kth.sePublications
Change search
Refine search result
12345 1 - 50 of 204
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of a Class of Nonlinear Dynamical Networks⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 868-873Article in journal (Refereed)
    Abstract [en]

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

  • 2.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Identication of a Class of Nonlinear Dynamical Networks2018Conference paper (Refereed)
    Abstract [en]

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

    Download full text (pdf)
    0131.pdf
  • 3.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Fundamental Limitations on the Accuracy of MIMO Linear Models Obtained by PEM for Systems Operating in Open Loop2009In: Proceedings of the Joint 48th IEEE Conference on Decision and Control (CDC’09) and 28th Chinese Control Conference (CCC’09), 2009, p. 482-487Conference paper (Refereed)
    Abstract [en]

    In this paper we show that the variance of estimated parametric models for open loopMultiple-Input Multiple-Output (MIMO) systems obtained by the prediction error method (PEM) satisfies a fundamental integral limitation. The fundamental limitation gives rise to a multivariable 'water-bed' effect.

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

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

  • 5.
    Bjurgert, Johan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Valenzuela, Patricio E.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Adaptive Boosting for System Identification2018In: IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, E-ISSN 2162-2388, Vol. 29, no 9, p. 4510-4514Article in journal (Refereed)
    Abstract [en]

    In the field of machine learning, the algorithm Adaptive Boosting has been successfully applied to a wide range of regression and classification problems. However, to the best of the authors' knowledge, the use of this algorithm to estimate dynamical systems has not been exploited. In this brief, we explore the connection between Adaptive Boosting and system identification, and give examples of an identification method that makes use of this connection. We prove that the resulting estimate converges to the true underlying system for an output-error model structure under reasonable assumptions in the large sample limit and derive a bound of the model mismatch for the noise-free case.

  • 6.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Approximate regularization path for nuclear norm based H2 model reduction2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, p. 3637-3641Conference paper (Refereed)
    Abstract [en]

    This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model reduction problem as a function of the design parameter. This is called the regularization path in sparse estimation and is a very important tool in order to find the appropriate balance between fit and complexity. We extend this to the more complicated nuclear norm case. The key idea is to determine when to exactly calculate the optimal solution using an upper bound based on the so-called duality gap. Hence, by solving a fixed number of optimization problems the whole regularization path up to a given tolerance can be efficiently computed. We illustrate this approach on some numerical examples.

  • 7.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Regularization Paths for Re-Weighted Nuclear Norm Minimization2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 11, p. 1980-1984Article in journal (Refereed)
    Abstract [en]

    We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.

  • 8.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Approximate Regularization Paths for Nuclear Norm Minimization using Singular Value Bounds: with Implementation and Extended Appendix2015Conference paper (Refereed)
    Abstract [en]

    The widely used nuclear norm heuristic for rank minimizationproblems introduces a regularization parameter which isdifficult to tune. We have recently proposed a method to approximatethe regularization path, i.e., the optimal solution asa function of the parameter, which requires solving the problemonly for a sparse set of points. In this paper, we extendthe algorithm to provide error bounds for the singular valuesof the approximation. We exemplify the algorithms on largescale benchmark examples in model order reduction. Here,the order of a dynamical system is reduced by means of constrainedminimization of the nuclear norm of a Hankel matrix.

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

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

  • 10. Brighenti, C.
    et al.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Input design using Markov chains for system identification2009In: Proceedings of the 48th IEEE Conference on  Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE conference proceedings, 2009, p. 1557-1562Conference paper (Refereed)
    Abstract [en]

    This paper studies the input design problem for system identification where time domain constraints have to be considered. A finite Markov chain is used to model the input of the system. This allows to directly include input amplitude constraints in the input model by properly choosing the state space of the Markov chain, which is defined so that the Markov chain generates a multi-level sequence. The probability distribution of the Markov chain is shaped in order to minimize the cost function considered in the input design problem. Stochastic approximation is used to minimize that cost function. With this approach, the input signal to apply to the system can be easily generated by extracting samples from the optimal distribution. A numerical example shows how this method can improve estimation with respect to other input realization techniques.

