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Numrering	Referens	Omslagsbild	Hitta
1.	González, R. A., et al. (författare) Optimal enforcement of causality in non-parametric transfer function estimation 2017 Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers Inc.. - 2475-1456. ; 1:2, s. 268-273 Tidskriftsartikel (refereegranskat)abstract 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.
2.	Olofsson, K. Erik J., et al. (författare) Predictor-based multivariable closed-loop system identification of the EXTRAP T2R reversed field pinch external plasma response 2011 Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 0741-3335 .- 1361-6587. ; 53:8, s. 084003- Tidskriftsartikel (refereegranskat)abstract The usage of computationally feasible overparametrized and nonregularized system identification signal processing methods is assessed for automated determination of the full reversed-field pinch external plasma response spectrum for the experiment EXTRAP T2R. No assumptions on the geometry of eigenmodes are imposed. The attempted approach consists of high-order autoregressive exogenous estimation followed by Markov block coefficient construction and Hankel matrix singular value decomposition. It is seen that the obtained 'black-box' state-space models indeed can be compared with the commonplace ideal magnetohydrodynamics (MHD) resistive thin-shell model in cylindrical geometry. It is possible to directly map the most unstable autodetected empirical system pole to the corresponding theoretical resistive shell MHD eigenmode.
3.	Rojas, Cristian R., et al. (författare) A Critical View on Benchmarks based on Randomly Generated Systems 2015 Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 1471-1476 Tidskriftsartikel (refereegranskat)abstract In data-based modelling communities, such as system identification, machine learning, signal processing and statistics, benchmarks are essential for testing and comparing old and new techniques for the estimation of models. During the last years, it has become customary in system identification to rely on data sets built from randomly generated systems. In this article we discuss the implications of this practice, in particular when using data sets generated with the MATLABr command drss, and advocate the cautious use of comparisons based on these benchmarks.
4.	Abdalmoaty, Mohamed R., 1986-, et al. (författare) Identification of a Class of Nonlinear Dynamical Networks⁎ 2018 Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873 Tidskriftsartikel (refereegranskat)abstract 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.
5.	Ansell, Brendan R. E., et al. (författare) Time-Dependent Transcriptional Changes in Axenic Giardia duodenalis Trophozoites 2015 Ingår i: PLoS Neglected Tropical Diseases. - : Public Library of Science (PLoS). - 1935-2727 .- 1935-2735. ; 9:12 Tidskriftsartikel (refereegranskat)abstract Giardia duodenalis is the most common gastrointestinal protozoan parasite of humans and a significant contributor to the global burden of both diarrheal disease and post-infectious chronic disorders. Although G. duodenalis can be cultured axenically, significant gaps exist in our understanding of the molecular biology and metabolism of this pathogen. The present study employed RNA sequencing to characterize the mRNA transcriptome of G. duodenalis trophozoites in axenic culture, at log (48 h of growth), stationary (60 h), and declining (96 h) growth phases. Using similar to 400-times coverage of the transcriptome, we identified 754 differentially transcribed genes (DTGs), mainly representing two large DTG groups: 438 that were down-regulated in the declining phase relative to log and stationary phases, and 281 that were up-regulated. Differential transcription of prominent antioxidant and glycolytic enzymes implicated oxygen tension as a key factor influencing the transcriptional program of axenic trophozoites. Systematic bioinformatic characterization of numerous DTGs encoding hypothetical proteins of unknown function was achieved using structural homology searching. This powerful approach greatly informed the differential transcription analysis and revealed putative novel antioxidant-coding genes, and the presence of a nearcomplete two-component-like signaling system that may link cytosolic redox or metabolite sensing to the observed transcriptional changes. Motif searching applied to promoter regions of the two large DTG groups identified different putative transcription factor-binding motifs that may underpin global transcriptional regulation. This study provides new insights into the drivers and potential mediators of transcriptional variation in axenic G. duodenalis and provides context for static transcriptional studies.
