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  • 1.
    Bemporad, Alberto
    et al.
    University of Siena, Italy.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Hybrid Systems via Mixed-Integer Programming2001Report (Other academic)
    Abstract [en]

    This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and wiener piecewise affine (W-PWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. We also discuss issues of state-space realization of HHARX and W-PWARX models into several existing discrete-time hybrid state-space forms.

  • 2.
    Cedersund, Gunnar
    et al.
    Linköping University, Department of Clinical and Experimental Medicine, Cell Biology. Linköping University, Faculty of Health Sciences.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Systems biology: Model Based Evaluation and Comparison of Potential Explanations for Given Biological Data2009In: The FEBS Journal, ISSN 1742-464X, E-ISSN 1742-4658, Vol. 276, no 4, p. 903-922Article, review/survey (Refereed)
    Abstract [en]

    Systems biology and its usage of mathematical modeling to analyse biological data is rapidly becoming an established approach to biology. A crucial advantage of this approach is that more information can be extracted from observations of intricate dynamics, which allows nontrivial complex explanations to be evaluated and compared. In this minireview we explain this process, and review some of the most central available analysis tools. The focus is on the evaluation and comparison of given explanations for a given set of experimental data and prior knowledge. Three types of methods are discussed: (a) for evaluation of whether a given model is sufficiently able to describe the given data to be nonrejectable; (b) for evaluation of whether a slightly superior model is significantly better; and (c) for a general evaluation and comparison of the biologically interesting features in a model. The most central methods are reviewed, both in terms of underlying assumptions, including references to more advanced literature for the theoretically oriented reader, and in terms of practical guidelines and examples, for the practically oriented reader. Many of the methods are based upon analysis tools from statistics and engineering, and we emphasize that the systems biology focus on acceptable explanations puts these methods in a nonstandard setting. We highlight some associated future improvements that will be essential for future developments of model based data analysis in biology.

  • 3.
    Cedersund, Gunnar
    et al.
    Linköping University, Faculty of Health Sciences. Linköping University, Department of Clinical and Experimental Medicine, Cell Biology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ulfhielm, Erik
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Danielsson, Anna
    Linköping University, Faculty of Health Sciences. Linköping University, Department of Clinical and Experimental Medicine, Cell Biology.
    Tidefelt, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Strålfors, Peter
    Linköping University, Faculty of Health Sciences. Linköping University, Department of Clinical and Experimental Medicine, Cell Biology.
    Model-Based Hypothesis Testing of Key Mechanisms in Initial Phase of Insulin Signaling2008In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 4, no 6Article in journal (Refereed)
    Abstract [en]

    Type 2 diabetes is characterized by insulin resistance of target organs, which is due to impaired insulin signal transduction. The skeleton of signaling mediators that provide for normal insulin action has been established. However, the detailed kinetics, and their mechanistic generation, remain incompletely understood. We measured time-courses in primary human adipocytes for the short-term phosphorylation dynamics of the insulin receptor (IR) and the IR substrate-1 in response to a step increase in insulin concentration. Both proteins exhibited a rapid transient overshoot in tyrosine phosphorylation, reaching maximum within 1 min, followed by an intermediate steady-state level after approximately 10 min. We used model-based hypothesis testing to evaluate three mechanistic explanations for this behavior: (A) phosphorylation and dephosphorylation of IR at the plasma membrane only, (B) the additional possibility for IR endocytosis, (C) the alternative additional possibility of feedback signals to IR from downstream intermediates. We concluded that (A) is not a satisfactory explanation, that (B) may serve as an explanation only if both internalization, dephosphorylation, and subsequent recycling are permitted, and that (C) is acceptable. These mechanistic insights cannot be obtained by mere inspection of the datasets, and they are rejections and thus stronger and more final conclusions than ordinary model predictions.

