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  • 1.
    Bako, Laurent
    et al.
    University of Lyon, France.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering. University of Calif Berkeley, CA 94720 USA.
    Analysis of a nonsmooth optimization approach to robust estimation2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 66, p. 132-145Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitrarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection; state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors. (C) 2016 Elsevier Ltd. All rights reserved.

  • 2.
    Bauwens, Maite
    et al.
    Vrije Universiteit Brussel, Belgium.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Barbe, Kurt
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    A Nonlinear Multi-Proxy Model Based on Manifold Learning to Reconstruct Water Temperature from High Resolution Trace Element Profiles in Biogenic Carbonates2010In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 3, no 3, p. 653-667Article in journal (Refereed)
    Abstract [en]

    A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ18O carbonate, which for freshwater influenced environments is hindered because the isotopic composition of the ambient water (related to salinity) affects the reconstructed temperature. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: Firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information of other trace elements in multi-proxy models. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enabled a temperature reconstruction with a root mean squared error of ±2.19 °C for a salinity range between 15 and 32.

  • 3.
    Bauwens, Maite
    et al.
    Vrije Universiteit Brussel, Belgium.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Barbé, Kurt
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    On Climate Reconstruction using Bivalve Shells: Three Methods to interpret the Chemical Signature of a Shell2010Report (Other academic)
    Abstract [en]

    The chemical composition of a bivalve shell is strongly coupled to the seasonal variations in the environment. The nonlinear nature of this relation however makes it hard to predict, e.g. the temperature, from the chemical composition of a shell. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potential tools for climate reconstructions with a preference for manifold based methods that results in smoother and a more precise temperature reconstruction.

  • 4.
    Bauwens, Maite
    et al.
    Vrije Universiteit Brussel, Belgium.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Barbé, Kurt
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    On Climate Reconstruction using Bivalve Shells: Three Methods to interpret the Chemical Signature of a Shell2009In: Proceedings of the 7th IFAC Symposium on Modelling and Control in Biomedical Systems (including Biological Systems), 2009, p. 407-412Conference paper (Refereed)
    Abstract [en]

    The chemical composition of a bivalve shell is strongly coupled to the seasonal variations in the environment. The nonlinear nature of this relation however makes it hard to predict, e.g. the temperature, from the chemical composition of a shell. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potential tools for climate reconstructions with a preference for manifold based methods that results in smoother and a more precise temperature reconstruction.

  • 5.
    Bauwens, Maite
    et al.
    Vrije Universiteit Brussel, Belgium.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Barbé, Kurt
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    On Climate Reconstruction Using Bivalve Shells: Three Methods To Interpret the Chemical Signature of a Shell2011In: Computer Methods and Programs in Biomedicine, ISSN 0169-2607, E-ISSN 1872-7565, Vol. 104, no 2, p. 104-111Article in journal (Refereed)
    Abstract [en]

    To improve our understanding of the climate process and to assess the human impact on current global warming, past climate reconstruction is essential. The chemical composition of a bivalve shell is strongly coupled to environmental variations and therefore ancient shells are potential climate archives. The nonlinear nature of the relation between environmental condition (e.g. the seawater temperature) and proxy composition makes it hard to predict the former from the latter, however. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the ambient temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potentially useful tools for climate reconstructions and that manifold based methods result in smoother and more precise temperature reconstruction.

  • 6.
    Burden, Sam
    et al.
    University of California at Berkeley, USA.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sastry, Shankar
    University of California at Berkeley, USA.
    Parameter Identification Near Periodic Orbits of Hybrid Dynamical Systems2012In: Proceedings of the 16th IFAC Symposium on System Identification, 2012, p. 1197-1202Conference paper (Refereed)
    Abstract [en]

    We present a novel identification framework that enables the use of first-order methods when estimating model parameters near a periodic orbit of a hybrid dynamical system. The proposed method reduces the space of initial conditions to a smooth manifold that contains the hybrid dynamics near the periodic orbit while maintaining the parametric dependence of the original hybrid model. First-order methods apply on this subsystem to minimize average prediction error, thus identifying parameters for the original hybrid system. We implement the technique and provide simulation results for a hybrid model relevant to terrestrial locomotion.

  • 7.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Goodwin, Graham C.
    University of Newcastle, Australia.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kernel Selection in Linear System Identification: Part II: A Classical Perspective2011In: Proceedings of the 50th IEEE Conference on Decision and Control, 2011, p. 4326-4331Conference paper (Refereed)
    Abstract [en]

    In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed. The ideas are tested on the same data bank as used in Part I of the companion papers. The resulting findings and conclusions in the two papers are very similar despite the different perspectives.

  • 8.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    On the Estimation of Transfer Functions, Regularizations and Gaussian Processes – Revisited2010In: Proceedings of the 18th IFAC World Congress, 2010, p. 2303-2308Conference paper (Refereed)
    Abstract [en]

    Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements.We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression.

  • 9.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 8, p. 1525-1535Article in journal (Refereed)
    Abstract [en]

    Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.

  • 10.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Decentralization of Particle Filters Using Arbitrary State Decomposition2010In: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, p. 7383-7388Conference paper (Refereed)
    Abstract [en]

    In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has an advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and thus can be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results from a numerical example indicates that the DPF has a potential to achieve the same level of performance as the regular PF, in a shorter execution time.

