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  • 1.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 784-789Article in journal (Refereed)
    Abstract [en]

    The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed.

  • 2.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of a Class of Nonlinear Dynamical Networks⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 868-873Article in journal (Refereed)
    Abstract [en]

    Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.

  • 3.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Eriksson, Oscar
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Bereza-Jarocinski, Robert
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Broman, David
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances2021In: Proceedings The 60th IEEE conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2021Conference paper (Refereed)
    Abstract [en]

    Differential-algebraic equations (DAEs) arise naturally as a result of equation-based object-oriented modeling. In many cases, these models contain unknown parameters that have to be estimated using experimental data. However, often the system is subject to unknown disturbances which, if not taken into account in the estimation, can severely affect the model's accuracy. For non-linear state-space models, particle filter methods have been developed to tackle this issue. Unfortunately, applying such methods to non-linear DAEs requires a transformation into a state-space form, which is particularly difficult to obtain for models with process disturbances. In this paper, we propose a simulation-based prediction error method that can be used for non-linear DAEs where disturbances are modeled as continuous-time stochastic processes. To the authors' best knowledge, there are no general methods successfully dealing with parameter estimation for this type of model. One of the challenges in particle filtering  methods are random variations in the minimized cost function due to the nature of the algorithm. In our approach, a similar phenomenon occurs and we explicitly consider how to sample the underlying continuous process to mitigate this problem. The method is illustrated numerically on a pendulum example. The results suggest that the method is able to deliver consistent estimates.

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    fulltext
  • 4.
    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, p. 3060-3065, article id 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.

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    fulltext
  • 5.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem2018In: 18th IFAC Symposium on System Identification, 2018Conference paper (Refereed)
    Abstract [en]

    The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presentedand discussed.

    Download full text (pdf)
    0028.pdf
  • 6.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors2018Conference paper (Refereed)
    Download full text (pdf)
    fulltext
  • 7.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions2020In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 119, article id 109055Article in journal (Refereed)
    Abstract [en]

    The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on the shape of the unknown distribution of the data, but also on how the model is parameterized. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on a partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.

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    fulltext
  • 8.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Linear Prediction Error Methods for Stochastic Nonlinear Models2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 49-63Article in journal (Refereed)
    Abstract [en]

    The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.

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    fulltext
    Download full text (pdf)
    fulltext
  • 9.
    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.

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    fulltext
  • 10.
    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.
    Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models2017In: The 20th IFAC World Congress, Elsevier, 2017, Vol. 50, p. 14058-14063Conference 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.

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    fulltext
  • 11.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Wahlberg, Bo
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    The Gaussian MLE versus the Optimally weighted LSE2020In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 37, no 6, p. 195-199Article in journal (Refereed)
    Abstract [en]

    In this note, we derive and compare the asymptotic covariance matrices of two parametric estimators: the Gaussian Maximum Likelihood Estimator (MLE), and the optimally weighted Least-Squares Estimator (LSE). We assume a general model parameterization where the model's mean and variance are jointly parameterized, and consider Gaussian and non-Gaussian data distributions.

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    fulltext
  • 12.
    Abdalmoaty, Mohamed
    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.
    Identication of a Class of Nonlinear Dynamical Networks2018Conference paper (Refereed)
    Abstract [en]

    Identifcation of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.

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    0131.pdf
  • 13.
    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, p. 632-637Article 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.

  • 14. 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 0018-9286, Vol. 41, no 9, p. 1367-1372Article 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.

  • 15.
    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, p. 85-90Conference paper (Refereed)
  • 16.
    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, p. 329-338Article in journal (Refereed)
  • 17.
    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, p. 103-108Conference paper (Refereed)
  • 18.
    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)
  • 19.
    Alberer, Daniel
    et al.
    Johannes Kepler Univ Linz, Inst Design & Control Mechatron Syst, Altenbergerstr 69, A-4040 Linz, Austria..
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    del Re, Luigi
    Johannes Kepler Univ Linz, Inst Design & Control Mechatron Syst, Altenbergerstr 69, A-4040 Linz, Austria..
    System Identification for Automotive Systems: Opportunities and Challenges2012In: Identification for automotive systems / [ed] Alberer, D Hjalmarsson, H DelRe, L, Springer Nature , 2012, p. 1-+Conference paper (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 feed-forward 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.

  • 20.
    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, p. 31-56Article in journal (Refereed)
  • 21.
    Auvert, Marine
    et al.
    KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems.
    Hjalmarsson, Håkan
    KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems.
    Johansson, Karl H.
    KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems.
    Karlsson, Gunnar
    KTH, Superseded Departments (pre-2005), 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.

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    flaps_rvk02
  • 22.
    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, p. 1335-1340Conference 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.