  • 4.
    Heintz, Fredrik
    et al.
    Linköping University, Department of Computer and Information Science. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    FlexDx: A Reconfigurable Diagnosis Framework2008In: Proceedings of the 19th International Workshop on Principles of Diagnosis (DX), 2008Conference paper (Refereed)
    Abstract [en]

    Detecting and isolating multiple faults is a computationally intense task which typically consists of computing a set of tests, and then computing the diagnoses based on the test results. This paper describes FlexDx, a reconfigurable diagnosis framework which reduces the computational burden by only running the tests that are currently needed. The method selects tests such that the isolation performance of the diagnostic system is maintained. Special attention is given to the practical issues introduced by a reconfigurable diagnosis framework such as FlexDx. For example, tests are added and removed dynamically, tests are partially performed on historic data, and synchronous and asynchronous processing are combined. To handle these issues FlexDx uses DyKnow, a stream-based knowledge processing middleware framework. The approach is exemplified on a relatively small dynamical system, which still illustrates the computational gain with the proposed approach.

  • 5.
    Iouditski, Anatoli
    et al.
    INRIA, France.
    Nazin, Alexander
    Institute of Control Science, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Adaptive DWO Estimator of a Regression Function2007Report (Other academic)
    Abstract [en]

    We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.

  • 6.
    Juloski, Aleksandar Lj.
    et al.
    Eindhoven University of Technology, Netherlands.
    Paoletti, Simone
    Università degli Studi di Siena, Italy.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Recent Techniques for the Identification of Piecewise Affine and Hybrid Systems2006In: Current Trends in Nonlinear Systems and Control: In Honor of Petar Kokotovic and Turi Nicosia / [ed] Laura Menini, Luca Zaccarian, Chaouki T. Abdallah, Petar V. Kokotovic, Turi Nicosia, Boston: Birkhäuser , 2006, p. 79-99Chapter in book (Other academic)
    Abstract [en]

    The problem of piecewise affine identification is addressed by studying four recently proposed techniques for the identification of PWARX/HHARX models, namely a Bayesian procedure, a bounded-error procedure, a clustering-based procedure and a mixed-integer programming procedure. The four techniques are compared on suitably defined one-dimensional examples, which help to highlight the features of the different approaches with respect to classification, noise and tuning parameters. The procedures are also tested on the experimental identification of the electronic component placement process in pick-and-place machines.

  • 7.
    Krysander, Mattias
    et al.
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.
    Heintz, Fredrik
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Dynamic Test Selection for Reconfigurable Diagnosis2008In: Proceedings of the 47th IEEE Conference on Decision and Control, IEEE , 2008, p. 1066-1072Conference paper (Refereed)
    Abstract [en]

    Detecting and isolating multiple faults is a computationally intense task which typically consists of computing a set of tests, and then computing the diagnoses based on the test results. This paper proposes a method to reduce the computational burden by only running the tests that are currently needed, and dynamically starting new tests when the need changes. A main contribution is a method to select tests such that the computational burden is reduced while maintaining the isolation performance of the diagnostic system. Key components in the approach are the test selection algorithm, the test initialization procedures, and a knowledge processing framework that supports the functionality needed. The approach is exemplified on a relatively small dynamical system, which still illustrates the complexity and possible computational gain with the proposed approach.

  • 8.
    Krysander, Mattias
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Heintz, Fredrik
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    FlexDx: A Reconfigurable Diagnosis Framework2010In: Engineering applications of artificial intelligence, ISSN 0952-1976, E-ISSN 1873-6769, Vol. 23, no 8, p. 1303-1313Article in journal (Refereed)
    Abstract [en]

    Detecting and isolating multiple faults is a computationally expensive task. It typically consists of computing a set of tests and then computing the diagnoses based on the test results. This paper describes FlexDx, a reconfigurable diagnosis framework which reduces the computational burden while retaining the isolation performance by only running a subset of all tests that is sufficient to find new conflicts. Tests in FlexDx are thresholded residuals used to indicate conflicts in the monitored system. Special attention is given to the issues introduced by a reconfigurable diagnosis framework. For example, tests are added and removed dynamically, tests are partially performed on historic data, and synchronous and asynchronous processing are combined. To handle these issues FlexDx has been implemented using DyKnow, a stream-based knowledge processing middleware framework. Concrete methods for each component in the FlexDx framework are presented. The complete approach is exemplified on a dynamic system which clearly illustrates the complexity of the problem and the computational gain of the proposed approach.