  • 11.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Decentralized Particle Filter with Arbitrary State Decomposition2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 2, p. 465-478Article in journal (Refereed)
    Abstract [en]

    In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.

  • 12.
    Eklund, Anders
    et al.
    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.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ynnerman, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). 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.
    A Brain Computer Interface for Communication Using Real-Time fMRI2010In: Proceedings of the 20th International Conference on Pattern Recognition, Los Alamitos, CA, USA: IEEE Computer Society, 2010, p. 3665-3669Conference paper (Refereed)
    Abstract [en]

    We present the first step towards a brain computer interface (BCI) for communication using real-time functional magnetic resonance imaging (fMRI). The subject in the MR scanner sees a virtual keyboard and steers a cursor to select different letters that can be combined to create words. The cursor is moved to the left by activating the left hand, to the right by activating the right hand, down by activating the left toes and up by activating the right toes. To select a letter, the subject simply rests for a number of seconds. We can thus communicate with the subject in the scanner by for example showing questions that the subject can answer. Similar BCI for communication have been made with electroencephalography (EEG). The subject then focuses on a letter while different rows and columns of the virtual keyboard are flashing and the system tries to detect if the correct letter is flashing or not. In our setup we instead classify the brain activity. Our system is neither limited to a communication interface, but can be used for any interface where five degrees of freedom is necessary.

  • 13.
    Eklund, Anders
    et al.
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Rydell, Joakim
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ynnerman, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). 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.
    Using Real-Time fMRI to Control a Dynamical System2009In: ISMRM 17th Scientific Meeting & Exhibition, 2009Conference paper (Refereed)
    Abstract [en]

    We present e method for controlling a dynamical system using real-time fMRI. The objective for the subject in the MR scanner is to balance an inverse pendulum by activating the left or right hand or resting. The brain activity is clasified each second by a neural network and the classification is sent to a pendulum simulator to change the state of the pendulum. The state of the inverse pendulum is shown to the subject in a pair of VR goggles. The subject was able to balance the inverse pendulum during a 7 minute test run.

  • 14.
    Eklund, Anders
    et al.
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Rydell, Joakim
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ynnerman, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). 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.
    Using Real-Time fMRI to Control a Dynamical System2009Report (Other academic)
    Abstract [en]

    We present e method for controlling a dynamical system using real-time fMRI. The objective for the subject in the MR scanner is to balance an inverse pendulum by activating the left or right hand or resting. The brain activity is clasified each second by a neural network and the classification is sent to a pendulum simulator to change the state of the pendulum. The state of the inverse pendulum is shown to the subject in a pair of VR goggles. The subject was able to balance the inverse pendulum during a 7 minute test run.

  • 15.
    Eklund, Anders
    et al.
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Rydell, Joakim
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Ynnerman, 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.
    Using Real-Time fMRI to Control a Dynamical System by Brain Activity Classification2010Report (Other academic)
    Abstract [en]

    We present a method for controlling a dynamical system using real-time fMRI. The objective for the subject in the MR scanner is to balance an inverted pendulum by activating the left or right hand or resting. The brain activity is classified each second by a neural network and the classification is sent to a pendulum simulator to change the force applied to the pendulum. The state of the inverted pendulum is shown to the subject in a pair of VR goggles. The subject was able to balance the inverted pendulum during several minutes, both with real activity and imagined activity. In each classification 9000 brain voxels were used and the response time for the system to detect a change of activity was on average 2-4 seconds. The developments here have a potential to aid people with communication disabilities, such as locked in people. Another future potential application can be to serve as a tool for stroke and Parkinson patients to be able to train the damaged brain area and get real-time feedback for more efficient training.

  • 16.
    Eklund, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ohlsson, Henrik
    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, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Rydell, Joakim
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ynnerman, Anders
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Using Real-Time fMRI to Control a Dynamical System by Brain Activity Classification2009In: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009: 12th International Conference, London, UK, September 20-24, 2009, Proceedings, Part I / [ed] Gerhard Goos, Juris Hartmanis and Jan van Leeuwen, Springer Berlin/Heidelberg, 2009, 1, p. 1000-1008Conference paper (Refereed)
    Abstract [en]

    We present a method for controlling a dynamical system using real-time fMRI. The objective for the subject in the MR scanner is to balance an inverted pendulum by activating the left or right hand or resting. The brain activity is classified each second by a neural network and the classification is sent to a pendulum simulator to change the force applied to the pendulum. The state of the inverted pendulum is shown to the subject in a pair of VR goggles. The subject was able to balance the inverted pendulum during several minutes, both with real activity and imagined activity. In each classification 9000 brain voxels were used and the response time for the system to detect a change of activity was on average 2-4 seconds. The developments here have a potential to aid people with communication disabilities, such as locked in people. Another future potential application can be to serve as a tool for stroke and Parkinson patients to be able to train the damaged brain area and get real-time feedback for more efficient training.

  • 17.
    Falck, Tillmann
    et al.
    Katholieke Universiteit Leuven, Belgium.
    Ohlsson, Henrik
    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.
    Suykens, Johan A.K.
    Katholieke Universiteit Leuven, Belgium.
    De Moor, Bart
    Katholieke Universiteit Leuven, Belgium.
    Segmentation of Time Series from Nonlinear Dynamical Systems2011In: Proceedings of the 18th IFAC World Congress, 2011, p. 13209-13214Conference paper (Refereed)
    Abstract [en]

    Segmentation of time series data is of interest in many applications, as for example in change detection and fault detection. In the area of convex optimization, the sum-of-norms regularization has recently proven useful for segmentation. Proposed formulations handle linear models, like ARX models, but cannot handle nonlinear models. To handle nonlinear dynamics, we propose integrating the sum-of-norms regularization with a least squares support vector machine (LS-SVM) core model. The proposed formulation takes the form of a convex optimization problem with the regularization constant trading off the fit and the number of segments.