    Download full text (pdf)
    IR-EE-RT_2009_006
  • 11.
    Djehiche, Boualem
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Mazhar, Othmane
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Finite impulse response models: A non-asymptotic analysis of the least squares estimator2021In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 27, no 2, p. 976-1000Article in journal (Refereed)
    Abstract [en]

    We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction bounds for the least squares estimator of the parameters. Our results are based on two concentration inequalities on the norm of sums of dependent covariate vectors and on the singular values of their covariance operator that are of independent value on their own and where the dependence arises from the time shift structure of the time series. These results generalize the known bounds for the independent case.

  • 12.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Annergren, Mariette
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian A.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Molander, Mats
    Sjöberg, Johan
    Application Set Approximation in Optimal Input Design for Model Predictive Control2014In: 2014 European Control Conference (ECC), 2014, p. 744-749Conference paper (Refereed)
    Abstract [en]

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

  • 13.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, Sch Elect Engn, ACCESS, SE-10044 Stockholm, Sweden..
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Applications Oriented Input Design for Closed-Loop System Identification: a Graph-Theory Approach2014In: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2014, p. 4125-4130Conference paper (Refereed)
    Abstract [en]

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

    Download full text (pdf)
    fulltext
  • 14.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Model Predictive Control oriented experiment design for system identification: A graph theoretical approach2017In: Journal of Process Control, ISSN 0959-1524, E-ISSN 1873-2771, Vol. 52, p. 75-84Article in journal (Refereed)
    Abstract [en]

    We present a new approach to Model Predictive Control (MPC) oriented experiment design for the identification of systems operating in closed-loop. The method considers the design of an experiment by minimizing the experimental cost, subject to probabilistic bounds on the input and output signals due to physical limitations of actuators, and quality constraints on the identified model. The excitation is done by intentionally adding a disturbance to the loop. We then design the external excitation to achieve the minimum experimental effort while we are also taking care of the tracking performance of MPC. The stability of the closed-loop system is guaranteed by employing robust MPC during the experiment. The problem is then defined as an optimization problem. However, the aforementioned constraints result in a non-convex optimization which is relaxed by using results from graph theory. The proposed technique is evaluated through a numerical example showing that it is an attractive alternative for closed-loop experiment design.

    Download full text (pdf)
    fulltext
  • 15.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications Oriented Input Design in Time-Domain Through Cyclic Methods2014Conference paper (Refereed)
    Abstract [en]

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

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

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

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

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

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

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

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

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

  • 20.
    Elton, Augustus
    et al.
    School of Engineering, University of Newcastle, Callaghan, Australia.
    González, Rodrigo A.
    Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
    Welsh, James S.
    School of Engineering, University of Newcastle, Callaghan, Australia.
    Oomen, Tom
    Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands; Delft Center for Systems and Control, Delft University of Technology, The Netherlands.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Blind Nonparametric Estimation of SISO Continuous-time Systems2023In: IFAC-PapersOnLine, Elsevier BV , 2023, Vol. 56, p. 4222-4227Conference paper (Refereed)
    Abstract [en]

    Blind system identification is aimed at finding parameters of a system model when the input is inaccessible. In this paper, we propose a blind system identification method that delivers a single-input single-output, continuous-time model in a nonparametric kernel form. We take advantage of the representer theorem to form a joint maximum a posteriori estimator of the input and system impulse response. The identified system model and input are optimised in sequence to overcome the blind problem with generalised cross validation used to select appropriate hyperparameters given some fixed input sequence. We demonstrate via Monte Carlo simulations the accuracy of the method in terms of estimating the input.