6.	Ebadat, Afrooz, et al. (författare) Applications Oriented Input Design in Time-Domain Through Cyclic Methods 2014 Konferensbidrag (refereegranskat)abstract 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.
7.	Oomen, T., et al. (författare) Iteratively learning the H∞-norm of multivariable systems applied to model-error-modeling of a vibration isolation system 2013 Ingår i: Proceedings of the American Control Conference 2013. - : American Automatic Control Council. - 9781479901777 ; , s. 6703-6708 Konferensbidrag (refereegranskat)abstract The aim of this paper is to develop a new data-driven approach for learning the H∞-norm of multivariable systems that can be used for model-error-modeling in robust feedback control. The proposed algorithm only requires iterative experiments on the system. Especially for the multivariable situation that is considered in this paper, these experiments have to be judiciously chosen. The proposed algorithm delivers an estimate of the H ∞-norm of an unknown multivariable system, without the need or explicit construction of a (parametric or non-parametric) model. The results are experimentally demonstrated on model-error-modeling of a multivariable industrial active vibration isolation system. Finally, connections to learning control algorithms are established.
8.	Ramírez, Jaime A., et al. (författare) Aportes a la Teoría y la Implementación del Método LSCR 2010 Ingår i: RIAI - Revista Iberoamericana de Automatica e Informatica Industrial. - 1697-7912. ; 7:3, s. 83-94 Tidskriftsartikel (refereegranskat)abstract The LSCR method (Leave-out-Sign-dominant-Correlation-Regions) provides confidence regions for the parameters of a system by evaluating a set of correlation functions calculated for the available data. To do the approximation for the whole region, the procedure must be repeated for each value of the parameter vector. The main attributes of LSCR are its validity for a finite set of data and the scarce assumptions on the noise. However, the procedure needs much computational effort, which limits its application to very simple cases. In this work some theoretical aspects of the LSCR method are improved and some implementation alternatives are suggested. It is also compared, in terms of computational effort, with Bootstrap, another way to obtain confidence regions.
9.	Rojas, Cristian R., 1980-, et al. (författare) Equivalence between Transfer-Matrix and Observed-State Feedback Control 2006 Ingår i: IEE Proceedings - Control Theory and Applications. - : Institution of Engineering and Technology (IET). - 1350-2379 .- 1359-7035. ; 153:2, s. 147-155 Tidskriftsartikel (refereegranskat)abstract An observed-state feedback is built for a given multiple input-multiple Output (MIMO) control loop, where the controller is specified in transfer-matrix form. This contribution solves for the first time, for MIMO systems, the classical problem of finding a feedback gain and an observer gain such that the observed-state feedback control loop has the same sensitivity as that provided by a one-degree-of-freedom classical control loop.
10.	Rojas, Ricardo A., et al. (författare) The inverse of sampling revisited 2001 Ingår i: Proceedings of the IASTED Conference on Intelligent Systems and Control (ISC-2001). Konferensbidrag (refereegranskat)
11.	Sanchez, B., et al. (författare) On the calculation of the D-optimal multisine excitation power spectrum for broadband impedance spectroscopy measurements 2012 Ingår i: Measurement science and technology. - : IOP Publishing. - 0957-0233 .- 1361-6501. ; 23:8, s. 085702- Tidskriftsartikel (refereegranskat)abstract The successful application of impedance spectroscopy in daily practice requires accurate measurements for modeling complex physiological or electrochemical phenomena in a single frequency or several frequencies at different (or simultaneous) time instants. Nowadays, two approaches are possible for frequency domain impedance spectroscopy measurements: (1) using the classical technique of frequency sweep and (2) using (non-)periodic broadband signals, i.e. multisine excitations. Both techniques share the common problem of how to design the experimental conditions, e.g. the excitation power spectrum, in order to achieve accuracy of maximum impedance model parameters from the impedance data modeling process. The original contribution of this paper is the calculation and design of the D-optimal multisine excitation power spectrum for measuring impedance systems modeled as 2R-1C equivalent electrical circuits. The extension of the results presented for more complex impedance models is also discussed. The influence of the multisine power spectrum on the accuracy of the impedance model parameters is analyzed based on the Fisher information matrix. Furthermore, the optimal measuring frequency range is given based on the properties of the covariance matrix. Finally, simulations and experimental results are provided to validate the theoretical aspects presented.
