperparameter. We assume that the input can be linearly described by few parameters. We estimate these parameters, together with the kernel hyperparameter and the noise variance, using an empirical Bayes approach. The related optimization problem is efficiently solved with a novel iterative scheme based on the Expectation-Maximization (EM) method. In particular, we show that each iteration consists of a set of simple update rules. Through some numerical experiments we show that the proposed method give very promising performance.

  • 31. Briat, C.
    et al.
    Yavuz, E.A
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    The Conservation of Information, Towards an Axiomatized Modular Modeling Approach to Congestion Control2015In: IEEE/ACM Transactions on Networking, ISSN 1063-6692, E-ISSN 1558-2566, Vol. 23, no 3, 851-865 p.Article in journal (Refereed)
    Abstract [en]

    We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgment rates and delays are mathematically modeled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packet-level simulations demonstrate the accuracy of the proposed model.

  • 32.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nonlinear state-dependent delay modeling and stability analysis of internet congestion control2010In: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, 1484-1491 p.Conference paper (Refereed)
    Abstract [en]

    It is shown that the queuing delay involved in the congestion control algorithm is state-dependent and does not depend on the current time. Then, using an accurate formulation for buffers, networks with arbitrary topologies can be built. At equilibrium, our model reduces to the widely used setup by Paganini et al. Using this model, the delay-derivative is analyzed and it is proved that the delay time-derivative does not exceed one for the considered topologies. It is then shown that the considered congestion control algorithm globally stabilizes a delay-free single buffer network. Finally, using a specific linearization result for systems with state-dependent delays from Cooke and Huang, we show the local stability of the single bottleneck network.

  • 33.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Yavuz, Emre Altug
    KTH, School of Electrical Engineering (EES), Communication Networks.
    An axiomatic fluid-flow model for congestion control analysis2011In: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC), 2011, 3122-3129 p.Conference paper (Refereed)
    Abstract [en]

    An axiomatic model for congestion control isderived. The proposed four axioms serve as a basis for theconstruction of models for the network elements. It is shownthat, under some assumptions, some models of the literature canbe recovered. A single-buffer/multiple-users topology is finallyderived and studied for illustration.

  • 34.
    Chotteau, Veronique
    et al.
    KTH, School of Biotechnology (BIO), Bioprocess Technology.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Tuning of dissolved oxygen and pH PID control parameters in large scale bioreactor by lag control2008In: Proceedings of the Cell Culture Engineering XI Conference, 2008Conference paper (Refereed)
    Abstract [en]

    Achieving satisfying DO and pH controllers are often challenges for pilot and large scale mammalian cultivation. Unsatisfactory DO or pH controls can imply fatal effects for the culture. Large scale bioreactors have long response times due to long mixing times compared to small scale systems where control tuning of DO and pH is not so challenging.

    A method was developed to tune the DO controller PID parameters of a 50 L bioreactor (wv) controlled by a continuous oxygen flow of microbubbles. DO control by continuous flow of pure oxygen microbubbles can oscillate quite widely showing instable behaviour. The method, called lag control here, was based on a lead lag control design by Bode analysis where the prediction part, i.e. ‘lead’ part was omitted. A comparison of this method with a pole placement approach showed the advantage of the lag control. It was decided to omit the derivate part which could lead to instability caused by the long delay observed between the applied oxygen flow and the response detected by the DO probe. Applying the lag control method resulted in a highly satisfactory DO control. In this system, the oxygen microbubbles were almost completely consumed before reaching the liquid surface as demonstrated by the absence of foam. So the oxygen flow used to maintain the DO gave an excellent indication of the cellular oxygen consumption. The control system was robust against all the perturbations of this system, i.e. cell growth, cell bleed, addition of air-saturated fresh medium, DO set point change and a second gas sparger used to strip out the carbon dioxide. The method was first tested with the sulphite oxidation method simulating the oxygen consumption with copper as catalyst to establish the PID parameters. Then the selected parameters were successfully used during cell cultivation. Following this, an adaptation of the method was done in order to avoid the sulphite oxidation method, which leaves copper traces in the bioreactor. This was successfully used in a 400 L bioreactor (wv) for the DO controller by continuous oxygen flow of microbbubles. The lag controller method was finally modified to tune the pH controller of the same 400 L bioreactor with control upward by alkali addition or downwards by pulsed carbon dioxide addition.