  • 21.
    Elton, Augustus
    et al.
    College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW, Australia.
    González, Rodrigo A.
    Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands.
    Welsh, James S.
    College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Fu, Minyue
    College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW, Australia.
    Parametric Continuous-Time Blind System Identification2023In: 2023 62nd IEEE Conference on Decision and Control, CDC2023, Institute of Electrical and Electronics Engineers (IEEE) , 2023, p. 1474-1479Conference paper (Refereed)
    Abstract [en]

    In this paper, the blind system identification problem for continuous-time systems is considered. A direct continuous-time estimator is proposed by utilising a state-variable-filter least squares approach. In the proposed method, coupled terms between the numerator polynomial of the system and input parameters appear in the parameter vector which are subsequently separated using a rank-1 approximation. An algorithm is then provided for the direct identification of a single-input single-output linear time-invariant continuous-time system which is shown to satisfy the property of correctness under some mild conditions. Monte Carlo simulations demonstrate the performance of the algorithm and verify that a model and input signal can be estimated to a proportion of their true values.

  • 22. Esparza, Alicia
    et al.
    Agüero, Juan C.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Godoy, Boris I.
    The University of Newcastle, Australia.
    Asymptotic statistical analysis for model-based control design strategies2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 5, p. 1041-1046Article in journal (Refereed)
    Abstract [en]

    In this paper, we generalize existing fundamental limitations on the accuracy of the estimation of dynamic models. In addition, we study the large sample statistical behavior of different estimation-based controller design strategies. In particular, fundamental limitations on the closed-loop performance using a controller obtained by Virtual Reference Feedback Tuning (VRFT) are studied. We also extend our results to more general estimation-based control design strategies. We present numerical examples to show the application of our results.

  • 23.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Identification of modules in dynamic networks: An empirical Bayes approach2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 4612-4617, article id 7798971Conference paper (Refereed)
    Abstract [en]

    We address the problem of identifying a specific module in a dynamic network, assuming known topology. We express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation Maximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method.

  • 24.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Effect of Noise Correlation in Parameter Identification of SIMO Systems2015In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 48, no 28, p. 326-331Article in journal (Refereed)
    Abstract [en]

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

  • 25.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Variance Analysis of identified Linear MIMO Models2015In: IEEE Explore, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

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

  • 26.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance Analysis of Linear SIMO Models with Spatially Correlated NoiseManuscript (preprint) (Other academic)
    Abstract [en]

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

  • 27.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance analysis of linear SIMO models with spatially correlated noise2017In: Automatica, ISSN 0005-1098, Vol. 77, p. 68-81Article in journal (Refereed)
    Abstract [en]

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

  • 28.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Geometric Approach to Variance Analysis of Cascaded Systems2013In: Proceedings of the 52nd Conference On Decision And Control, IEEE conference proceedings, 2013, p. 6496-6501Conference paper (Refereed)
    Abstract [en]

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

  • 29.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance Results for Parallel Cascade Serial Systems2014In: Proceedings of 19th IFAC World Congress, 2014Conference paper (Refereed)
    Abstract [en]

    Modelling dynamic networks is important in different fields of science. At present, little is known about how different inputs and sensors contribute to the statistical properties concerning an estimate of a specific dynamic system in a network. We consider two forms of parallel serial structures, one multiple-input-multiple-output structure and one single-input multiple-output structure. The quality of the estimated models is analysed by means of the asymptotic covariance matrix, with respect to input signal characteristics, noise characteristics, sensor locations and previous knowledge about the remaining systems in the network. It is shown that an additive property applies to the information matrix for the considered structures. The impact of input signal selection, sensor locations and incorporation of previous knowledge isillustrated by simple examples.

    Download full text (pdf)
    fulltext
  • 30.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Least Squares Method for Identification of Feedback Cascade Systems2015In: 17th IFAC Symposium on System Identification SYSID 2015 — Beijing, China, 19–21 October 2015, IFAC Papers Online, 2015, Vol. 48, p. 98-103Conference paper (Refereed)
    Abstract [en]

    The problem of identification of systems in dynamic networks is considered. Although the prediction error method (PEM) can be applied to the overall system, the non-standard model structure requires solving a non-convex optimization problem. Alternative methods have been proposed, such as instrumental variables and indirect PEM. In this paper, we first consider acyclic cascade systems, and argue that these methods have different ranges of applicability. Then, for a network with feedback connection, we propose an approach to deal with the fact that indirect PEM yields a non-convex problem in that case. A numerical simulation may indicate that this approach is competitive with other existing methods.