  • 23.
    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, p. 3070-3078Article 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.

  • 24.
    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.

  • 25.
    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, p. 6454-6459Conference 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.

  • 26.
    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, p. 543-551Article 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.

  • 27.
    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, p. 458-463Conference 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.

  • 28.
    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, p. 197-220Chapter in book (Other academic)
  • 29.
    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, p. 892-897Conference 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.

  • 30.
    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, p. 1597-1602Conference 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.

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    IR-EE-RT 2009:012
  • 31.
    Bereza-Jarocinski, Robert
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Eriksson, Oscar
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Abdalmoaty, Mohamed R-H
    Uppsala Univ, Div Syst & Control, S-75105 Uppsala, Sweden..
    Broman, David
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Stochastic Approximation for Identification of Non-Linear Differential-Algebraic Equations with Process Disturbances2022In: 2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2022, p. 6712-6717Conference paper (Refereed)
    Abstract [en]

    Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function-whose minimizer is a consistent estimator of the true parameters-using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.

    Download full text (pdf)
    fulltext
  • 32.
    Bombois, X.
    et al.
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, Ecully, France.;CNRS, Paris, France..
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Network topology detection via uncertainty analysis of an identified static model2021In: IFAC PAPERSONLINE, Elsevier BV , 2021, Vol. 54, no 7, p. 595-600Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a methodology to detect the topology of a dynamic network that is based on the analysis of the uncertainty of the static characteristic of the matrix of transfer functions between the external excitations and the node signals.

  • 33.
    Bombois, Xavier
    et al.
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, Ecully, France.;CNRS, Paris, France..
    Colin, Kevin
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Van den Hof, Paul M. J.
    Eindhoven Univ Technol, Control Syst Grp, Dept Elect Engn, Eindhoven, Netherlands..
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    On the informativity of direct identification experiments in dynamical networks2023In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 148, p. 110742-, article id 110742Article in journal (Refereed)
    Abstract [en]

    Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.

  • 34. 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, p. 9953-9958Conference 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).

  • 35.
    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, Elsevier BV , 2009, Vol. 42, no PART 1, p. 934-939Conference 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.

  • 36.
    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, p. 577-584Article 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.

  • 37. Bombois, Xavier
    et al.
    Korniienko, A.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Scorletti, G.
    Optimal identification experiment design for the interconnection of locally controlled systems2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, p. 169-179Article in journal (Refereed)
    Abstract [en]

    This paper considers the identification of the modules of a network of locally controlled systems (multi-agent systems). Its main contribution is to determine the least perturbing identification experiment that will nevertheless lead to sufficiently accurate models of each module for the global performance of the network to be improved by a redesign of the decentralized controllers. Another contribution is to determine the experimental conditions under which sufficiently informative data (i.e. data leading to a consistent estimate) can be collected for the identification of any module in such a network. 

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    fulltext
  • 38.
    Bombois, Xavier
    et al.
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France.;Ctr Natl Rech Sci CNRS, Paris, France..
    Morelli, Federico
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France..
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Bako, Laurent
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France..
    Colin, Kevin
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Robust optimal identification experiment design for multisine excitation2021In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 125, article id 109431Article in journal (Refereed)
    Abstract [en]

    In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.

  • 39. Bottegal, G.
    et al.
    Risuleo, Riccardo Sven
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zamani, M.
    Ninness, B.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On maximum likelihood identification of errors-in-variables models2017In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 50, no 1, p. 2824-2829Article in journal (Refereed)
    Abstract [en]

    In this paper, we revisit maximum likelihood methods for identification of errors-in-variables systems. We assume that the system admits a parametric description, and that the input is a stochastic ARMA process. The cost function associated with the maximum likelihood criterion is minimized by introducing a new iterative solution scheme based on the expectation-maximization method, which proves fast and easily implementable. Numerical simulations show the effectiveness of the proposed method.

  • 40.
    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, p. 1073-1078Conference 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.

  • 41.
    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, p. 2636-2641Conference 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.

  • 42.
    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, p. 2109-2114Conference 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.

  • 43.
    Bottegal, Giulio
    et al.
    Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pillonetto, Gianluigi
    Department of Information Engineering, University of Padova, Padova, Italy.
    A new kernel-based approach to system identification with quantized output data2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 85, p. 145-152Article 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.

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    fulltext
  • 44.
    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, E-ISSN 2405-8963, Vol. 48, no 28, p. 455-460Article 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.

  • 45.
    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.

  • 46. 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, p. 851-865Article 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.

  • 47.
    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, p. 1484-1491Conference 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.

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    network_cdc10
  • 48.
    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, p. 3122-3129Conference 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.

  • 49.
    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.

  • 50.
    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, p. 327-330Conference 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.

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