12.	Töth, R., et al. (författare) Sparse estimation or rational dynamical models 2012 Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 983-988 Konferensbidrag (refereegranskat)abstract In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. This can be motivated either from appealing to a parsimony principle (Occam's razor) or from the view point of the utilization complexity in terms of control synthesis, prediction, etc. At the same time, the need for an accurate description of the system behavior without knowing its complete dynamical structure often leads to model parameterizations describing a rich set of possible hypotheses; an unavoidable choice, which suggests sparsity of the desired parameter estimate. An elegant way to impose this expectation of sparsity is to estimate the parameters by penalizing the criterion with the ℓ 0 norm of the parameters, which is often implemented as solving an optimization program based on a convex relaxation (e.g. ℓ 1/ LASSO, nuclear norm, ⋯). However, in order to apply these methods, the (unpenalized) cost function must be convex. This imposes a severe constraint on the types of model structures or estimation methods on which these relaxations can be applied. In this paper, we extend the use of convex relaxation techniques for sparsity to general rational plant model structures estimated by using prediction error minimization. This is done by combining the LASSO and the Steiglitz-McBride approaches. To demonstrate the advantages of the proposed solution an extensive simulation study is provided.
13.	Agüero, Juan C., et al. (författare) Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation 2012 Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 48:4, s. 632-637 Tidskriftsartikel (refereegranskat)abstract In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.
14.	Agüero, Juan C., et al. (författare) Fundamental Limitations on the Accuracy of MIMO Linear Models Obtained by PEM for Systems Operating in Open Loop 2009 Ingår i: Proceedings of the Joint 48th IEEE Conference on Decision and Control (CDC’09) and 28th Chinese Control Conference (CCC’09). - 9781424438716 ; , s. 482-487 Konferensbidrag (refereegranskat)abstract 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.
15.	Bjurgert, Johan, et al. (författare) On Adaptive Boosting for System Identification 2018 Ingår i: IEEE Transactions on Neural Networks and Learning Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 2162-237X .- 2162-2388. ; 29:9, s. 4510-4514 Tidskriftsartikel (refereegranskat)abstract 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.
16.	Blomberg, Niclas, et al. (författare) Approximate regularization path for nuclear norm based H2 model reduction 2014 Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE conference proceedings. ; , s. 3637-3641 Konferensbidrag (refereegranskat)abstract 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.
17.	Blomberg, Niclas, et al. (författare) Regularization Paths for Re-Weighted Nuclear Norm Minimization 2015 Ingår i: IEEE Signal Processing Letters. - 1070-9908 .- 1558-2361. ; 22:11, s. 1980-1984 Tidskriftsartikel (refereegranskat)abstract 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.
18.	Bombois, Xavier, et al. (författare) Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging 2011 Ingår i: Proceedings of the 18th IFAC World Congress. ; , s. 9953-9958 Konferensbidrag (refereegranskat)abstract 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).
19.	Brighenti, C., et al. (författare) Input design using Markov chains for system identification 2009 Ingår i: 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. ; , s. 1557-1562 Konferensbidrag (refereegranskat)abstract 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.
20.	Dettù, Federico, et al. (författare) From Data to Control : A Two-Stage Simulation-Based Approach 2024 Ingår i: 2024 European Control Conference, ECC 2024. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 3428-3433 Konferensbidrag (refereegranskat)abstract For many industrial processes, a digital twin is available, which is essentially a highly complex model whose parameters may not be properly tuned for the specific process. By relying on the availability of such a digital twin, this paper introduces a novel approach to data-driven control, where the digital twin is used to generate samples and suitable controllers for various perturbed versions of its parameters. A supervised learning algorithm is then employed to estimate a direct mapping from the data to the best controller to use. This map consists of a model reduction step, followed by a neural network architecture whose output provides the parameters of the controller. The data-to-controller map is pre-computed based on artificially generated data, but its execution once deployed is computationally very efficient, thus providing a simple and inexpensive way to tune and re-calibrate controllers directly from data. The benefits of this novel approach are illustrated via numerical simulations.