    Download full text (pdf)
    fulltext
  • 31.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    On Estimating Initial Conditions in Unstructured Models2015In: 2015 54th IEEE Conference on Decision and Control (CDC), IEEE conference proceedings, 2015, p. 2725-2730Conference paper (Refereed)
    Abstract [en]

    Estimation of structured models is an importantproblem in system identification. Some methods, as an intermediatestep to obtain the model of interest, estimate theimpulse response parameters of the system. This approachdates back to the beginning of subspace identification and isstill used in recently proposed methods. A limitation of thisprocedure is that, when obtaining these parameters from ahigh-order unstructured model, the initial conditions of thesystem are typically unknown, which imposes a truncation ofthe measured output data for the estimation. For finite samplesizes, discarding part of the data limits the performance ofthe method. To deal with this issue, we propose an approachthat uses all the available data, and estimates also the initialconditions of the system. Then, as examples, we show how thisapproach can be applied to two methods in a beneficial manner.Finally, we use a simulation study to exemplify the potential ofthe approach.

    Download full text (pdf)
    fulltext
  • 32.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Weighted Least Squares Method for Estimation of Unstable Systems2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 341-346, article id 7798292Conference paper (Refereed)
    Abstract [en]

    Estimating unstable systems typically requires additional system identification techniques. In this paper, we consider the weighted null-space fitting method, a three step method that is asymptotically efficient for stable systems. This method first estimates a high order ARX model and then reduces it to a structured model with lower variance using weighted least squares. However, with unstable systems, the method cannot be used to simultaneously estimate the stable and unstable poles. To solve this, we observe that the unstable poles can be estimated from the high order ARX model with relative high accuracy, and use this as an estimate for the unstable poles of the model of interest. Then, the remaining parameters in this model can be estimated by weighted least squares. Because the complete set of parameters is not estimated jointly, asymptotic efficiency is lost. Nevertheless, a simulation study shows good performance.

  • 33.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A weighted least-squares method for parameter estimation in structured models2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, p. 3322-3327Conference paper (Refereed)
    Abstract [en]

    Parameter estimation in structured models is generally considered a difficult problem. For example, the prediction error method (PEM) typically gives a non-convex optimization problem, while it is difficult to incorporate structural information in subspace identification. In this contribution, we revisit the idea of iteratively using the weighted least-squares method to cope with the problem of non-convex optimization. The method is, essentially, a three-step method. First, a high order least-squares estimate is computed. Next, this model is reduced to a structured estimate using the least-squares method. Finally, the structured estimate is re-estimated, using weighted least-squares, with weights obtained from the first structured estimate. This methodology has a long history, and has been applied to a range of signal processing problems. In particular, it forms the basis of iterative quadratic maximum likelihood (IQML) and the Steiglitz-McBride method. Our contributions are as follows. Firstly, for output-error models, we provide statistically optimal weights. We conjecture that the method is asymptotically efficient under mild assumptions and support this claim by simulations. Secondly, we point to a wide range of structured estimation problems where this technique can be applied. Finally, we relate this type of technique to classical prediction error and subspace methods by showing that it can be interpreted as a link between the two, sharing favorable properties with both domains.

