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  • 1.
    Andersson, Peter
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Adaptive Forgetting in Recursive Identification through Multiple Models1985In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 42, no 5, p. 1175-1193Article in journal (Refereed)
    Abstract [en]

    A new recursive identification method, adaptive forgetting through multiple models (AFMM) is presented and evaluated using computer simulations. AFMM is especially suited for identification of systems with jumping or rapidly changing parameters. It can be viewed as a particular way of implementing adaptive gains or adaptive forgetting factors for recursive identification. The new method essentially consists of multiple recursive least-squares (RLS) algorithms running in parallel, each with a corresponding weighting factor. The simulations indicate that AFMM is able to track rapidly changing parameters well, and that the method is robust in several respects.

  • 2.
    Braun, Martin W.
    et al.
    Arizona State University, USA.
    Rivera, Daniel E.
    Arizona State University, USA.
    Stenman, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A 'Model-on-Demand' Identification Methodology for Nonlinear Process Systems2001In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 74, no 18, p. 1708-1717Article in journal (Refereed)
    Abstract [en]

    An identification methodology based on multi-level pseudo-random sequence (multi-level PRS) input signals and 'Model-on-Demand' (MoD) estimation is presented for single-input, single-output non-linear process applications. 'Model-on-Demand' estimation allows for accurate prediction of non-linear systems while requiring few user choices and without solving a non-convex optimization problem, as is usually the case with global modelling techniques. By allowing the user to incorporate a priori information into the specification of design variables for multi-level PRS input signals, a sufficiently informative input-output dataset for MoD estimation is generated in a 'plant-friendly' manner. The usefulness of the methodology is demonstrated in case studies involving the identification of a simulated rapid thermal processing (RTP) reactor and a pilot-scale brine-water mixing tank. On the resulting datasets, MoD estimation displays performance comparable to that achieved via semi-physical modelling and semi-physical modelling combined with neural networks. The MoD estimator, however, achieves this level of performance with substantially lower engineering effort.

  • 3.
    Braun, MW
    et al.
    Arizona State Univ, Dept Chem & Mat Engn, Control Syst Engn Lab, Tempe, AZ 85287 USA Linkoping Univ, Dept Elect Engn, Div Automat Control, SE-58183 Linkoping, Sweden.
    Rivera, DE
    Arizona State Univ, Dept Chem & Mat Engn, Control Syst Engn Lab, Tempe, AZ 85287 USA Linkoping Univ, Dept Elect Engn, Div Automat Control, SE-58183 Linkoping, Sweden.
    Stenman, A
    Arizona State Univ, Dept Chem & Mat Engn, Control Syst Engn Lab, Tempe, AZ 85287 USA Linkoping Univ, Dept Elect Engn, Div Automat Control, SE-58183 Linkoping, Sweden.
    A 'Model-on-Demand' identification methodology for non-linear process systems2001In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 74, no 18, p. 1708-1717Article in journal (Refereed)
    Abstract [en]

    An identification methodology based on multi-level pseudo-random sequence (multi-level PRS) input signals and 'Model-on-Demand' (MoD) estimation is presented for single-input, single-output non-linear process applications. 'Model-on-Demand' estimation allows for accurate prediction of non-linear systems while requiring few user choices and without solving a non-convex optimization problem, as is usually the case with global modelling techniques. By allowing the user to incorporate a priori information into the specification of design variables for multi-level PRS input signals, a sufficiently informative input-output dataset for MoD estimation is generated in a 'plant-friendly' manner. The usefulness of the methodology is demonstrated in case studies involving the identification of a simulated rapid thermal processing (RTP) reactor and a pilot-scale brine-water mixing tank. On the resulting datasets, MoD estimation displays performance comparable to that achieved via semi-physical modelling and semi-physical modelling combined with neural networks. The MoD estimator, however, achieves this level of performance with substantially lower engineering effort.