21.	Djehiche, Boualem, 1962-, et al. (författare) Finite impulse response models : A non-asymptotic analysis of the least squares estimator 2021 Ingår i: Bernoulli. - : Bernoulli Society for Mathematical Statistics and Probability. - 1350-7265 .- 1573-9759. ; 27:2, s. 976-1000 Tidskriftsartikel (refereegranskat)abstract 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.
22.	Ebadat, Afrooz, et al. (författare) Application Set Approximation in Optimal Input Design for Model Predictive Control 2014 Ingår i: 2014 European Control Conference (ECC). - 9783952426913 ; , s. 744-749 Konferensbidrag (refereegranskat)abstract 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.
23.	Ebadat, Afrooz, et al. (författare) Applications Oriented Input Design for Closed-Loop System Identification : a Graph-Theory Approach 2014 Ingår i: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781467360906 ; , s. 4125-4130 Konferensbidrag (refereegranskat)abstract 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.
24.	Ebadat, Afrooz, et al. (författare) Model Predictive Control oriented experiment design for system identification : A graph theoretical approach 2017 Ingår i: Journal of Process Control. - : ELSEVIER SCI LTD. - 0959-1524 .- 1873-2771. ; 52, s. 75-84 Tidskriftsartikel (refereegranskat)abstract 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.
25.	Eckhard, Diego, et al. (författare) Cost function shaping of the output error criterion 2017 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 76, s. 53-60 Tidskriftsartikel (refereegranskat)abstract 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.
26.	Eckhard, Diego, et al. (författare) Input design as a tool to improve the convergence of PEM 2013 Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 49:11, s. 3282-3291 Tidskriftsartikel (refereegranskat)abstract 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.
27.	Eckhard, Diego, et al. (författare) Mean-squared error experiment design for linear regression models 2012 Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 1629-1634 Konferensbidrag (refereegranskat)abstract 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.
28.	Eckhard, Diego, et al. (författare) On the convergence of the Prediction Error Method to its global minimum 2012 Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 698-703 Konferensbidrag (refereegranskat)abstract 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.
29.	Elton, Augustus, et al. (författare) Blind Nonparametric Estimation of SISO Continuous-time Systems 2023 Ingår i: IFAC-PapersOnLine. - : Elsevier BV. ; , s. 4222-4227 Konferensbidrag (refereegranskat)abstract 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.
30.	Elton, Augustus, et al. (författare) Parametric Continuous-Time Blind System Identification 2023 Ingår i: 2023 62nd IEEE Conference on Decision and Control, CDC2023. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 1474-1479 Konferensbidrag (refereegranskat)abstract 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.
31.	Esparza, Alicia, et al. (författare) Asymptotic statistical analysis for model-based control design strategies 2011 Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 47:5, s. 1041-1046 Tidskriftsartikel (refereegranskat)abstract 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.
32.	Everitt, Niklas, 1987-, et al. (författare) A Geometric Approach to Variance Analysis of Cascaded Systems 2013 Ingår i: Proceedings of the 52nd Conference On Decision And Control. - : IEEE conference proceedings. - 9781467357173 ; , s. 6496-6501 Konferensbidrag (refereegranskat)abstract 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.
33.	Everitt, Niklas, et al. (författare) Identification of modules in dynamic networks : An empirical Bayes approach 2016 Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509018376 ; , s. 4612-4617 Konferensbidrag (refereegranskat)abstract 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.