    Download full text (pdf)
    fulltext
  • 34.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Parametric Identification Using Weighted Null-Space Fitting2019In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 7, p. 2798-2813Article in journal (Refereed)
    Abstract [en]

    In identification of dynamical systems, the prediction error method with a quadratic cost function provides asymptotically efficient estimates under Gaussian noise, but in general it requires solving a nonconvex optimization problem, which may imply convergence to nonglobal minima. An alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class, starting with the estimate of a nonparametric ARX model with least squares. Then, the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem, which can be obtained with weighted least squares. The method is suitable for both open- and closed-loop data, and can be applied to many common parametric model structures, including output-error, ARMAX, and Box-Jenkins. The price to pay is the increase of dimensionality in the nonparametric model, which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold. In this paper, we conduct a rigorous analysis of these properties: namely, consistency, and asymptotic efficiency. Also, we perform a simulation study illustrating the performance of WNSF and identify scenarios where it can be particularly advantageous compared with state-of-the-art methods.

    Download full text (pdf)
    fulltext
  • 35.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristián R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 102, p. 45-57Article in journal (Refereed)
    Abstract [en]

    Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum. However, a too flexible noise model (i.e., too many parameters) increases the model complexity, which can cause additional numerical problems for PEM. In this paper, we consider the weighted null-space fitting (WNSF) method. With this method, the system is first modeled using a non-parametric ARX model, which is then reduced to a parametric model of interest using weighted least squares. In the reduction step, a parametric noise model does not need to be estimated if it is not of interest. Because the flexibility of the noise model is increased with the sample size, this will still provide consistent estimates in closed loop and asymptotically efficient estimates in open loop. In this paper, we prove these results, and we derive the asymptotic covariance for the estimation error obtained in closed loop, which is optimal for an infinite-order noise model. For this purpose, we also derive a new technical result for geometric variance analysis, instrumental to our end. Finally, we perform a simulation study to illustrate the benefits of the method when the noise model cannot be parametrized by a low-order model.

    Download full text (pdf)
    fulltext
  • 36. Godoy, B. I.
    et al.
    Valenzuela, Patricio E.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Aguero, J. C.
    Ninness, B.
    A novel input design approach for systems with quantized output data2014In: 2014 European Control Conference, ECC, IEEE , 2014, p. 1049-1054Conference paper (Refereed)
    Abstract [en]

    In this paper, we explore the problem of input design for systems with quantized measurements. For the input design problem, we calculate and optimize a function of the Fisher Information Matrix (FIM). The calculation of the FIM is greatly simplified by using known relationships of the derivative of the likelihood function, and the auxiliary function arising from the Expectation Maximization (EM) algorithm. To optimize the FIM, we design an experiment using a recently published method based on graph theory. A numerical example shows that the proposed experiment can be successfully used in quantized systems.

  • 37.
    Gonzalez, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Welsh, James S.
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW, Australia..
    An asymptotically optimal indirect approach to continuous-time system identification2018In: 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2018, p. 638-643Conference paper (Refereed)
    Abstract [en]

    The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by the indirect prediction error method, we propose an estimator that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification.

  • 38. González, R. A.
    et al.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, R. A.
    Optimal enforcement of causality in non-parametric transfer function estimation2017In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 1, no 2, p. 268-273Article in journal (Refereed)
    Abstract [en]

    Traditionally, non-parametric impulse and frequency response functions are estimated by taking the ratio of power spectral density estimates. However, this approach may often lead to non-causal estimates. In this letter, we derive a closed form expression for the impulse response estimator by smoothed empirical transfer function estimate, which allows optimal enforcement of causality on non-parametric estimators based on spectral analysis. The new method is shown to be asymptotically unbiased and of minimum covariance in a positive semidefinite sense among a broad class of linear estimators. Numerical simulations illustrate the performance of the new estimator. 