  • 9.
    Lind, Ingela
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    SUPANOVA for Nonlinear Regression2006Report (Other academic)
    Abstract [en]

    SUPANOVA is a combination of support vector machines and the ANOVA function expansion. In this contribution a comparison between SUPANOVA and other nonlinear model structures is made. These other model structures are artificial neural networks with sigmoidal basis functions, trees, and piece-wise linear models.

  • 10.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bemporad, Alberto
    University of Siena, Italy.
    Identification of Hybrid Systems via Mixed-Integer Programming2001In: Proceedings of the 40th IEEE Conference on Decision and Control, 2001, p. 786-792 vol.1Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and wiener piecewise affine (W-PWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. We also discuss issues of state-space realization of HHARX and W-PWARX models into several existing discrete-time hybrid state-space forms.

  • 11.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Iouditski, Anatoli
    INRIA, France.
    Alexander, Nazin
    Institute of Control Science, Russia.
    Adaptive DWO Estimator of a Regression Function2004In: Proceedings of the 2004 IFAC Symposium on Nonlinear Control Systems, 2004Conference paper (Refereed)
    Abstract [en]

    We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.

  • 12.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nazin, Alexander
    Institute of Control Sciences, Russia.
    A Non-Asymptotic Approach to Local Modelling2002In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, p. 638-643 vol.1Conference paper (Refereed)
    Abstract [en]

    Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

  • 13.
    Lyzell, Christian
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    The Use of Nonnegative Garrote for Order Selection of ARX Models2008Report (Other academic)
    Abstract [en]

    Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into account, where the regressors are ordered via the time lag. To this end, a modified variant of the nonnegative garrote method will be analyzed.

  • 14.
    Lyzell, Christian
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    The Use of Nonnegative Garrote for Order Selection of ARX Models2008In: Proceedings of the 47th IEEE Conferance on Decision and Control, 2008, , p. 1974-1979p. 1974-1979Conference paper (Refereed)
    Abstract [en]

    Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into account, where the regressors are ordered via the time lag. To this end, a modified variant of the nonnegative garrote method will be analyzed.

  • 15.
    Nazin, Alexander
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Study of the DWO Approach to Function Estimation at a Given Point: Approximately Constant and Approximately Linear Function Classes2003Report (Other academic)
    Abstract [en]

    In this report, the Direct Weight Optimization (DWO) approach to function estimation is studied for two special function classes: The classes of approximately constant and approximately linear functions. These classes consist of functions whose deviation from a constant/affine function is bounded by a known constant. Upper and lower bounds for the asymptotic maximum MSE are given, some of whic halso hold in the non-asymptotic case.

  • 16.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization for Approximately Linear Functions: Optimality and Design2006In: Proceedings of the 14th IFAC Symposium on System Identification, 2006, p. 796-801Conference paper (Refereed)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to estimating a regression function is studied here for the class of approximately linear functions, i.e., functions whose deviation from an affine function is bounded by a known constant. Upper and lower bounds for the asymptotic maximum MSE are given, some of which also hold in the non-asymptotic case and for an arbitrary fixed design. Their coincidence is then studied. Particularly, under mild conditions, it can be shown that there is always an interval in which the DWO-optimal estimator is optimal among all estimators. Experiment design issues are also studied.

  • 17.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization for Approximately Linear Functions: Optimality and Design2007Report (Other academic)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to estimating a regression function is studied here for the class of approximately linear functions, i.e., functions whose deviation from an affine function is bounded by a known constant. Upper and lower bounds for the asymptotic maximum MSE are given, some of which also hold in the non-asymptotic case and for an arbitrary fixed design. Their coincidence is then studied. Particularly, under mild conditions, it can be shown that there is always an interval in which the DWO-optimal estimator is optimal among all estimators. Experiment design issues are also studied.