34.	Everitt, Niklas, 1987- (författare) Module identification in dynamic networks: parametric and empirical Bayes methods 2017 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract The purpose of system identification is to construct mathematical models of dynamical system from experimental data. With the current trend of dynamical systems encountered in engineering growing ever more complex, an important task is to efficiently build models of these systems. Modelling the complete dynamics of these systems is in general not possible or even desired. However, often, these systems can be modelled as simpler linear systems interconnected in a dynamic network. Then, the task of estimating the whole network or a subset of the network can be broken down into subproblems of estimating one simple system, called module, embedded within the dynamic network.The prediction error method (PEM) is a benchmark in parametric system identification. The main advantage with PEM is that for Gaussian noise, it corresponds to the so called maximum likelihood (ML) estimator and is asymptotically efficient. One drawback is that the cost function is in general nonconvex and a gradient based search over the parameters has to be carried out, rendering a good starting point crucial. Therefore, other methods such as subspace or instrumental variable methods are required to initialize the search. In this thesis, an alternative method, called model order reduction Steiglitz-McBride (MORSM) is proposed. As MORSM is also motivated by ML arguments, it may also be used on its own and will in some cases provide asymptotically efficient estimates. The method is computationally attractive since it is composed of a sequence of least squares steps. It also treats the part of the network of no direct interest nonparametrically, simplifying model order selection for the user.A different approach is taken in the second proposed method to identify a module embedded in a dynamic network. Here, the impulse response of the part of the network of no direct interest is modelled as a realization of a Gaussian process. The mean and covariance of the Gaussian process is parameterized by a set of parameters called hyperparameters that needs to be estimated together with the parameters of the module of interest. Using an empirical Bayes approach, all parameters are estimated by maximizing the marginal likelihood of the data. The maximization is carried out by using an iterative expectation/conditional-maximization scheme, which alternates so called expectation steps with a series of conditional-maximization steps. When only the module input and output sensors are used, the expectation step admits an analytical expression. The conditional-maximization steps reduces to solving smaller optimization problems, which either admit a closed form solution, or can be efficiently solved by using gradient descent strategies. Therefore, the overall optimization turns out computationally efficient. Using markov chain monte carlo techniques, the method is extended to incorporate additional sensors.Apart from the choice of identification method, the set of chosen signals to use in the identification will determine the covariance of the estimated modules. To chose these signals, well known expressions for the covariance matrix could, together with signal constraints, be formulated as an optimization problem and solved. However, this approach does neither tell us why a certain choice of signals is optimal nor what will happen if some properties change. The expressions developed in this part of the thesis have a different flavor in that they aim to reformulate the covariance expressions into a form amenable for interpretation. These expressions illustrate how different properties of the identification problem affects the achievable accuracy. In particular, how the power of the input and noise signals, as well as model structure, affect the covariance.
35.	Everitt, Niklas, et al. (författare) On the Effect of Noise Correlation in Parameter Identification of SIMO Systems 2015 Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 326-331 Tidskriftsartikel (refereegranskat)abstract 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.
36.	Everitt, Niklas, et al. (författare) On the Variance Analysis of identified Linear MIMO Models 2015 Ingår i: IEEE Explore. - : Institute of Electrical and Electronics Engineers (IEEE). Konferensbidrag (refereegranskat)abstract 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.
37.	Everitt, Niklas, 1987-, et al. (författare) Variance Analysis of Linear SIMO Models with Spatially Correlated Noise Annan publikation (övrigt vetenskapligt/konstnärligt)abstract 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.
38.	Everitt, Niklas, et al. (författare) Variance analysis of linear SIMO models with spatially correlated noise 2017 Ingår i: Automatica. - : Elsevier. - 0005-1098. ; 77, s. 68-81 Tidskriftsartikel (refereegranskat)abstract 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.
39.	Everitt, Niklas, 1987-, et al. (författare) Variance Results for Parallel Cascade Serial Systems 2014 Ingår i: Proceedings of 19th IFAC World Congress. - : Elsevier BV. Konferensbidrag (refereegranskat)abstract 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.
40.	Ferizbegovic, Mina (författare) Dual control concepts for linear dynamical systems 2022 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract We study simultaneous learning and control of linear dynamical systems. In such a setting, control policies are derived with respect to two objectives: i) to control the system as well as possible, given the current knowledge of system dynamics (exploitation), and ii) to gather as much information as possible about the unknown system that can improve control (exploration).These two objectives are often in conflict, and this phenomenon is known as the exploration-exploitation trade-off.More specifically, in the context of simultaneous learning and control, we consider: linear quadratic regulation (LQR) problem, model reference control, and data-driven control based on Willems \textit{et al.}'s fundamental lemma. First, we consider the LQR problem with unknown dynamics. We present robust and certainty equivalence (CE) model-based control methods that balance exploration and exploitation. We focus on control policies that can be iteratively updated after sequentially collecting data.We propose robust (with respect to parameter uncertainty) LQR design methods. To quantify uncertainty, we derive a methodbased on Bayesian inference, which is directly applicable to robust control synthesis. To begin, we derive a robust controller to minimize the worst-case cost, with high probability, given the empirical observation of the system. This robust controller synthesis is then used to derive a robust dual controller, which updates its control policy after collecting data. An episode in which data is collected is called exploration, and the episode using an updated control policy called exploitation. The objective is to minimize the worst-case cost of the updated control policy, requiring that a given exploration budget constrains the worst-case cost during exploration. Additionally, we derive methods that balance exploration and exploitation to minimize the cumulative worst-case cost for a fixed number of episodes. In this thesis, we refer to such a problem as robust reinforcement learning. Essentially, it is a robust dual controller aiming to minimize the cumulative worst-case cost, and that updates its control policy in each episode.Numerical experiments show that the proposed methods perform better than existing state-of-the-art algorithms. Moreover, experiments also indicate that the exploration prioritizes the uncertainty reduction in the parameters that matter most for control.A control policy using the CE principle for LQR consists of a sum of an optimal controller calculated using estimated dynamics at time $t$, and an additive external excitation. It has been shown over the years that the optimal asymptotic rate of regret is in many instances $\mathcal{O}(\sqrt{T})$. In particular, this rate can be obtained by adding a white noise external excitation, with a variance decaying as $\gamma/\sqrt{T}$, where $\gamma$ is a predefined constant. As the amount of excitation is pre-determined, such approaches can be viewed as open-loop control of the external excitation. In this thesis, we approach the problem of designing the external excitation from a feedback perspective leveraging the well-known benefits of feedback control for decreasing sensitivity to external disturbances and system-model mismatch, as compared to open-loop strategies. The benefits of this approach over the open-loop approach can be seen in the case of unmodeled dynamics and disturbances. However, even when using the benefits of feedback control, we do not calculate the optimal amount of external excitation. To find the optimal amount of external excitation, we suggest exploration strategies that are based on a time-dependent scaling $\gamma_t$ and can attain cumulative regret similar to or lower than cumulative regret obtained for optimal scaling $\gamma^*$ according to numerical examples.Second, we consider the model reference control problem with the goal of proposing a data-driven robust control design method based on an average risk criterion, which we call Bayes control. We show that this approach has very close ties to the Bayesian kernel-based method, but the conceptual difference lies in the use of a deterministic respective stochastic setting for the system parameters. Finally, we consider data-driven control using Willems \textit{et al.}'s fundamental lemma. First, we propose variations of the fundamental lemma that, instead of a data trajectory, utilize correlation functions in the time domain, as well as power spectra of the input and the output in the frequency domain. Since data-driven control using the fundamental lemma can become a very expensive computation task for large datasets, the proposed variations are easy to computeeven for large datasets and can be efficient as a data compression technique. Second, we study connections of data informativity conditions between the results based on the fundamental lemma (finite time), and classical system identification. We show that finite time informativity conditions for state-space systems are closely linked to the identifiability conditions derived from the fundamental lemma. We prove that the obtained persistency of excitation conditions for infinite time are sufficient conditions for finite time informativity. Moreover, we reveal that the obtained conditions for a finite time in closed-loop are stricter than in classical system identification. This is a consequence of the noiseless data setting in the fundamental lemma that precludes the possibility of noise to excite the system in a feedback setting.