  • 18.
    Khoshfetrat Pakazad, Sina
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Sparse Control Using Sum-of-norms Regularized Model Predictive Control2013Conference paper (Refereed)
  • 19.
    Lauer, Fabien
    et al.
    University of Lorraine, France.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering. University of Calif Berkeley, CA 94720 USA.
    Finding sparse solutions of systems of polynomial equations via group-sparsity optimization2015In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 62, no 2, p. 319-349Article in journal (Refereed)
    Abstract [en]

    The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. Then, two approaches are considered to find these group-sparse solutions. The first one is based on a convex relaxation resulting in a second-order cone programming formulation which can benefit from efficient reweighting techniques for sparsity enhancement. For this approach, sufficient conditions for the exact recovery of the sparsest solution to the polynomial system are derived in the noiseless setting, while stable recovery results are obtained for the noisy case. Though lacking a similar analysis, the second approach provides a more computationally efficient algorithm based on a greedy strategy adding the groups one-by-one. With respect to previous work, the proposed methods recover the sparsest solution in a very short computing time while remaining at least as accurate in terms of the probability of success. This probability is empirically analyzed to emphasize the relationship between the ability of the methods to solve the polynomial system and the sparsity of the solution.

  • 20.
    Lindsten, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Callmer, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Geo-Referencing for UAV Navigation using Environmental Classification2010Report (Other academic)
    Abstract [en]

    A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

  • 21.
    Lindsten, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Callmer, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Geo-Referencing for UAV Navigation using Environmental Classification2010In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation, 2010, p. 1420-1425Conference paper (Refereed)
    Abstract [en]

    A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

  • 22.
    Lindsten, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Clustering using Sum-of-Norms Regularization: With Application to Particle Filter Output Computation2011Report (Other academic)
    Abstract [en]

    We present a novel clustering method, formulated as a convex optimization problem. The method is based on over-parameterization and uses a sum-of-norms (SON) regularization to control the trade-off between the model fit and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specified a priori. We apply SON clustering to cluster the particles in a particle filter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative.

  • 23.
    Lindsten, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Clustering using Sum-of-Norms Regularization: With Application to Particle Filter Output Computation2011In: Proceedings of the 2011 IEEE Statistical Signal Processing Workshop, 2011, p. 201-204Conference paper (Refereed)
    Abstract [en]

    We present a novel clustering method, formulated as a convex optimization problem. The method is based on over-parameterization and uses a sum-of-norms (SON) regularization to control the trade-off between the model fit and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specified a priori. We apply SON clustering to cluster the particles in a particle filter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative.

  • 24.
    Lindsten, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    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.
    Just Relax and Come Clustering!: A Convexification of k-Means Clustering2011Report (Other academic)
    Abstract [en]

    k-means clustering is a popular approach to clustering. It is easy to implement and intuitive but has the disadvantage of being sensitive to initialization due to an underlying nonconvex optimization problem. In this paper, we derive an equivalent formulation of k-means clustering. The formulation takes the form of a L0-regularized least squares problem. We then propose a novel convex, relaxed, formulation of k-means clustering. The sum-of-norms regularized least squares formulation inherits many desired properties of k-means but has the advantage of being independent of initialization.

  • 25.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hjalmarsson, Hakan
    Royal Institute of Technology, Sweden.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Four Encounters with System Identification2011In: European Journal of Control, ISSN 0947-3580, E-ISSN 1435-5671, Vol. 17, no 5-6, p. 449-471Article in journal (Refereed)
    Abstract [en]

    Model-based engineering becomes more and more important in industrial practice. System identification is a vital technology for producing the necessary models, and has been an active area of research and applications in the automatic control community during half a century. At the same time, increasing demands require the area to constantly develop and sharpen its tools. This paper deals with how system identification does that by amalgamating concepts, features and methods from other fields. It describes encounters with four areas in systems theory and engineering: Networked Systems, Particle Filtering Techniques, Sparsity and Compressed Sensing, and Machine Learning. The impacts on System Identification methodology by these encounters are described and illustrated.

  • 26.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bauwens, Maite
    Vrije Universiteit Brussel, Belgium.
    On Manifolds, Climate Reconstruction and Bivalve Shells2009In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009, p. 5738-5743Conference paper (Refereed)
    Abstract [en]

    To estimate the past climate, for example the ocean temperature 1000 years ago, one has to turn to naturally occurring climate recorders. There exist a number of climate recorders in nature from which the past temperature can be extracted. However, only a few natural archives are able to record climate fluctuations with high enough resolution so that the seasonal variations can be reconstructed. One such archive is a bivalve shell. The chemical composition of a shell of a bivalve depends on a number of chemical and physical parameters of the water in which the shell was composed. Of these parameters, the water temperature is probably the most important one. It should therefore be possible to estimate the water temperature for the years the shell was built, from measurements of the shell's chemical composition. In this paper, we explore this possibility. We do this by first observing that the chemical compositions lie on a one-dimensional manifold parameterized by the water temperature. This manifold is then utilized in the regression to obtain accurate estimates of past water temperatures.

  • 27.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bauwens, Maite
    Vrije Universiteit Brussel, Belgium.
    On Manifolds, Climate Reconstruction and Bivalve Shells2010Report (Other academic)
    Abstract [en]

    To estimate the past climate, for example the ocean temperature 1000 years ago, one has to turn to naturally occurring climate recorders. There exist a number of climate recorders in nature from which the past temperature can be extracted. However, only a few natural archives are able to record climate fluctuations with high enough resolution so that the seasonal variations can be reconstructed. One such archive is a bivalve shell. The chemical composition of a shell of a bivalve depends on a number of chemical and physical parameters of the water in which the shell was composed. Of these parameters, the water temperature is probably the most important one. It should therefore be possible to estimate the water temperature for the years the shell was built, from measurements of the shell's chemical composition. In this paper, we explore this possibility. We do this by first observing that the chemical compositions lie on a one-dimensional manifold parameterized by the water temperature. This manifold is then utilized in the regression to obtain accurate estimates of past water temperatures.

  • 28.
    Nguyen, Tan Khoa
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Hernell, Frida
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ljung, Patric
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology.
    Forsell, Camilla
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology.
    Andersson, Mats
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ynnerman, Anders
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Concurrent Volume Visualization of Real-Time fMRI2010In: Proceedings of the 8th IEEE/EG International Symposium on Volume Graphics / [ed] Ruediger Westermann and Gordon Kindlmann, Goslar, Germany: Eurographics - European Association for Computer Graphics, 2010, p. 53-60Conference paper (Refereed)
    Abstract [en]

    We present a novel approach to interactive and concurrent volume visualization of functional Magnetic Resonance Imaging (fMRI). While the patient is in the scanner, data is extracted in real-time using state-of-the-art signal processing techniques. The fMRI signal is treated as light emission when rendering a patient-specific high resolution reference MRI volume, obtained at the beginning of the experiment. As a result, the brain glows and emits light from active regions. The low resolution fMRI signal is thus effectively fused with the reference brain with the current transfer function settings yielding an effective focus and context visualization. The delay from a change in the fMRI signal to the visualization is approximately 2 seconds. The advantage of our method over standard 2D slice based methods is shown in a user study. We demonstrate our technique through experiments providing interactive visualization to the fMRI operator and also to the test subject in the scanner through a head mounted display.

  • 29.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Regression on Manifolds with Implications for System Identification2008Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The trend today is to use many inexpensive sensors instead of a few expensive ones, since the same accuracy can generally be obtained by fusing several dependent measurements. It also follows that the robustness against failing sensors is improved. As a result, the need for high-dimensional regression techniques is increasing.

    As measurements are dependent, the regressors will be constrained to some manifold. There is then a representation of the regressors, of the same dimension as the manifold, containing all predictive information. Since the manifold is commonly unknown, this representation has to be estimated using data. For this, manifold learning can be utilized. Having found a representation of the manifold constrained regressors, this low-dimensional representation can be used in an ordinary regression algorithm to find a prediction of the output. This has further been developed in the Weight Determination by Manifold Regularization (WDMR) approach.

    In most regression problems, prior information can improve prediction results. This is also true for high-dimensional regression problems. Research to include physical prior knowledge in high-dimensional regression i.e., gray-box high-dimensional regression, has been rather limited, however. We explore the possibilities to include prior knowledge in high-dimensional manifold constrained regression by the means of regularization. The result will be called gray-box WDMR. In gray-box WDMR we have the possibility to restrict ourselves to predictions which are physically plausible. This is done by incorporating dynamical models for how the regressors evolve on the manifold.

  • 30.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Regularization for Sparseness and Smoothness: Applications in System Identification and Signal Processing2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In system identification, the Akaike Information Criterion (AIC) is a well known method to balance the model fit against model complexity. Regularization here acts as a price on model complexity. In statistics and machine learning, regularization has gained popularity due to modeling methods such as Support Vector Machines (SVM), ridge regression and lasso. But also when using a Bayesian approach to modeling, regularization often implicitly shows up and can be associated with the prior knowledge. Regularization has also had a great impact on many applications, and very much so in clinical imaging. In e.g., breast cancer imaging, the number of sensors is physically restricted which leads to long scantimes. Regularization and sparsity can be used to reduce that. In Magnetic Resonance Imaging (MRI), the number of scans is physically limited and to obtain high resolution images, regularization plays an important role.

    Regularization shows-up in a variety of different situations and is a well known technique to handle ill-posed problems and to control for overfit. We focus on the use of regularization to obtain sparseness and smoothness and discuss novel developments relevant to system identification and signal processing.

    In regularization for sparsity a quantity is forced to contain elements equal to zero, or to be sparse. The quantity could e.g., be the regression parameter vectorof a linear regression model and regularization would then result in a tool for variable selection. Sparsity has had a huge impact on neighboring disciplines, such as machine learning and signal processing, but rather limited effect on system identification. One of the major contributions of this thesis is therefore the new developments in system identification using sparsity. In particular, a novel method for the estimation of segmented ARX models using regularization for sparsity is presented. A technique for piecewise-affine system identification is also elaborated on as well as several novel applications in signal processing. Another property that regularization can be used to impose is smoothness. To require the relation between regressors and predictions to be a smooth function is a way to control for overfit. We are here particularly interested in regression problems with regressors constrained to limited regions in the regressor-space e.g., a manifold. For this type of systems we develop a new regression technique, Weight Determination by Manifold Regularization (WDMR). WDMR is inspired byapplications in biology and developments in manifold learning and uses regularization for smoothness to obtain smooth estimates. The use of regularization for smoothness in linear system identification is also discussed.