  • 4.
    Falkeborn, Rikard
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Löfberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Low-Rank Exploitation in Semidefinite Programming for Control2011In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 84, no 12, p. 1975-1982Article in journal (Refereed)
    Abstract [en]

    Many control-related problems can be cast as semidefinite programs. Even though there exist polynomial time algorithms and excellent publicly available solvers, the time it takes to solve these problems can be excessive. What many of these problems have in common, in particular in control, is that some of the variables enter as matrix-valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this article, we describe how this can be done, and show how our code, called STRUL, can be used in conjunction with the semidefinite programming solver SDPT3. The idea behind the structure exploitation is classical and is implemented in LMI Lab, but we show that when using a modern semidefinite programming framework such as SDPT3, the computational time can be significantly reduced. Finally, we describe how the modelling language YALMIP has been changed in such a way that our code, which can be freely downloaded, can be interfaced using standard YALMIP commands. This greatly simplifies modelling and usage.

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  • 5.
    Fnaiech, Farhat
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. On leave from ENSET, Tunisia.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Recursive Identification of Bilinear Systems1987In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 45, no 2, p. 453-470Article in journal (Refereed)
    Abstract [en]

    Methods of identifying bilinear systems from recorded input-output data are discussed in this article. A short survey of the existing literature on the topic is given. ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation. Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem.

  • 6.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Accuracy of Recursively Identified ARX Models1991In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 54, no 2, p. 465-480Article in journal (Refereed)
    Abstract [en]

    Recursive identification of time varying systems using ARX models is considered, with focus on the accuracy of the transfer function estimates. Three recursive identification algorithms are studied, the least mean squares algorithm, the recursive least squares algorithm and the Kalman filter respectively. The model accuracy is studied in terms of algorithm design variables, input and disturbance signal properties and variations of the true system. Using asymptotic methods approximate expressions for the model quality are derived. The derived expressions are validated by simulations.

  • 7.
    Gunnarsson, Svante
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Rahic, Enes
    Ozbek, Markus
    On the Use of Accelerometers in Iterative Learning Control of a Flexible Robot Arm2007In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 80, no 3, p. 363-373Article in journal (Refereed)
    Abstract [en]

    Iterative learning control (ILC) is applied to a robot arm with joint flexibility. The ILC algorithm uses an estimate of the arm angle, where the estimate is computed using measurements of the motor angle and the arm angular acceleration. The design of the ILC algorithm is evaluated experimentally on a laboratory scale robot arm with good results.

  • 8.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Vandenberghe, Lieven
    University of Calif Los Angeles, CA 90024 USA .
    Sampling method for semidefinite programmes with non-negative Popov function constraints2014In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 87, no 2, p. 330-345Article in journal (Refereed)
    Abstract [en]

    An important class of optimisation problems in control and signal processing involves the constraint that a Popov function is non-negative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finite-dimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality reformulation requires an auxiliary matrix variable and often results in a very large semidefinite programming problem. Several recently published methods exploit problem structure in these semidefinite programmes to alleviate the computational cost associated with the large matrix variable. These algorithms are capable of solving much larger problems than general-purpose semidefinite programming packages. In this paper, we address the same problem by presenting an alternative to the linear matrix inequality formulation of the non-negative Popov function constraint. We sample the constraint to obtain an equivalent set of inequalities of low dimension, thus avoiding the large matrix variable in the linear matrix inequality formulation. Moreover, the resulting semidefinite programme has constraints with low-rank structure, which allows the problems to be solved efficiently by existing semidefinite programming packages. The sampling formulation is obtained by first expressing the Popov function inequality as a sum-of-squares condition imposed on a polynomial matrix and then converting the constraint into an equivalent finite set of interpolation constraints. A complexity analysis and numerical examples are provided to demonstrate the performance improvement over existing techniques.

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  • 9.
    Harju Johansson, Janne
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An Inexact Interior-Point Method for System Analysis2010In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 83, no 3, p. 601-616Article in journal (Refereed)
    Abstract [en]

    In this article, a primal-dual interior-point algorithm for semidefinite programming that can be used for analysing e.g. polytopic linear differential inclusions is tailored in order to be more computationally efficient. The key to the speedup is to allow for inexact search directions in the interior-point algorithm. These are obtained by aborting an iterative solver for computing the search directions prior to convergence. A convergence proof for the algorithm is given. Two different preconditioners for the iterative solver arc proposed. The speedup is in many cases more than an order of magnitude. Moreover, the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off-the-shelf interior-point solvers.

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    FULLTEXT01
  • 10.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Dong, Yi
    Institute for Software Integrated Systems, Vanderbilt University, Nashville, USA.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, Faculty of Science & Engineering.
    Biswas, Gautam
    Institute for Software Integrated Systems, Vanderbilt University, Nashville, USA.
    Sensor selection for fault diagnosis in uncertain systems2020In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 93, no 3, p. 629-639Article in journal (Refereed)
    Abstract [en]

    Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.

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    Sensor selection for fault diagnosis in uncertain systems
  • 11.
    Kailath, Thomas
    et al.
    Stanford University, CA, USA.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Explicit Strict Sense State-Space Realizations of Nonstationary Processes1985In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 42, no 5, p. 971-988Article in journal (Refereed)
    Abstract [en]

    This paper addresses the following problem: Given a possibly non-stationary second-order or Gaussian stochastic process over a certain time interval, find all state-space realizations that produce the given process as their output. A constructive solution to this problem is described. In particular, the degrees of freedom left in this problem are explicitly displayed in terms of additional random variables and processes injected into the state-space description. Special attention is paid to output-induced, or internal, state-space realizations, that is, those for which the state vector is completely determined by the given process. The development is self-contained, the approach and proofs are fairly elementary, and explicit formulas are given for the various realizations.

  • 12.
    Kailath, Thomas
    et al.
    Stanford University, CA, USA.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Two Filter Smooting Formulae by Diagonalization of the Hamiltonian Equations1982In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 36, no 4, p. 663-673Article in journal (Refereed)
    Abstract [en]

    We present a new approach to two filter smoothing formulae via diagonalization of the general time variant hamiltonian equations of the linear estimation problem. This approach shows the special role of the famous Mayno-Fraser two filter formulae and also provides insight into certain invariance properties of backwards Kalman filter estimates.

  • 13.
    Kukreja, Sunil L
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A suboptimal bootstrap method for structure detection of non-linear output-error models with application to human ankle dynamics2005In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 78, no 12, p. 937-948Article in journal (Refereed)
    Abstract [en]

    . cation of non-linear systems involves estimating unknown parameters and structure detection, selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. For nonlinear systems simple output additive noise can generate multiplicative terms between the input, output and noise. The terms associated with noise need to be modelled to obtain unbiased parameter estimates, significantly increasing the number of candidate terms to be estimated and considered. In special cases, it may be possible to use an output error (OE) model structure and the instrumental variable (IV) estimator to obtain unbiased parameters without modelling the noise. This significantly reduces the dimensionality of the structure computation problem. Therefore, in this paper, we propose a suboptimal bootstrap structure detection (SOBSD) algorithm for non-linear OE models. Performance of this SOBSD algorithm was evaluated by using it to estimate the structure of (i) a simulated NARMAX model describing ankle dynamics and (ii) application to experimental data. The results demonstrate that the SOBSD method is simple to use and provides good results for non-linear OE models.

  • 14.
    Linder, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Identification of systems with unknown inputs using indirect input measurements2017In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 90, no 4, p. 729-745Article in journal (Refereed)
    Abstract [en]

    A common issue with many system identification problems is that the true input to the system is unknown. This paper extends a previously presented indirect modelling framework that deals with identification of systems where the input is partially or fully unknown. In this framework, unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs. The resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties. Since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output, estimation of the indirect model has similar challenges as a closed-loop estimation problem. In fact, due to the generality of the indirect modelling framework, it unifies a number of already existing system identification problems that are contained as special cases. For completeness, the paper is concluded with one method that can be used to estimate the indirect model as well as an experimental verification to show the applicability of the framework.

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  • 15.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Convergence of an Adaptive Filter Algorithm1978In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 27, no 5, p. 673-693Article in journal (Refereed)
    Abstract [en]

    A state-space representation of a dynamical, stochastic system is given. A corresponding model, parametrized in a particular way, is considered and an algorithm for the estimation of its parameters is analysed. The class of estimation algorithms thus considered contains general output error methods and model reference methods applied to stochastic systems. It also contains adaptive filtering schemes and, e.g. the extended least squares method.

    It is shown that if a certain transfer function associated with the true system is positive real, then the estimation algorithm converges with probability 1 to a value that gives a correct input-output model.

  • 16.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Chen, Tianshi
    Chinese Univ Hong Kong, Peoples R China.
    Mu, Biqiang
    Chinese Acad Sci, Peoples R China.
    A shift in paradigm for system identification2020In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 93, no 2, p. 173-180Article in journal (Refereed)
    Abstract [en]

    System identification is a mature research area with well established paradigms, mostly based on classical statistical methods. Recently, there has been considerable interest in so called kernel-based regularisation methods applied to system identification problem. The recent literature on this is extensive and at times difficult to digest. The purpose of this contribution is to provide an accessible account of the main ideas and results of kernel-based regularisation methods for system identification. The focus is to assess the impact of these new techniques on the field and traditional paradigms.

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  • 17.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Morf, Martin
    Stanford University, CA, USA.
    Falconer, David
    Bell Telephone Laboratoires, NJ, USA.
    Fast Calculation of Gain Matrices for Recursive Estimation Schemes1978In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 27, no 1, p. 1-19Article in journal (Refereed)
    Abstract [en]

    A sequence of vectors {x(t)} with dimension N is given, such that x(t+1) is obtained from x(t) by introducing p new elements, deleting p old ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Npoperations and memory locations, in contrast to the conventional way which requires proportional-to-N 2operations and memory locations. A non-symmetric case is also treated.

  • 18.
    Millnert, Mille
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identification of ARX Models with Markovian Parameters1987In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 45, no 6, p. 2045-2058Article in journal (Refereed)
    Abstract [en]

    Many different recursive identification methods for time-varying systems have been suggested in the literature. An assumption that the variations in the system parameters are slow is common for all the methods. When using the methods on systems with faster variations, one is forced to compromise between alertness to parameter variations on one hand and noise sensitivity on the other. The topic of this paper is to investigate if this compromise can be avoided for a special class of systems. The systems considered are such that their dynamic changes between some different typical modes. The philosophy behind the approach taken in the paper is to separate the observations into different sets corresponding to the different modes. The parameters of the different modes can then be estimated using the separated data sets. Technically, this parallel modelling is achieved by describing the system parameters as the realizations of a Markov chain. A parameter-identification algorithm for time-varying ARX models is then given in the paper. The behaviour of the algorithm is then investigated using simulations and some analysis. The analysis and the simulations show that a major problem is the initialization of the algorithm. Based on the analysis, modifications are made to the algorithm that improve the convergence properties.

  • 19.
    Norrlöf, Mikael
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Time and Frequency Domain Convergence Properties in Iterative Learning Control2002In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 75, no 14, p. 1114-1126Article in journal (Refereed)
    Abstract [en]

    The convergence properties of iterative learning control (ILC) algorithms are considered. The analysis is carried out in a framework using linear iterative systems, which enables several results from the theory of linear systems to be applied. This makes it possible to analyse both first-order and high-order ILC algorithms in both the time and frequency domains. The time and frequency domain results can also be tied together in a clear way. Results are also given for the iteration-variant case, i.e. when the dynamics of the system to be controlled or the ILC algorithm itself changes from iteration to iteration.

  • 20.
    Nyberg, Mattias
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering.
    Criterions for detectability and strong detectability of faults in linear systems2002In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 75, no 7, p. 490-501Article in journal (Refereed)
    Abstract [en]

    A fault is (strongly) detectable if it is possible to construct a residual generator that is sensitive to the (constant) fault while decoupling all disturbances. Existing fault detectability criterions are reviewed and in two cases, improved versions are derived. For strong fault detectability, three new criterions are presented. To prove all criterions, a framework of polynomial bases is utilized. With these new and improved criterions, there exists now a criterion for models given both on transfer function form and state-space form, and for both fault detectability and strong fault detectability investigations. Recommendations are given on what criterion to use in different situations.

  • 21.
    Petersson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Löfberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Optimisation-based modelling of LPV systems using an -objective2014In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 87, no 8, p. 1536-1548Article in journal (Refereed)
    Abstract [en]

    A method to identify linear parameter varying models through minimisation of an -norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use -norm is twofold. To begin with, it is a well-known and widely used system norm, and second, the cost functions described in this paper become differentiable when using the -norm. This enables us to have a measure of first-order optimality and to use standard quasi-Newton solvers to solve the problem. The specific structure of the problem is utilised in great detail to compute cost functions and gradients efficiently. Additionally, a regularised version of the method, which also has a nice computational structure, is presented. The regularised version is shown to have an interesting interpretation with connections to worst-case approaches.

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  • 22.
    Sjöberg, Jonas
    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.
    Overtraining, Regularization and Searching for Minimum with Application to Neural Nets1995In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 62, no 6, p. 1391-1407Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss the role of criterion minimization as a means for parameter estimation. Most traditional methods, such as maximum likelihood and prediction error identification are based on these principles. However, somewhat surprisingly, it turns out that it is not always ‘optimal’ to try to find the absolute minimum point of the criterion. The reason is that ‘stopped minimization’ (where the iterations have been terminated before the absolute minimum has been reached) has more or less identical properties as using regularization (adding a parametric penalty term). Regularization is known to have beneficial effects on the variance of the parameter estimates and it reduces the ‘variance contribution’ of the misfit. This also explains the concept of ‘overtraining’ in neural nets. How does one know when to terminate the iterations then? A useful criterion would be to stop iterations when the criterion function applied to a validation data set no longer decreases. However, in this paper, we show that applying this technique extensively may lead to the fact that the resulting estimate is an unregularized estimate for the total data set: estimation + validation data.

  • 23.
    Skeppstedt, Anders
    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.
    Millnert, Mille
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Construction of Composite Models from Observed Data1992In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 55, no 1, p. 141-152Article in journal (Refereed)
    Abstract [en]

    Most processes of realistic complexity cannot be described by simple linear relationships. An alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collection of simple models along with rules concerning when to use which one. In this paper we describe a method for constructing such composite models from observed data. It is assumed that the dynamics of the process changes with some 'operating-point vector’, which is assumed to be a measurable quantity. Based on input-output measurements and measurements of the operating-point vector, a composite model is constructed which consists of piecewise linear models. Different regions of the operating point space thus give different linear dynamics. The dynamics as well as the region boundaries are determined from the data. The basic idea is to utilize a method from recursive identification, which is able to track slow as well as rapid dynamic changes. A classification procedure is then applied to the models produced by this identification procedure, and finally borders are created between the different classified models. Techniques for supervised pattern recognition are used for the latter step. The whole construction procedure is illustrated with an example.

  • 24.
    Solbrand, Göte
    et al.
    Uppsala University, Sweden.
    Ahlén, Anders
    Uppsala University, Sweden.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Recursive Methods for Off-Line Identification1985In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 41, no 1, p. 177-191Article in journal (Refereed)
    Abstract [en]

    Many recursive identification methods have been developed for on-line estimation of parameters in dynamical systems. Such methods can also be applied to data for off-line problems, usually by passing the data through the recursive identifier a few times. In this paper such an approach is discussed. Suppose that a recursive identification method is applied to a data string obtained by concatenation of the original finite-data record. It is proved that the recursive identification method will then converge to a (local) minimum of the off-line finite-data identification criterion. We also provide some arguments as to why recursive identification may be a competitive way of performing the minimization. When using the data more than once it is a priori not clear how to treat the initial values and the forgetting factor. The problem is investigated and comparisons are made with an off-line prediction error method. Practical experiments show that the execution time for a repeated recursive algorithm is less than or equal to that of the off-line algorithm, and that the obtained accuracies are comparable.

  • 25.
    Verdult, Vincent
    et al.
    Delft University of Technology, The Netherlands.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Verhaegen, Michel
    Delft University of Technology, The Netherlands.
    Identification of Composite Local Linear State-Space Models using a Projected Gradient Search2002In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 75, no 16, p. 1385-1398Article in journal (Refereed)
    Abstract [en]

    An identification method is described to determine a weighted combination of local linear state-space models from input and output data. Normalized radial basis functions are used for the weights, and the system matrices of the local linear models are fully parameterized. By iteratively solving a non-linear optimization problem, the centres and widths of the radial basis functions and the system matrices of the local models are determined. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is described. It is pointed out that when the weights depend only on the input, the dynamical gradient calculations in the identification method are stable. When the weights also depend on the output, certain difficulties might arise. The methods are illustrated using serveral examples that have been studied in the literature before.

  • 26.
    Wahlberg, Bo
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Limit Result for Sampled Systems1988In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 48, no 3, p. 1267-1283Article in journal (Refereed)
    Abstract [en]

    Properties of discrete time systems obtained by sampling continuous time systems are described. By introducing prefilters, we can treat different ways of sampling within one framework. Results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given. These results are generalizations of the results of Åström, Hagander and Sternby (1984) on the convergence of poles and zeros for zero-order hold sampled transfer functions. Sampled noise models are also analysed. Knowledge of these properties is very important in, for example, discrete time simulations of continuous time systems, and identification of continuous time models based on discrete time measurements.

  • 27.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Maximum likelihood estimation of linear SISO models subject to missing output data and missing input data2014In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 87, no 11, p. 2354-2364Article in journal (Refereed)
    Abstract [en]

    In this paper we describe an approach to maximum likelihood estimation of linear single input single output (SISO) models when both input and output data are missing. The criterion minimised in the algorithms is the Euclidean norm of the prediction error vector scaled by a particular function of the covariance matrix of the observed output data. We also provide insight into when simpler and in general sub-optimal schemes are indeed optimal. The algorithm has been prototyped in MATLAB, and we report numerical results that support the theory.

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  • 28.
    Wallén, Johanna
    et al.
    Combitech AB, Linköping, Sweden.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Analysis of boundary effects in iterative learning control2013In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 86, no 3, p. 410-415Article in journal (Refereed)
    Abstract [en]

    Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.

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    fulltext
  • 29.
    Åkerblad, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Efficient Solution of Second Order Cone Program for Model Predictive Control2004In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 77, no 1, p. 55-77Article in journal (Refereed)
    Abstract [en]

    In model predictive control an optimization problem has to be solved at each sampling instant. The objective in this article is to derive efficient methods to solve this optimization problem. The approach taken is to use interior point optimization methods. The model predictive control problem considered here has a quadratic objective and constraints which can be both linear and quadratic. The key to an efficient implementation is to rewrite the optimization problem as a second order cone program. To solve this optimization problem a feasible primal-dual interior point method is employed. By using a feasible method it is possible to determine when the problem is feasible or not by formalizing the search for strictly feasible initial points as yet another primal-dual interior point problem. There are several different ways to rewrite the optimization problem as a second order cone program. However, done carefully, it is possible to use very efficient scalings as well as Riccati recursions for computing the search directions. The use of Riccati recursions makes the computational complexity grow at most as script, O sign(N 3/2) with the time horizon, compared to script O sign(N3) for more standard implementations.

1 - 29 of 29
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