41.	Ferizbegovic, Mina (författare) Robust learning and control of linear dynamical systems 2020 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract We consider the linear quadratic regulation problem when the plant is an unknown linear dynamical system. We present robust model-based methods based on convex optimization, which minimize the worst-case cost with respect to uncertainty around model estimates. To quantify uncertainty, we derive a methodbased on Bayesian inference, which is directly applicable to robust control synthesis.We focus on control policies that can be iteratively updated after sequentially collecting data. More specifically, we seek to design control policies that balance exploration (reducing model uncertainty) and exploitation (control of the system) when exploration must be safe (robust).First, we derive a robust controller to minimize the worst-case cost, with high probability, given the empirical observation of the system. This robust controller synthesis is then used to derive a robust dual controller, which updates its control policy after collecting data. An episode in which data is collected is called exploration, and the episode using an updated control policy is exploitation. The objective is to minimize the worst-case cost of the updated control policy, requiring that a given exploration budget constrains the worst-case cost during exploration.We look into robust dual control in both finite and infinite horizon settings. The main difference between the finite and infinite horizon settings is that the latter does not consider the length of the exploration and exploitation phase, but it rather approximates the cost using the infinite horizon cost. In the finite horizon setting, we discuss how different exploration lengths affect the trade-off between exploration and exploitation.Additionally, we derive methods that balance exploration and exploitation to minimize the cumulative worst-case cost for a fixed number of episodes. In this thesis, we refer to such a problem as robust reinforcement learning. Essentially, it is a robust dual controller aiming to minimize the cumulative worst-case cost, and that updates its control policy in each episode.Numerical experiments show that the proposed methods have better performance compared to existing state-of-the-art algorithms. Moreover, experiments also indicate that the exploration prioritizes the uncertainty reduction in the parameters that matter most for control.
42.	Galrinho, Miguel, et al. (författare) A Weighted Least Squares Method for Estimation of Unstable Systems 2016 Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509018376 ; , s. 341-346 Konferensbidrag (refereegranskat)abstract 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.
43.	Galrinho, Miguel, et al. (författare) A weighted least-squares method for parameter estimation in structured models 2014 Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE conference proceedings. ; , s. 3322-3327 Konferensbidrag (refereegranskat)abstract 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.
44.	Galrinho, Miguel, et al. (författare) Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting 2019 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 102, s. 45-57 Tidskriftsartikel (refereegranskat)abstract 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.
45.	Galrinho, Miguel, et al. (författare) Parametric Identification Using Weighted Null-Space Fitting 2019 Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 64:7, s. 2798-2813 Tidskriftsartikel (refereegranskat)abstract 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.
46.	Godoy, B. I., et al. (författare) A novel input design approach for systems with quantized output data 2014 Ingår i: 2014 European Control Conference, ECC. - : IEEE. - 9783952426913 ; , s. 1049-1054 Konferensbidrag (refereegranskat)abstract 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.
47.	González, Rodrigo A., et al. (författare) A Finite-Sample Deviation Bound for Stable Autoregressive Processes 2020 Ingår i: A Finite-Sample Deviation Bound for Stable Autoregressive Processes. - : ML Research Press. ; , s. 1-10 Konferensbidrag (refereegranskat)abstract 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.
48.	González, Rodrigo A., et al. (författare) A fully Bayesian approach to kernel-based regularization for impulse response estimation⁎ 2018 Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 186-191 Tidskriftsartikel (refereegranskat)abstract 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.
49.	Gonzalez, Rodrigo A., et al. (författare) An asymptotically optimal indirect approach to continuous-time system identification 2018 Ingår i: 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781538613955 ; , s. 638-643 Konferensbidrag (refereegranskat)abstract 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.
50.	González, Rodrigo A., et al. (författare) An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification 2023 Ingår i: IFAC-PapersOnLine. - : Elsevier BV. ; , s. 4204-4209 Konferensbidrag (refereegranskat)abstract 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.

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