  • 35.
    Chotteau, Véronique
    et al.
    KTH, School of Biotechnology (BIO), Bioprocess Technology.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tuning of dissolved oxygen and pH PID control parameters in large scale bioreactor by lag control2012In: Proceedings of the 21st Annual Meeting of the European Society for Animal Cell Technology (ESACT), 2012, 327-330 p.Conference paper (Refereed)
    Abstract [en]

    A method has been developed to tune the DO and pH controller PID parameters for pilot / large scale mammalian cultivation. Our approach is to identify a model of the variable to be controlled (e.g. DO, pH) and to design several possible PID controllers based on this model. The controllers were first tested in computer simulations, followed by wet simulation and finally the best controller was tested on the real process. The approach is developed for the tuning of the DO controller of a 50 L bioreactor using microbubble continuous oxygen flow. The method, called lag control here, is based on a lead lag control design using Bode analysis where the prediction part is omitted. Experiments show that the approach results in a highly satisfactory DO control. The oxygen microbubbles were almost completely consumed before reaching the liquid surface so the oxygen flow used to maintain the DO gave an excellent indication of the cellular oxygen consumption. The control system was robust against all the perturbations, i.e. cell growth, cell bleed, addition of air-saturated fresh medium, DO set point change and a second gas sparger used to strip out the carbon dioxide. This approach was also successfully used for the tuning of a 400 L bioreactor DO controller and pH controller.

  • 36.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Annergren, Mariette
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian A.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Molander, Mats
    Sjöberg, Johan
    Application Set Approximation in Optimal Input Design for Model Predictive Control2014In: 2014 European Control Conference (ECC), 2014, 744-749 p.Conference paper (Refereed)
    Abstract [en]

    This contribution considers one central aspect of experiment design in system identification, namely application set approximation. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to plant-modeling missmatch is quantified by an application cost function. A convex approximation of the set of models that satisfy the control specification is typically required in optimal input design. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

  • 37.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Molinari, Marco
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Varagnolo, Damiano
    Division of Signals and Systems, Department of Computer Science, Electrical and Space Engineering, Luleå University of Innovation and Technology.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multi-room occupancy estimation through adaptive gray-box models2015In: Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, IEEE conference proceedings, 2015, 3705-3711 p.Conference paper (Other academic)
    Abstract [en]

    We consider the problem of estimating the occupancylevel in buildings using indirect information such as CO2 concentrations and ventilation levels. We assume that oneof the rooms is temporarily equipped with a device measuringthe occupancy. Using the collected data, we identify a gray-boxmodel whose parameters carry information about the structuralcharacteristics of the room. Exploiting the knowledge of thesame type of structural characteristics of the other rooms inthe building, we adjust the gray-box model to capture the CO2dynamics of the other rooms. Then the occupancy estimatorsare designed using a regularized deconvolution approach whichaims at estimating the occupancy pattern that best explainsthe observed CO2 dynamics. We evaluate the proposed schemethrough extensive simulation using a commercial software tool,IDA-ICE, for dynamic building simulation.

  • 38.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Varagnolo, Damiano
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Blind identification strategies for room occupancy estimation2015Conference paper (Refereed)
    Abstract [en]

    We propose and test on real data a two-tier estimation strategy for inferring occupancy levels from measurements of CO2 concentration and temperature levels. The first tier is a blind identification step, based either on a frequentist Maximum Likelihood method, implemented using non-linear optimization, or on a Bayesian marginal likelihood method, implemented using a dedicated Expectation-Maximization algorithm. The second tier resolves the ambiguity of the unknown multiplicative factor, and returns the final estimate of the occupancy levels. The overall procedure addresses some practical issues of existing occupancy estimation strategies. More specifically, first it does not require the installation of special hardware, since it uses measurements that are typically available in many buildings. Second, it does not require apriori knowledge on the physical parameters of the building, since it performs system identification steps. Third, it does not require pilot data containing measured real occupancy patterns (i.e., physically counting people for some periods, a typically expensive and time consuming step), since the identification steps are blind.

  • 39.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Valenzuela, Patricio E
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications oriented input design for closed-loop system identification: a graph-theory approach2014In: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, 4125-4130 p.Conference paper (Refereed)
    Abstract [en]

    A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.

  • 40.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications Oriented Input Design in Time-Domain Through Cyclic Methods2014Conference paper (Refereed)
    Abstract [en]

    In this paper we propose a method for applications oriented input design for linear systems in open-loop under time-domain constraints on the amplitude of input and output signals. The method guarantees a desired control performance for the estimated model in minimum time, by imposing some lower bound on the information matrix. The problem is formulated as a time-domain optimization problem, which is non-convex. This is addressed through an alternating method, where we separate the problem into two steps and at each step we optimize the cost function with respect to one of two variables. We alternate between these two steps until convergence. A time recursive input design algorithm is performed, which enables us to use the algorithm with control. Therefore, a receding horizon framework is used to solve each optimization problem. Finally, we illustrate the method with a numerical example which shows the good ability of the proposed approach in generating an optimal input signal.

  • 41. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Cost function shaping of the output error criterion2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, 53-60 p.Article in journal (Refereed)
    Abstract [en]

    Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

  • 42. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cost function shaping of the output error criterion2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, 53-60 p.Article in journal (Refereed)
    Abstract [en]

    Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

  • 43. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Input design as a tool to improve the convergence of PEM2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 11, 3282-3291 p.Article in journal (Refereed)
    Abstract [en]

    The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima.

  • 44. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the convergence of the Prediction Error Method to its global minimum2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, 698-703 p.Conference paper (Refereed)
    Abstract [en]

    The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.

  • 45. Eckhard, Diego
    et al.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gevers, Michel
    Mean-squared error experiment design for linear regression models2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, 1629-1634 p.Conference paper (Refereed)
    Abstract [en]

    This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.

  • 46.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Effect of Noise Correlation in Parameter Identification of SIMO Systems2015In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 48, no 28, 326-331 p.Article in journal (Refereed)
    Abstract [en]

    The accuracy of identified linear time-invariant single-input multi-output (SIMO) models can be improved when the disturbances affecting the output measurements are spatially correlated. Given a linear parametrization of the modules composing the SIMO structure, we show that the correlation structure of the noise sources and the model structure of the othe modules determine the variance of a parameter estimate. In particular we show that increasing the model order only increases the variance of other modules up to a point. We precisely characterize the variance error of the parameter estimates for finite model orders. We quantify the effect of noise correlation structure, model structure and signal spectra.

  • 47.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Variance Analysis of identified Linear MIMO Models2015In: IEEE Explore, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

    We study the accuracy of identified linear time-invariant multi-input multi-output (MIMO) systems. Under a stochastic framework, we quantify the effect of the spatial correlation and choice of model structure on the covariance matrix of the transfer function estimates. In particular, it is shown how the variance of a transfer function estimate depends on signal properties and model orders of other modules composing the MIMO system.

  • 48.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance analysis of linear SIMO models with spatially correlated noise2017In: Automatica, ISSN 0005-1098, Vol. 77, 68-81 p.Article in journal (Refereed)
    Abstract [en]

    In this paper we address the identification of linear time-invariant single-input multi-output (SIMO) systems. In particular, we assess the performance of the prediction error method by quantifying the variance of the parameter estimates. Using an orthonormal representation for the modules composing the SIMO structure, we show that the parameter estimate of a module depends on the model structure of the other modules, and on the correlation structure of the output disturbances. We provide novel results which quantify the variance-error of the parameter estimates for finite model orders, where the effects of noise correlation structure, model structure and input spectrum are visible. In particular, we show that a sensor does not increase the accuracy of a module if common dynamics have to be estimated. When a module is identified using less parameters than the other modules, we derive the noise correlation structure that gives the minimum total variance. The implications of our results are illustrated through numerical examples and simulations.

  • 49.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance Analysis of Linear SIMO Models with Spatially Correlated NoiseManuscript (preprint) (Other academic)
    Abstract [en]

    Substantial improvement in accuracy of identied linear time-invariant single-input multi-output (SIMO) dynamical models ispossible when the disturbances aecting the output measurements are spatially correlated. Using an orthogonal representation for the modules composing the SIMO structure, in this paper we show that the variance of a parameter estimate of a module is dependent on the model structure of the other modules, and the correlation structure of the disturbances. In addition, we quantify the variance-error for the parameter estimates for finite model orders, where the effect of noise correlation structure, model structure and signal spectra are visible. From these results, we derive the noise correlation structure under which the mentioned model parameterization gives the lowest variance, when one module is identied using less parameters than the other modules.

  • 50.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Geometric Approach to Variance Analysis of Cascaded Systems2013In: Proceedings of the 52nd Conference On Decision And Control, IEEE conference proceedings, 2013, 6496-6501 p.Conference paper (Refereed)
    Abstract [en]

    Modeling complex and interconnected systems is a key issue in system identification. When estimating individual subsystems of a network of interconnected system, it is of interest to know the improvement of model-accuracy in using different sensors and actuators. In this paper, using a geometric approach, we quantify the accuracy improvement from additional sensors when estimating the first of a set of subsystems connected in a cascade structure. We present results on how the zeros of the first subsystem affect the accuracy of the corresponding model. Additionally we shed some light on how structural properties and experimental conditions determine the accuracy. The results are particularized to FIR systems, for which the results are illustrated by numerical simulations. A surprising special case occurs when the first subsystem contains a zero on the unit circle; as the model orders grows large, thevariance of the frequency function estimate, evaluated at thecorresponding frequency of the unit-circle zero, is shown to be the same as if the other subsystems were completely known.

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