    The thesis also presents a real-time functional Magnetic Resonance Imaging (fMRI) bio-feedback setup. The setup has served as proof of concept and been the foundation for several real-time fMRI studies.

    List of papers
    1. Segmentation of ARX-Models using Sum-of-Norms Regularization
    Open this publication in new window or tab >>Segmentation of ARX-Models using Sum-of-Norms Regularization
    2010 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 6, p. 1107-1111Article in journal (Refereed) Published
    Abstract [en]

    Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps. a generalization of L1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.

    Place, publisher, year, edition, pages
    Elsevier, 2010
    Keywords
    Segmentation, Regularization, ARX-models
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-58384 (URN)10.1016/j.automatica.2010.03.013 (DOI)000278675500020 ()
    Projects
    CADICS
    Available from: 2010-08-13 Created: 2010-08-11 Last updated: 2017-12-12
    2. Identification of Piecewise Affine Systems Using Sum-of-Norms Regularization
    Open this publication in new window or tab >>Identification of Piecewise Affine Systems Using Sum-of-Norms Regularization
    2011 (English)In: Proceedings of the 18th IFAC World Congress, 2011, p. 6640-6645Conference paper, Published paper (Refereed)
    Abstract [en]

    Systems today often consist of logic switches working besides continuous physical systems. The demand for novel hybrid system identification algorithms is therefore of growing interest and essential for the development of control algorithms for this type of systems. An important type of hybrid systems is piecewise affine systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. The regressor parameters are forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem with sum-of-norms regularization over regressor parameter differences, a generalization of l1-regularization. The regularization constant is used to trade off fit and the number of partitions of the model.

    Keywords
    Hybrid systems modeling and control, Nonlinear system identification, Nonparametric methods
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-60984 (URN)10.3182/20110828-6-IT-1002.00611 (DOI)978-3-902661-93-7 (ISBN)
    Conference
    18th IFAC World Congress, Milano, Italy, 28 August-2 September, 2011
    Projects
    CADICS
    Funder
    Swedish Foundation for Strategic Research Swedish Research Council
    Available from: 2013-04-04 Created: 2010-11-01 Last updated: 2013-07-10Bibliographically approved
    3. Smoothed State Estimates under Abrupt Changes using Sum-of-Norms Regularization
    Open this publication in new window or tab >>Smoothed State Estimates under Abrupt Changes using Sum-of-Norms Regularization
    2012 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 4, p. 595-605Article in journal (Refereed) Published
    Abstract [en]

    The presence of abrupt changes, such as impulsive and load disturbances, commonly occur in applications, but make the state estimation problem considerably more difficult than in the standard setting with Gaussian process disturbance. Abrupt changes often introduce a jump in the state, and the problem is therefore readily and often treated by change detection techniques. In this paper, we take a different approach. The state smoothing problem for linear state space models is here formulated as a constrained least-squares problem with sum-of-norms regularization, a generalization of l1-regularization. This novel formulation can be seen as a convex relaxation of the well known generalized likelihood ratio method by Willsky and Jones. Another nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps. Good practical choices of this parameter along with an extension to nonlinear state space models are given. 

    Place, publisher, year, edition, pages
    Elsevier, 2012
    Keywords
    State estimation, Impulsive disturbance, Load disturbance, Smoothing, Sparsity, Regularization, Change detection
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-60985 (URN)10.1016/j.automatica.2011.08.063 (DOI)000302766400002 ()
    Projects
    CADICS
    Funder
    Swedish Research Council
    Available from: 2010-11-01 Created: 2010-11-01 Last updated: 2017-12-12
    4. Trajectory Generation Using Sum-of-Norms Regularization
    Open this publication in new window or tab >>Trajectory Generation Using Sum-of-Norms Regularization
    2010 (English)In: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, p. 540-545Conference paper, Published paper (Refereed)
    Abstract [en]

    Many tracking problems are split into two sub-problems, first a smooth reference trajectory is generated that meet the control design objectives, and then a closed loop control system is designed to follow this reference trajectory as well as possible. Applications of this kind include (autonomous) vehicle navigation systems and robotics. Typically, a spline model is used for trajectory generation and another physical and dynamical model is used for the control design. Here we propose a direct approach where the dynamical model is used to generate a control signal that takes the state trajectory through the waypoints specified in the design goals. The strength of the proposed formulation is the methodology to obtain a control signal with compact representation and that changes only when needed, something often wanted in tracking. The formulation takes the shape of a constrained least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. The formulation also gives a tool to, e.g. in model predictive control, prevent chatter in the input signal, and also select the most suitable instances for applying the control inputs.

    Keywords
    Closed loop systems, Control system synthesis, Least squares approximations, Predictive control
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-60983 (URN)10.1109/CDC.2010.5717368 (DOI)978-1-4244-7745-6 (ISBN)
    Conference
    49th IEEE Conference on Decision and Control, Atlanta, GA, USA, 15-17 December, 2010
    Projects
    CADICS
    Available from: 2010-11-01 Created: 2010-11-01 Last updated: 2013-07-09
    5. Weight Determination by Manifold Regularization
    Open this publication in new window or tab >>Weight Determination by Manifold Regularization
    2010 (English)In: Distributed Decision-Making and Control / [ed] Rolf Johansson and Anders Rantzer, Springer London, 2010, p. 195-214Chapter in book (Refereed)
    Abstract [en]

    A new type of linear kernel smoother is derived and studied. The smoother, referred to as weight determination by manifold regularization, is the solution to a regularized least squares problem. The regularization avoids overfitting and can be used to express prior knowledge of an underlying smooth function. An interesting property ofthe kernel smoother is that it is well suited for systems govern by the semi-supervised smoothness assumption. Several examples are given to illustrate this property. We also discuss why these types of techniques can have a potential interest for the system identification community.

    Place, publisher, year, edition, pages
    Springer London, 2010
    Series
    Lecture Notes in Control and Information Sciences, ISSN 0170-8643 ; 417
    Keywords
    Regularization, Weight determination
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-60987 (URN)10.1007/978-1-4471-2265-4_9 (DOI)978-1-4471-2264-7 (ISBN)978-1-4471-2265-4 (ISBN)
    Available from: 2010-11-01 Created: 2010-11-01 Last updated: 2013-09-29
    6. On the Estimation of Transfer Functions, Regularizations and Gaussian Processes – Revisited
    Open this publication in new window or tab >>On the Estimation of Transfer Functions, Regularizations and Gaussian Processes – Revisited
    2010 (English)In: Proceedings of the 18th IFAC World Congress, 2010, p. 2303-2308Conference paper, Published paper (Refereed)
    Abstract [en]

    Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements.We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression.

    Keywords
    System identification, Transfer function estimation, Reqularization
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-60986 (URN)10.3182/20110828-6-IT-1002.00573 (DOI)978-3-902661-93-7 (ISBN)
    Conference
    18th IFAC World Congress, Milano, Italy, 28 August-2 September, 2011
    Funder
    Swedish Foundation for Strategic Research Swedish Research Council
    Note

    Submitted

    Available from: 2010-11-01 Created: 2010-11-01 Last updated: 2016-01-11
    7. Enabling Bio-Feedback using Real-Time fMRI
    Open this publication in new window or tab >>Enabling Bio-Feedback using Real-Time fMRI
    Show others...
    2008 (English)In: 47th IEEE Conference on Decision and Control, 2008, CDC 2008, IEEE , 2008, p. 3336-3341Conference paper, Published 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.

    Place, publisher, year, edition, pages
    IEEE, 2008
    Series
    IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
    Keywords
    fMRI, System identification, Bio-feedback
    National Category
    Engineering and Technology Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-44641 (URN)10.1109/CDC.2008.4738759 (DOI)000307311603077 ()77222 (Local ID)978-1-4244-3123-6 (ISBN)e-978-1-4244-3124-3 (ISBN)77222 (Archive number)77222 (OAI)
    Conference
    47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008
    Note

    ©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Henrik Ohlsson, Joakim Rydell, Anders Brun, Jacob Roll, Mats Andersson, Anders Ynnerman and Hans Knutsson, Enabling Bio-Feedback Using Real-Time fMRI, 2008, Proceedings of the 47th IEEE Conference on Decision and Control, 2008, 3336.

    Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2015-10-08Bibliographically approved
  • 31.
    Ohlsson, Henrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Studies on implementation of digital filters with high throughput and low power consumption2003Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we discuss design and implementation of frequency selective digital filters with high throughput and low power consumption. The thesis includes proposed arithmetic transformations of lattice wave digital filters that aim at increasing the throughput and reduce the power consumption of the filter implementation. The thesis also includes two case studies where digital filters with high throughput and low power consumption are required.

    A method for obtaining high throughput as well as reduced power consumption of digital filters is arithmetic transformation of the filter structure. In this thesis arithmetic transformations of first- and second-order Richards' allpass sections composed by symmetric two-port adaptors and implemented using carry-save arithmetic are proposed. Such filter sections can be used for implementation of lattice wave digital filters and bireciprocal lattice wave digital filters. The latter structures are efficient for implementation of interpolators and decimators by factors of two. The proposed transformations increase the throughput of the filter implementation. The increased throughput can be traded for reduced power consumption through power supply voltage scaling.

    In the thesis two typical applications for digital filters with high throughput and low power consumption are studied, a digital down converter for a multiple antenna radar system and a combined interpolation and decimation filter for oversampled ADCs and DACs in an OFDM system. For both these cases several different filter structures have been considered

    and evaluated with respect to arithmetic complexity and throughput. The purpose with these evaluations were to find the most power efficient implementations.

    For the digital down converter, three different filter structures, combining FIR filters and wave digital filters, have been implemented in VHDL and mapped to a standard cell design using a cell library in a 0.18 μm CMOS process. For the combined interpolator and decimator, four different novel filter structures were considered. One of these structures was implemented using a standard cell library in a 0.35 μm CMOS process. The functionality of the implementation has been verified and the power consumption of the filter chip has been measured.

  • 32.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bauwens, Maite
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Barbé, Kurt
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Three Ways to do Temperature Reconstruction Based on Bivalve-Proxy Information2010Report (Other academic)
  • 33.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bauwens, Maite
    Vrije Universiteit Brussel, Belgium.
    Beelaerts, Veerle
    Vrije Universiteit Brussel, Belgium.
    Barbé, Kurt
    Vrije Universiteit Brussel, Belgium.
    Schoukens, Johan
    Vrije Universiteit Brussel, Belgium.
    Dehairs, Frank
    Vrije Universiteit Brussel, Belgium.
    Three Ways to do Temperature Reconstruction Based on Bivalve-Proxy Information2009In: Proceedings of the 28th Benelux Meeting on Systems and Control, 2009Conference paper (Refereed)
  • 34.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Chen, Tianshi
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Khoshfetrat Pakazad, Sina
    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.
    Sastry, Shankar
    University of California at Berkeley, USA.
    Distributed Change Detection2012In: Proceedings of the 16th IFAC Symposium on System Identification, 2012, p. 77-82Conference paper (Refereed)
    Abstract [en]

    Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The change detection problem is first formulated as a convex optimization problem and then solved distributively with the alternating direction method of multipliers (ADMM). To further reduce the computational burden on each sensor, a homotopy solution is also derived. The proposed method have interesting connections with Lasso and compressed sensing and the theory developed for these methods are therefore directly applicable.

  • 35.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Chen, Tianshi
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Khoshfetratpakazad, Sina
    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.
    Sastry, S. Shankar
    University of Calif Berkeley, CA 94720 USA .
    Scalable anomaly detection in large homogeneous populations2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 5, p. 1459-1465Article in journal (Refereed)
    Abstract [en]

    Anomaly detection in large populations is a challenging but highly relevant problem. It is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomalous systems. The number of hypothesis grows rapidly with the number of systems and approximate solutions become a necessity for any problem of practical interest. In this paper we take an optimization approach to this multi-hypothesis problem. It is first shown to be equivalent to a non-convex combinatorial optimization problem and then is relaxed to a convex optimization problem that can be solved distributively on the systems and that stays computationally tractable as the number of systems increase. An interesting property of the proposed method is that it can under certain conditions be shown to give exactly the same result as the combinatorial multi-hypothesis problem and the relaxation is hence tight.

  • 36.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. Univ Calif Berkeley, CA 94720 USA .
    Eldar, Yonina C.
    Technion Israel Institute Technology, Israel .
    Yang, Allen Y.
    University of Calif Berkeley, CA 94720 USA .
    Shankar Sastry, S.
    University of Calif Berkeley, CA 94720 USA .
    Compressive Shift Retrieval2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, p. 6034-6038Article in journal (Refereed)
    Abstract [en]

    The classical shift retrieval problem considers two signals in vector form that are related by a shift. This problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. We also illustrate the concept of superresolution for shift retrieval. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift.

  • 37.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Boyd, Stephen
    Stanford University, USA.
    Smoothed State Estimates under Abrupt Changes using Sum-of-Norms Regularization2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 4, p. 595-605Article in journal (Refereed)
    Abstract [en]

    The presence of abrupt changes, such as impulsive and load disturbances, commonly occur in applications, but make the state estimation problem considerably more difficult than in the standard setting with Gaussian process disturbance. Abrupt changes often introduce a jump in the state, and the problem is therefore readily and often treated by change detection techniques. In this paper, we take a different approach. The state smoothing problem for linear state space models is here formulated as a constrained least-squares problem with sum-of-norms regularization, a generalization of l1-regularization. This novel formulation can be seen as a convex relaxation of the well known generalized likelihood ratio method by Willsky and Jones. Another nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps. Good practical choices of this parameter along with an extension to nonlinear state space models are given. 

  • 38.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Boyd, Stephen
    Stanford University, USA.
    State Smoothing by Sum-of-Norms Regularization2010In: Proceedings of the 49th Conference on Decision and Control, 2010, p. 2880-2885Conference paper (Refereed)
    Abstract [en]

    The presence of abrupt changes, such as impulsive disturbances and load disturbances, make state estimation considerably more difficult than the standard setting with Gaussian process noise. Nevertheless, this type of disturbances is commonly occurring in applications which makes it an important problem. An abrupt change often introduces a jump in the state and the problem is therefore readily treated by change detection techniques. In this paper, we take a rather different approach. The state smoothing problem for linear state space models is here formulated as a least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps.

  • 39.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Boyd, Stephen
    Stanford University .
    Trajectory Generation Using Sum-of-Norms Regularization2010In: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, p. 540-545Conference paper (Refereed)
    Abstract [en]

    Many tracking problems are split into two sub-problems, first a smooth reference trajectory is generated that meet the control design objectives, and then a closed loop control system is designed to follow this reference trajectory as well as possible. Applications of this kind include (autonomous) vehicle navigation systems and robotics. Typically, a spline model is used for trajectory generation and another physical and dynamical model is used for the control design. Here we propose a direct approach where the dynamical model is used to generate a control signal that takes the state trajectory through the waypoints specified in the design goals. The strength of the proposed formulation is the methodology to obtain a control signal with compact representation and that changes only when needed, something often wanted in tracking. The formulation takes the shape of a constrained least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. The formulation also gives a tool to, e.g. in model predictive control, prevent chatter in the input signal, and also select the most suitable instances for applying the control inputs.

  • 40.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Convex Approach to Subspace Clustering2011In: Proceedings of the 50th IEEE Conference on Decision and Control, 2011, p. 1467-1472Conference paper (Refereed)
    Abstract [en]

    The identification of multiple affine subspaces from a set of data is of interest in fields such as system identification, data compression, image processing and signal processing and in the literature referred to as subspace clustering. If the origin of each sample would be known, the problem would be trivially solved by applying principal component analysis to samples originated from the same subspace. Now, not knowing what samples that originates from what subspace, the problem becomes considerably more difficult. We present a novel convex formulation for subspace clustering. The proposed method takes the shape of a least-squares problem with sum-of-norms regularization over optimization parameter differences, a generalization of the ℓ1-regularization. The regularization constant is used to trade off fit and the identified number of affine subspaces.

  • 41.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gray-Box Identification for High-Dimensional Manifold Constrained Regression2009In: Proceedings of the 15th IFAC Symposium on System Identification, 2009, p. 1292-1297Conference paper (Refereed)
    Abstract [en]

    High-dimensional gray-box identification is a fairly unexplored part of system identification. Nevertheless, system identification problems tend to be more high-dimensional nowadays. In this paper we deal with high-dimensional regression with regressors constrained to some manifold. A recent technique in this class is weight determination by manifold regularization (WDMR). WDMR, however, is a black-box identification method. We show how WDMR can be extended to a gray-box method and illustrate the scheme with some examples.

  • 42.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gray-Box Identification for High-Dimensional Manifold Constrained Regression2009Report (Other academic)
    Abstract [en]

    High-dimensional gray-box identification is a fairly unexplored part of system identification. Nevertheless, system identification problems tend to be more high-dimensional nowadays. In this paper we deal with high-dimensional regression with regressors constrained to some manifold. A recent technique in this class is weight determination by manifold regularization (WDMR). WDMR, however, is a black-box identification method. We show how WDMR can be extended to a gray-box method and illustrate the scheme with some examples.

  • 43.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Piecewise Affine Systems Using Sum-of-Norms Regularization2011In: Proceedings of the 18th IFAC World Congress, 2011, p. 6640-6645Conference paper (Refereed)
    Abstract [en]

    Systems today often consist of logic switches working besides continuous physical systems. The demand for novel hybrid system identification algorithms is therefore of growing interest and essential for the development of control algorithms for this type of systems. An important type of hybrid systems is piecewise affine systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. The regressor parameters are forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem with sum-of-norms regularization over regressor parameter differences, a generalization of l1-regularization. The regularization constant is used to trade off fit and the number of partitions of the model.

  • 44.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of Switched Linear Regression Models using Sum-of-Norms Regularization2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 4, p. 1045-1050Article in journal (Refereed)
    Abstract [en]

    This paper proposes a general convex framework for the identification of switched linear systems. The proposed framework uses over-parameterization to avoid solving the otherwise combinatorially forbidding identification problem, and takes the form of a least-squares problem with a sum-of-norms regularization, a generalization of the 1-regularization. The regularization constant regulates the complexity and is used to trade off the fit and the number of submodels.

  • 45.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Semi-Supervised Regression and System Identification2010Report (Other academic)
    Abstract [en]

    System Identification and Machine Learning are developing mostly as independent subjects, although the underlying problem is the same: To be able to associate “outputs” with “inputs”. Particular areas in machine learning of substantial current interest are manifold learning and unsupervised and semi-supervised regression. We outline a general approach to semi-supervised regression, describe its links to Local Linear Embedding, and illustrate its use for various problems. In particular, we discuss how these techniques have a potential interest for the system identification world.

  • 46.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Semi-Supervised Regression and System Identification2010In: Three Decades of Progress in Systems and Control: Dedicated to Chris Byrnes and Anders Lindquist / [ed] Xiaoming Hu, Ulf Jonsson, Bo Wahlberg and Bijoy Ghosh, Springer Berlin/Heidelberg, 2010, p. 343-360Chapter in book (Other academic)
    Abstract [en]

    In this edited collection we commemorate the 60th birthday of Prof. Christopher Byrnes and the retirement of Prof. Anders Lindquist from the Chair of Optimization and Systems Theory at KTH. These papers were presented in part at a 2009 workshop in KTH, Stockholm, honoring the lifetime contributions of Professors Byrnes and Lindquist in various fields of applied mathematics.

  • 47.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Weight Determination by Manifold Regularization2010In: Distributed Decision-Making and Control / [ed] Rolf Johansson and Anders Rantzer, Springer London, 2010, p. 195-214Chapter in book (Refereed)
    Abstract [en]

    A new type of linear kernel smoother is derived and studied. The smoother, referred to as weight determination by manifold regularization, is the solution to a regularized least squares problem. The regularization avoids overfitting and can be used to express prior knowledge of an underlying smooth function. An interesting property ofthe kernel smoother is that it is well suited for systems govern by the semi-supervised smoothness assumption. Several examples are given to illustrate this property. We also discuss why these types of techniques can have a potential interest for the system identification community.

  • 48.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Boyd, Stephen
    Stanford University, USA.
    Segmentation of ARX-Models using Sum-of-Norms Regularization2010Report (Other academic)
    Abstract [en]

    Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps. a generalization of L1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.

  • 49.
    Ohlsson, Henrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Boyd, Stephen
    Stanford University, USA.
    Segmentation of ARX-Models using Sum-of-Norms Regularization2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 6, p. 1107-1111Article in journal (Refereed)
    Abstract [en]

    Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps. a generalization of L1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.

  • 50.
    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.

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