  • 18.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization in Nonlinear Function Estimation and System Identification2007In: Proceedings of the 6th International Conference on System Identification and Control Problems (SICPRO '07), 2007Conference paper (Refereed)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to estimating a regression function and its application to nonlinear system identification has been proposed and developed during the last few years by the authors. Computationally, the approach is typically reduced to a quadratic or conic programming and can be effectively realized. The obtained estimates demonstrate optimality or sub-optimality in a minimax sense w.r.t. the mean-square error criterion under weak design conditions. Here we describe the main ideas of the approach and represent an overview of the obtained results.

  • 19.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization in Nonlinear Function Estimation and System Identification2007Report (Other academic)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to estimating a regression function and its application to nonlinear system identification has been proposed and developed during the last few years by the authors. Computationally, the approach is typically reduced to a quadratic or conic programming and can be effectively realized. The obtained estimates demonstrate optimality or sub-optimality in a minimax sense w.r.t. the mean-square error criterion under weak design conditions. Here we describe the main ideas of the approach and represent an overview of the obtained results.

  • 20.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Grama, Ion
    Université de Bretagne Sud, France.
    Direct Weight Optimization in Statistical Estimation and System Identification2008In: Proceedings of the 7th International Conference on System Identification and Control Problems, 2008Conference paper (Refereed)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to statistical estimation and the application to nonlinear system identification has been proposed and developed during the last few years. Computationally, the approachis typically reduced to a convex (e.g., quadratic or conic) program, whichcan be solved efficiently. The optimality or sub-optimality of the obtained estimates, in a minimax sense w.r.t. the estimation error criterion, can be analyzed under weak a priori conditions. The main ideas of the approach are discussed here and an overview of the obtained results is presented.

  • 21.
    Nazin, Alexander
    et al.
    Institute of Control Sciences, Russia.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Grama, Ion
    Université de Bretagne Sud, France.
    Direct Weight Optimization in Statistical Estimation and System Identification2007Report (Other academic)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach to statistical estimation and the application to nonlinear system identification has been proposed and developed during the last few years. Computationally, the approachis typically reduced to a convex (e.g., quadratic or conic) program, whichcan be solved efficiently. The optimality or sub-optimality of the obtained estimates, in a minimax sense w.r.t. the estimation error criterion, can be analyzed under weak a priori conditions. The main ideas of the approach are discussed here and an overview of the obtained results is presented.

  • 22.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Brun, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Andersson, Mats
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization Applied to Discontinuous Functions2008In: 47th IEEE Conference on Decision and Control, 2008. CDC 2008, IEEE , 2008, p. 117-122Conference paper (Refereed)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, all function classes for which DWO has been studied have included only continuous functions. However, in many applications it would be desirable also to be able to handle discontinuous functions. Inspired by the bilateral filter method from image processing, such an extension of the DWO framework is proposed for the smoothing problem. Examples show that the properties of the new approach regarding the handling of discontinuities are similar to the bilateral filter, while at the same time DWO offers a greater flexibility with respect to different function classes handled.

  • 23.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Brun, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Andersson, Mats
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Direct Weight Optimization Applied to Discontinuous Functions2008Report (Other academic)
    Abstract [en]

    The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, all function classes for which DWO has been studied have included only continuous functions. However, in many applications it would be desirable also to be able to handle discontinuous functions. Inspired by the bilateral filter method from image processing, such an extension of the DWO framework is proposed for the smoothing problem. Examples show that the properties of the new approach regarding the handling of discontinuities are similar to the bilateral filter, while at the same time DWO offers a greater flexibility with respect to different function classes handled.

  • 24.
    Ohlsson, Henrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Roll, Jacob
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Glad, Torkel
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Ljung, Lennart
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Using Manifold Learning for Nonlinear System Identification2007In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, p. 170-175Conference paper (Refereed)
    Abstract [en]

    A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given.

  • 25.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Using Manifold Learning for Nonlinear System Identification2007Report (Other academic)
    Abstract [en]

    A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given.

  • 26.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Manifold-Constrained Regressors in System Identification2008Report (Other academic)
    Abstract [en]

    High-dimensional regression problems are becoming more and more common with emerging technologies. However, in many cases data are constrained to a low dimensional manifold. The information about the output is hence contained in a much lower dimensional space, which can be expressed by an intrinsic description. By first finding the intrinsic description, a low dimensional mapping can be found to give us a two step mapping from regressors to output. In this paper a methodology aimed at manifold-constrained identification problems is proposed. A supervised and a semi-supervised method are presented, where the later makes use of given regressor data lacking associated output values for learning the manifold. As it turns out, the presented methods also carry some interesting properties also when no dimensional reduction is performed.

  • 27.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Manifold-Constrained Regressors in System Identification2008In: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, p. 1364-1369Conference paper (Refereed)
    Abstract [en]

    High-dimensional regression problems are becoming more and more common with emerging technologies. However, in many cases data are constrained to a low dimensional manifold. The information about the output is hence contained in a much lower dimensional space, which can be expressed by an intrinsic description. By first finding the intrinsic description, a low dimensional mapping can be found to give us a two step mapping from regressors to output. In this paper a methodology aimed at manifold-constrained identification problems is proposed. A supervised and a semi-supervised method are presented, where the later makes use of given regressor data lacking associated output values for learning the manifold. As it turns out, the presented methods also carry some interesting properties also when no dimensional reduction is performed.

  • 28.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Rydell, Joakim
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Brun, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Andersson, Mats
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Ynnerman, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Enabling Bio-Feedback Using Real-Time fMRI2008Report (Other academic)
    Abstract [en]

    Despite the enormous complexity of the human mind, fMRI techniques are able to partially observe the state of a brain in action. In this paper we describe an experimental setup for real-time fMRI in a bio-feedback loop. One of the main challenges in the project is to reach a detection speed, accuracy and spatial resolution necessary to attain sufficient bandwidth of communication to close the bio-feedback loop. To this end we have banked on our previous work on real-time filtering for fMRI and system identification, which has been tailored for use in the experiment setup. In the experiments presented the system is trained to estimate where a person in the MRI scanner is looking from signals derived from the visual cortex only. We have been able to demonstrate that the user can induce an action and perform simple tasks with her mind sensed using real-time fMRI. The technique may have several clinical applications, for instance to allow paralyzed and "locked in" people to communicate with the outside world. In the meanwhile, the need for improved fMRI performance and brain state detection poses a challenge to the signal processing community. We also expect that the setup will serve as an invaluable tool for neuro science research in general.

  • 29.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Rydell, Joakim
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Brun, Anders
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Andersson, Mats
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Ynnerman, Anders
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Enabling Bio-Feedback using Real-Time fMRI2008In: 47th IEEE Conference on Decision and Control, 2008, CDC 2008, IEEE , 2008, p. 3336-3341Conference paper (Refereed)
    Abstract [en]

    Despite the enormous complexity of the human mind, fMRI techniques are able to partially observe the state of a brain in action. In this paper we describe an experimental setup for real-time fMRI in a bio-feedback loop. One of the main challenges in the project is to reach a detection speed, accuracy and spatial resolution necessary to attain sufficient bandwidth of communication to close the bio-feedback loop. To this end we have banked on our previous work on real-time filtering for fMRI and system identification, which has been tailored for use in the experiment setup. In the experiments presented the system is trained to estimate where a person in the MRI scanner is looking from signals derived from the visual cortex only. We have been able to demonstrate that the user can induce an action and perform simple tasks with her mind sensed using real-time fMRI. The technique may have several clinical applications, for instance to allow paralyzed and "locked in" people to communicate with the outside world. In the meanwhile, the need for improved fMRI performance and brain state detection poses a challenge to the signal processing community. We also expect that the setup will serve as an invaluable tool for neuro science research in general.