  • 39.
    González, Rodrigo A.
    et al.
    Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
    Cedeño, Angel L.
    Electronic Engineering Department, Universidad Técnica Federico Santa María, Valparaíso, Chile; Advanced Center for Electrical and Electronic Engineering, AC3E, Valparaíso, Chile.
    Coronel, María
    Advanced Center for Electrical and Electronic Engineering, AC3E, Valparaíso, Chile.
    Agüero, Juan C.
    Electronic Engineering Department, Universidad Técnica Federico Santa María, Valparaíso, Chile; Advanced Center for Electrical and Electronic Engineering, AC3E, Valparaíso, Chile.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification2023In: IFAC-PapersOnLine, Elsevier BV , 2023, Vol. 56, p. 4204-4209Conference paper (Refereed)
    Abstract [en]

    This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time signal whenever it crosses fixed and regularly partitioned thresholds. The knowledge of the intersample behavior of the output data is exploited in this work to derive an expectation-maximization (EM) algorithm for parameter estimation of the state-space and noise covariance matrices. For this purpose, we use the incremental discrete-time equivalent of the system, which leads to EM iterations of the continuous-time state-space matrices that can be computed by standard filtering and smoothing procedures. The effectiveness of the identification method is tested via Monte Carlo simulations.

  • 40.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    James S., Welsh
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Enforcing stability through ellipsoidal inner approximations in the indirect approach for continuous-time system identification2020Conference paper (Refereed)
    Abstract [en]

    Recently, a new indirect approach method for continuous-time system identification has been proposed that provides complete freedom on the number of poles and zeros of the linear and time-invariant continuous-time model structure. However, this procedure has reliability issues, as it may deliver unstable estimates even if the initialisation model and true system are stable. In this paper, we propose a method to overcome this problem. By generating ellipsoids that contain parameter vectors whose coefficients yield stable polynomials, we introduce a convex constraint in the indirect prediction error method formulation, and show that the proposed method enjoys optimal asymptotic properties while being robust in small and noisy data set scenarios. The effectiveness of the novel method is tested through extensive simulations.

    Download full text (pdf)
    fulltext
  • 41.
    González, Rodrigo A.
    et al.
    Control Systems Technology Section, Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands..
    Pan, Siqi
    School of Engineering, University of Newcastle, Callaghan, 2308 NSW, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Welsh, James S.
    School of Engineering, University of Newcastle, Callaghan, 2308 NSW, Australia.
    Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop2024In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 166, article id 111697Article in journal (Refereed)
    Abstract [en]

    Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.

  • 42.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    A Finite-Sample Deviation Bound for Stable Autoregressive Processes2020In: A Finite-Sample Deviation Bound for Stable Autoregressive Processes, ML Research Press , 2020, Vol. 120, p. 1-10Conference paper (Refereed)
    Abstract [en]

    In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR(n) processes. By relying on martingale concentration inequalities and a tail-bound for χ2 distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR(n) process. We discuss extensions and limitations of our approach.

  • 43.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    A fully Bayesian approach to kernel-based regularization for impulse response estimation⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 186-191Article in journal (Refereed)
    Abstract [en]

    Kernel-based regularization has recently been shown to be a successful method for impulse response estimation. This technique usually requires choosing a vector of hyper-parameters in order to form an appropriate regularization matrix. In this paper, we develop an alternative way to obtain kernel-based regularization estimates by Bayesian model mixing. This new approach is tested against state-of-the-art methods for hyperparameter tuning in regularized FIR estimation, with favorable results in many cases.

  • 44.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Finite sample deviation and variance bounds for first order autoregressive processes2020In: 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE, 2020, p. 5380-5384Conference paper (Refereed)
    Abstract [en]

    In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by at least a positive epsilon from its true value. Our results consider both stable and unstable processes. Afterwards, we obtain problem-dependent non-asymptotic bounds on the variance of this estimator, valid for sample sizes greater than or equal to seven. Via simulations we analyze the conservatism of our bounds, and show that they reliably capture the true behavior of the quantities of interest.

  • 45.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Non-causal regularized least-squares for continuous-time system identification with band-limited input excitations2021In: Proceedings 2021 60th IEEE conference on decision and control (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2021, p. 114-119Conference paper (Refereed)
    Abstract [en]

    In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is band-limited. The sinc interpolation property of these input signals yields equivalent discrete-time representations that are non-causal. This observation, often overlooked in the literature, is exploited in this work to study non-parametric frequency response estimators of linear continuous-time systems. We study the properties of non-causal least-square estimators for continuous-time system identification, and propose a kernel-based non-causal regularized least-squares approach for estimating the band-limited equivalent impulse response. The proposed methods are tested via extensive numerical simulations.