  • 30.
    Paoletti, Simone
    et al.
    University of Siena, Italy.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Garulli, Andrea
    University of Siena, Italy.
    Vicino, Antonio
    University of Siena, Italy.
    Input-Output Realization of Piecewise Affine State Space Models2007In: Proceedings of the 46th IEEE Conference on Decision and Control, 2007, p. 3164-3169Conference paper (Refereed)
    Abstract [en]

    This paper addresses the conversion of discrete-time single input-single output piecewise affine (PWA) models from state space to input-output form. Necessary and sufficient conditions are given for a PWA state space model to admit equivalent input-output representations. When an equivalent input-output model exists, a constructive procedure is presented to derive both its parameters and the partition of the regressors domain. It is shown that the number of modes and the number of parameters may grow considerably when converting a PWA state space model into an equivalent input-output representation. Numerical examples highlight the role of the derived necessary and sufficient conditions for input-output realization of PWA state space models.

  • 31.
    Paoletti, Simone
    et al.
    University of Siena, Italy.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Garulli, Andrea
    University of Siena, Italy.
    Vicino, Antonio
    University of Siena, Italy.
    On the Input-Output Representation of Piecewise Affine State Space Models2010In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 1, p. 60-73Article in journal (Refereed)
    Abstract [en]

    This paper addresses the conversion of discrete-time piecewise affine (PWA) state space models into input-output form. Necessary and sufficient conditions for the existence of equivalent input-output representations of a given PWA state space model are derived. Connections to the observability properties of PWA models are investigated. Under a technical assumption, it is shown that every finite-time observable PWA model admits an equivalent input-output representation. When an equivalent input-output model exists, a constructive procedure is presented to derive its equations. Several examples illustrate the proposed results.

  • 32.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Wiener Models via Mixed-Integer Programming2001In: Proceedings of the Third Conference on Computer Science and Systems Engineering, 2001, p. 297-304Conference paper (Refereed)
    Abstract [en]

    Many successful tools have been proposed by several researchers for safety analysis, stability analysis, and control/scheduling synthesis for hybrid systems. However, one important area which has not received much attention in the hybrid systems community is the identication of piecewise affne systems. As a step in that direction, we present an algorithm for identifying piecewise affne Wiener models from input-output data. Two notable properties of the algorithm are that the globally optimal solution is found, and that the complexity is polynomial with respect to the number of data. The basic ideas of this algorithm can also be directly transfered to a larger class of piecewise affine systems.

  • 33.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Wiener Models via Mixed-Integer Programming2002In: Proceedings of Reglermöte 2002, 2002, p. 268-273Conference paper (Other academic)
    Abstract [en]

    Many successful tools have been proposed by several researchers for safety analysis, stability analysis, and control/scheduling synthesis for hybrid systems. However, one important area which has not received much attention in the hybrid systems community is the identification of piecewise affine systems. As a step in that direction, an algorithm for identifying piecewise affine Wiener models from input-output data is presented. Two notable properties of the algorithm are that the globally optimal solution is found, and that the complexity is polynomial with respect to the number of data. The basic ideas of this algorithm can also be directly transfered to a larger class of piecewise affine systems.

  • 34.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Wiener Models via Mixed-Integer Programming2001Report (Other academic)
    Abstract [en]

    Many successful tools have been proposed by several researchers for safety analysis, stability analysis, and control/scheduling synthesis for hybrid systems. However, one important area which has not received much attention in the hybrid systems community is the identication of piecewise affne systems. As a step in that direction, we present an algorithm for identifying piecewise affne Wiener models from input-output data. Two notable properties of the algorithm are that the globally optimal solution is found, and that the complexity is polynomial with respect to the number of data. The basic ideas of this algorithm can also be directly transfered to a larger class of piecewise affine systems.

  • 35.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Invariance of Approximating Automata for Piecewise Linear Systems1999In: Proceedings of the Second Conference on Computer Science and Systems Engineering, 1999, p. 163-168Conference paper (Other academic)
    Abstract [en]

    Piecewise linear systems - systems that switch between different linear subsystems at different occasions - occur in many applications. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This report considers one such method, and gives some algorithms for investigating how sensitive it is to changes in the underlying subsystems. These algorithms can be used either for robustness analysis or for control design.

  • 36.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Invariance of Approximating Automata for Piecewise Linear Systems1999Report (Other academic)
    Abstract [en]

    Piecewise linear systems - systems that switch between different linear subsystems at different occasions - occur in many applications. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This report considers one such method, and gives some algorithms for investigating how sensitive it is to changes in the underlying subsystems. These algorithms can be used either for robustness analysis or for control design.

  • 37.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Invariance of Approximating Automata for Piecewise Linear Systems with Uncertainties2000In: Proceedings of Reglermöte 2000, 2000, p. 228-233Conference paper (Other academic)
    Abstract [en]

    Piecewise linear systems - systems that switch between dierent linear subsystems at dierent occasions - occur in many applications. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This report considers one such method, and gives some algorithms for investigating how sensitive it is to changes in the underlying subsystems. These algorithms can be used either for robustness analysis or for control design.

  • 38.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Invariance of Approximating Automata for Piecewise Linear Systems with Uncertainties2000In: Hybrid Systems: Computation and Control: Third International Workshop, HSCC 2000 Pittsburgh, PA, USA, March 23–25, 2000 Proceedings / [ed] Nancy Lynch and Bruce H. Krogh, Berlin: Springer Berlin/Heidelberg, 2000, Vol. 1790, p. 396-406Chapter in book (Refereed)
    Abstract [en]

    A special class of hybrid systems, that occurs in many applications, are the piecewise linear systems. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This paper considers one such method, and gives a method for investigating how sensitive it is to changes in the dynamics of the underlying linear subsystems. This method can be used either for robustness analysis or for control design.

  • 39.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Invariance of Approximating Automata for Piecewise Linear Systems with Uncertainties2000In: Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control, Springer Berlin/Heidelberg, 2000, p. 396-406Conference paper (Refereed)
    Abstract [en]

    A special class of hybrid systems, that occurs in many applications, are the piecewise linear systems. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This paper considers one such method, and gives a method for investigating how sensitive it is to changes in the dynamics of the underlying linear subsystems. This method can be used either for robustness analysis or for control design.

  • 40.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Piecewise Linear Solution Paths for Parametric Piecewise Quadratic Programs2008In: Proceedings of the 17th IFAC World Congress, 2008, p. 2732-2737Conference paper (Refereed)
    Abstract [en]

    Recently, pathfollowing algorithms for parametric optimization problems withpiecewise linear solution paths have been developed within the field of regularized regression.This paper presents a generalization of these algorithms to a wider class of problems, namely aclass of parametric piecewise quadratic programs and related problems. By using pathfollowingalgorithms that exploit the piecewise linearity, the entire solution paths can be very efficientlycomputed. Possible applications include design parameter selection for identification methodssuch as Direct Weight Optimization.

  • 41.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Piecewise Linear Solution Paths for Parametric Piecewise Quadratic Programs with Application to Direct Weight Optimization2007Report (Other academic)
    Abstract [en]

    Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression. This paper presents a generalization of these algorithms to a wider class of problems, namely a class of parametric piecewise quadratic programs and related problems. By using pathfollowing algorithms that exploit the piecewise linearity, the entire solution paths can be very efficiently computed. Possible applications include design parameter selection for identification methods such as Direct Weight Optimization.

  • 42.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Piecewise Linear Solution Paths with Application to Direct Weight Optimization2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 11, p. 2745-2753Article in journal (Refereed)
    Abstract [en]

    Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression. This paper presents a generalization of these algorithms to a wider class of problems. It is shown that the approach can be applied to the nonparametric system identification method, Direct Weight Optimization (DWO), and be used to enhance the computational efficiency of this method. The most important design parameter in the DWO method is a parameter (lambda) controlling the bias-variance trade-off, and the use of parametric optimization with piecewise linear solution paths means that the DWO estimates can be efficiently computed for all values of lambda simultaneously. This allows for designing computationally attractive adaptive bandwidth selection algorithms. One such algorithm for DWO is proposed and demonstrated in two examples.

  • 43.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Verification of Piecewise Affine Systems2002In: Proceedings of the 15th IFAC World Congress, 2002, p. 221-221Conference paper (Refereed)
    Abstract [en]

    Piecewise affine systems is an important class of hybrid systems. They consist of several affine dynamic subsystems, between which switchings occur at different occasions. In this paper, a verification method for piecewise affine systems is considered, and a method to determine how sensitive the verified properties are to changes in the dynamics and the locations of the switching surfaces is proposed. This information can then be used for robustness analysis or control design.

  • 44.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Verification of Piecewise Affine Systems2003Report (Other academic)
    Abstract [en]

    Piecewise affine systems is an important class of hybrid systems. They consist of several affine dynamic subsystems, between which switchings occur at different occasions. In this paper, a verification method for piecewise affine systems is considered, and a method to determine how sensitive the verified properties are to changes in the dynamics and the locations of the switching surfaces is proposed. This information can then be used for robustness analysis or control design.

  • 45.
    Roll, Jacob
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robustness and Control Design Issues for a Verification Method for Piecewise Affine Systems2000Report (Other academic)
    Abstract [en]

    A special class of hybrid systems, that occurs in many applications, are the piecewise affine systems. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This paper considers one such method, and gives some methods for investigating how sensitive it is to changes in the dynamics and switching points of the real system. This method can be used either for robustness analysis or for control design.

  • 46.
    Roll, Jacob
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bemporad, Alberto
    University of Siena, Italy.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Systems via Mixed-Integer Programming2003Report (Other academic)
    Abstract [en]

    This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where the estimation data only seldom switches between the different submodels, we also suggest a way of trading off between optimality and complexity by using a change detection approach.

  • 47.
    Roll, Jacob
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bemporad, Alberto
    University of Siena, Italy.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Systems via Mixed-Integer Programming2004In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 40, no 1, p. 37-50Article in journal (Refereed)
    Abstract [en]

    This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where the estimation data only seldom switches between the different submodels, we also suggest a way of trading off between optimality and complexity by using a change detection approach.

  • 48.
    Roll, Jacob
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Consistent Nonparametric Estimation of NARX Systems Using Convex Optimization2005In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, 2005, p. 3129-3134Conference paper (Refereed)
    Abstract [en]

    In this paper, a nonparametric method based on quadratic programming (QP) for identification of nonlinear autoregressive systems with exogenous inputs (NARX systems) is presented. We consider a mixed parametric/nonparametric model structure. The output is assumed to be the sum of a parametric linear part and a nonparametric Lipschitz continuous part. The consistency of the estimator is shown assuming only that an upper bound on the true Lipschitz constant is given. In addition, different types of prior knowledge about the system can easily be incorporated. Examples show that the method can give accurate estimates also for small data sets and that the estimate of the linear part sometimes can be improved compared to the linear least squares estimate.

  • 49.
    Roll, Jacob
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Consistent Nonparametric Estimation of NARX Systems Using Convex Optimization2005Report (Other academic)
    Abstract [en]

    In this paper, a nonparametric method based on quadratic programming (QP) for identification of nonlinear autoregressive systems with exogenous inputs (NARX systems) is presented. We consider a mixed parametric/nonparametric model structure. The output is assumed to be the sum of a parametric linear part and a nonparametric Lipschitz continuous part. The consistency of the estimator is shown assuming only that an upper bound on the true Lipschitz constant is given. In addition, different types of prior knowledge about the system can easily be incorporated. Examples show that the method can give accurate estimates also for small data sets and that the estimate of the linear part sometimes can be improved compared to the linear least squares estimate.

  • 50.
    Roll, Jacob
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lind, Ingela
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Connections Between Optimisation-Based Regressor Selection and Analysis of Variance2006Report (Other academic)
    Abstract [en]

    Earlier contributions have shown that Analysis of Variance (ANOVA) can be successfully used for finding good regressors for nonlinear models in a nonlinear black-box system identification context. In this paper, it is shown that the ANOVA problem can be recast as an optimisation problem. Two modified, convex versions of the ANOVA optimisation problem are then proposed, and it turns out that they are closely related to the nn-garrote and wavelet shrinkage methods, respectively. In the case of balanced data, it is also shown that the methods have a nice orthogonality property in the sense that different groups of parameters can be computed independently.

12 1 - 50 of 68
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