  • 46.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pan, Siqi
    Welsh, James
    Refined instrumental variable methods for unstable continuous-time systems in closed-loop2022In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820Article in journal (Refereed)
    Abstract [en]

    In continuous-time system identification, refined instrumental variable methods are widely used in open and closed-loop settings. Although their robustness and performance are well documented for stable systems, these estimators are not reliable for estimating unstable continuous-time models. The main difficulty we encounter in modeling unstable systems with refined instrumental variables is that the filtered regressor and instrument vectors, as well as the filtered output, become severely ill-conditioned if the model is unstable during the iterative process. In this work, we propose a solution to this problem by including a tailor-made all-pass filter in the prefiltering step. This approach is used for obtaining an extension of the least-squares state-variable filter method, as well as extensions for the refined instrumental variable method for continuous-time systems (RIVC) and its simplified embodiment(SRIVC), that admit the identification of unstable systems and are shown to minimize the prediction error upon convergence and as the sample size goes to infinity. In addition, several implementations of these methods are proposed depending on the intersample behavior of the input (zero and first-order hold, multisine and arbitrary). The particular case when the plant has integral action is explicitly considered in this work. In an indirect system identification setting, an extension of the closed loop version of the SRIVC method is also proposed and discussed in detail. Monte Carlo simulations are used to assess the performance of our methods. 

  • 47.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH Royal Institute of Technology.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pan, Siqi
    Welsh, James S.
    Consistent identification of continuous-time systems under multisine input signal excitationManuscript (preprint) (Other academic)
    Abstract [en]

    For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with input signals that cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.

  • 48.
    González, Rodrigo A.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pan, Siqi
    Univ Newcastle, Sch Elect Engn & Comp, Callaghan, NSW 2308, Australia..
    Welsh, James S.
    Univ Newcastle, Sch Elect Engn & Comp, Callaghan, NSW 2308, Australia..
    Consistent identification of continuous-time systems under multisine input signal excitation2021In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 133, article id 109859Article in journal (Refereed)
    Abstract [en]

    For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with continuous-time multisine signals, which cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.

  • 49.
    González, Rodrigo A.
    et al.
    Eindhoven Univ Technol, Control Syst Technol Res Sect, NL-5612 AZ Eindhoven, Netherlands..
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pan, Siqi
    Univ Newcastle, Sch Engn, Callaghan, NSW 2308, Australia..
    Welsh, James S.
    Univ Newcastle, Sch Engn, Callaghan, NSW 2308, Australia..
    On the Relation Between Discrete and Continuous-Time Refined Instrumental Variable Methods2023In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 7, p. 2233-2238Article in journal (Refereed)
    Abstract [en]

    The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this letter, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.

  • 50.
    González, Rodrigo A.
    et al.
    Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pan, Siqi
    School of Engineering, University of Newcastle, Callaghan, NSW, Australia.
    Welsh, James S.
    School of Engineering, University of Newcastle, Callaghan, NSW, Australia.
    Parsimonious Identification of Continuous-Time Systems: A Block-Coordinate Descent Approach2023In: 22nd IFAC World CongressYokohama, Japan, July 9-14, 2023, Elsevier BV , 2023, Vol. 56, p. 4216-4221Conference paper (Refereed)
    Abstract [en]

    The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this knowledge, which leads to interpretable and parsimonious models. However, some applications lead to model structures that lack parsimonious descriptions using unfactored transfer functions, which are commonly used in standard direct approaches for continuous-time system identification. In this paper we characterize this parsimony problem, and develop a block-coordinate descent algorithm that delivers parsimonious models by sequentially estimating an additive decomposition of the transfer function of interest. Numerical simulations show the efficacy of the proposed approach.

12345 1 - 50 of 204
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf