SwePub - sökning: WFRF:(Ljung Lennart 1946 )

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1.	Ljung, Lennart, 1946-, et al. (författare) An Alternative Motivation for the Indirect Approach to Closed-Loop Identification 1997 Rapport (övrigt vetenskapligt/konstnärligt)abstract Direct prediction error identification of systems operating in closed loop may lead to biased results due to the correlation between the input and the output noise. The authors study this error, what factors affect it, and how it may be avoided. In particular, the role of the noise model is discussed and the authors show how the noise model should be parameterized to avoid the bias. Apart from giving important insights into the properties of the direct method, this provides a nonstandard motivation for the indirect method.
2.	Ljung, Lennart, 1946-, et al. (författare) Snabb lösning av integralekvationer 1978 Rapport (övrigt vetenskapligt/konstnärligt)
3.	Ljung, Lennart, 1946-, et al. (författare) Snabb lösning av integralekvationer för tekniska problem 1979 Rapport (övrigt vetenskapligt/konstnärligt)
4.	Ljung, Stefan, et al. (författare) Error Propagation Properties of Recursive Least-Squares Adaptation Algorithms 1984 Ingår i: Proceedings of the 9th IFAC World Congress. - : Pergamon. - 0080316662 ; , s. 70-74 Konferensbidrag (refereegranskat)abstract The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
5.	Ljung, Stefan, et al. (författare) Error Propagation Properties of Recursive Least Squares Adaptation Algorithms 1983 Rapport (övrigt vetenskapligt/konstnärligt)abstract The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
6.	Ljung, Stefan, et al. (författare) Error Propagation Properties of Recursive Least Squares Adaptation Algorithms 1985 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 21:2, s. 157-167 Tidskriftsartikel (refereegranskat)abstract The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
7.	Ljung, Stefan, et al. (författare) Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels 1980 Rapport (övrigt vetenskapligt/konstnärligt)abstract A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
8.	Ljung, Stefan, et al. (författare) Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels 1982 Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 22:1, s. 54-72 Tidskriftsartikel (refereegranskat)abstract A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
9.	Ljung, Stefan, et al. (författare) Fast Numerical Solution of Integral Equations with Stationary Kernels 1978 Rapport (övrigt vetenskapligt/konstnärligt)
10.	Abrahamsson, Tomas, et al. (författare) A Study of some Approaches to Vibration Data Analysis 1993 Rapport (övrigt vetenskapligt/konstnärligt)abstract Using data from extensive vibrational tests of the new aircraft Saab 2000 three different methods for vibration analysis are studied. These methods are ERA (eigensystem realization algorithm), N4SID (a subspace method) and PEM (prediction error approach). We find that both the ERA and N4SID methods give good initial model parameter estimates that can be further improved by the use of PEM. We also find that all methods give good insights into the vibrational modes.
11.	Akcay, H., et al. (författare) On the choice of norms in system identification 1996 Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372 Tidskriftsartikel (refereegranskat)abstract In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all â„“p-norms, p â‰€ 2 < âˆž for F(C). Â©1996 IEEE.
12.	Akçay, Hüseyin, et al. (författare) On the Choice of Norms in System Identification 1994 Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108 Rapport (övrigt vetenskapligt/konstnärligt)abstract In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
13.	Aljanaideh, Khaled F., et al. (författare) New Features in the System Identification Toolbox - Rapprochements with Machine Learning 2021 Ingår i: IFAC PAPERSONLINE. - : ELSEVIER. - 2405-8963. ; , s. 369-373 Konferensbidrag (refereegranskat)abstract The R2021b release of the System Identification ToolboxTM for MATLAB contains new features that enable the use of machine learning techniques for nonlinear system identification. With this release it is possible to build nonlinear ARX models with regression tree ensemble and Gaussian process regression mapping functions. The release contains several other enhancements including, but not limited to, (a) online state estimation using the extended Kalman filter and the unscented Kalman filter with code generation capability; (b) improved handling of initial conditions for transfer functions and polynomial models; (c) a new architecture of nonlinear black-box models that streamlines regressor handling, reduces memory footprint and improves numerical accuracy; and (d) easy incorporation of identification apps in teaching tools and interactive examples by leveraging the Live Editor tasks of MATLAB. Copyright (C) 2021 The Authors.
14.	Andersson, Peter, et al. (författare) A Test Case for Adaptive Control : Car Steering 1981 Ingår i: Proceedings of the 1981 IFAC Symposium on Theory and Applications of Digital Control. - Linköping : Linköping University. - 9780080276182 Rapport (övrigt vetenskapligt/konstnärligt)
15.	Andersson, Torbjörn, et al. (författare) Identification Aspects of Inter-Sample Input Behavior 1994 Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 137-142 Konferensbidrag (refereegranskat)abstract In this contribution aspects of inter-sample input signal behavior are examined. The starting point is that parametric identification always is performed on basis of discrete-time data. This is valid for identification of discrete-time models as well as continuous-time models. The usual assumptions on the input signal are; i) it is band-limited, ii) it is piecewise constant or iii) it is piecewise linear. One point made in this paper is that if a discrete-time model is used, the best possible (in the model structure) adjustment to data is made. This is independent of the assumption on the input signal. However, a transformation of the obtained discrete model to a continuous one is not possible without additional assumptions on the input signal. The other point made is that the frequency functions of the discrete models very well coincides with the frequency functions of the discretized continuous time models and the continuous time transfer function fitted in the frequency domain.
16.	Bauer, Dietmar, et al. (författare) Some facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms 2000 Rapport (övrigt vetenskapligt/konstnärligt)abstract In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.
17.	Bauer, Dietmar, et al. (författare) Some Facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms 2002 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 38:5, s. 763-773 Tidskriftsartikel (refereegranskat)abstract In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.
18.	Bengtsson, Bengt, et al. (författare) Reglerproblem för Händelsestörda och Händelsestyrda System 1982 Rapport (övrigt vetenskapligt/konstnärligt)
19.	Bergman, Niclas, et al. (författare) Terrain Navigation using Bayesian Statistics 1999 Ingår i: IEEE Control Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 1066-033X .- 1941-000X. ; 19:3, s. 33-40 Tidskriftsartikel (refereegranskat)abstract The performance of terrain-aided navigation of aircraft depends on the size of the terrain gradient in the area. The point-mass filter (PMF) described in this work yields an approximate Bayesian solution that is well suited for the unstructured nonlinear estimation problem in terrain navigation. It recursively propagates a density function of the aircraft position. The shape of the point-mass density reflects the estimate quality; this information is crucial in navigation applications, where estimates from different sources often are fused in a central filter. Monte Carlo simulations show that the approximation can reach the optimal performance, and realistic simulations show that the navigation performance is very high compared with other algorithms and that the point-mass filter solves the recursive estimation problem for all the types of terrain covered in the test. The main advantages of the PMF is that it works for many kinds of nonlinearities and many kinds of noise and prior distributions. The mesh support and resolution are automatically adjusted and controlled using a few intuitive design parameters. The main disadvantage is that it cannot solve estimation problems of very high dimension since the computational complexity of the algorithm increases drastically with the dimension of the state space. The implementation used in this work shows real-time performance for 2D and in some cases 3D models, but higher state dimensions are usually intractable.
20.	Bergman, Niclas, et al. (författare) Terrain Navigation using Bayesian Statistics 1999 Rapport (övrigt vetenskapligt/konstnärligt)abstract In aircraft navigation the demands on reliability and safety are very high. The importance of accurate position and velocity information becomes crucial when flying an aircraft at low altitudes, and especially during the landing phase. Not only should the navigation system have a consistent description of the position of the aircraft, but also a description of the surrounding terrain, buildings and other objects that are close to the aircraft. Terrain navigation is a navigation scheme that utilizes variations in the terrain height along the aircraft flight path. Integrated with an Inertial Navigation System (INS), it yields high performance position estimates in an autonomous manner, ie without any support information sent to the aircraft. In order to obtain these position estimates, a nonlinear recursive estimation problem must be solved on-line. Traditionally, this filtering problem has been solved by local linearization of the terrain at one or several assumed aircraft positions. Due to changing terrain characteristics, these linearizations will in some cases result in diverging position estimates. In this work, we show how the Bayesian approach gives a comprehensive framework for solving the recursive estimation problem in terrain navigation. Instead of approximating the model of the estimation problem, the analytical solution is approximately implemented. The proposed navigation filter computes a probability mass distribution of the aircraft position and updates this description recursively with each new measurement. The navigation filter is evaluated over a commercial terrain database, yielding accurate position estimates over several types of terrain characteristics. Moreover, in a Monte Carlo analysis, it shows optimal performance as it reaches the Cramér-Rao lower bound.
21.	Björklund, Svante, et al. (författare) A Review of Time-Delay Estimation Techniques 2003 Ingår i: Proceedings of the 42nd IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780379241 ; , s. 2502-2507 vol.3 Rapport (övrigt vetenskapligt/konstnärligt)abstract This paper reviews and evaluates suggested methods for estimating the time-delay of linear systems in automatic control applications. A classification of the methods according to the underlying principles is suggested. The evaluation, done by analyzing the estimates of the methods from extensive simulated data in open loop, shows that different classes of methods have different properties and are suitable in different cases. Some method are clearly inferior to others. Recommendations are given on how to choose estimation method and input signal.
22.	Björklund, Svante, et al. (författare) An Improved Phase Method for Time-Delay Estimation 2010 Rapport (övrigt vetenskapligt/konstnärligt)abstract A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures.
23.	Björklund, Svante, et al. (författare) An Improved Phase Method for Time-Delay Estimation 2009 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 45:10, s. 2467-2470 Tidskriftsartikel (refereegranskat)abstract A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures.
24.	Caines, Peter, et al. (författare) Asymptotic Normality and Accuracy of Prediction Error Estimation 1976 Ingår i: Proceedings of JACC 1976. Konferensbidrag (refereegranskat)
25.	Caines, Peter E., et al. (författare) Prediction Error Estimators : Asymptotic Normality and Accuracy 1976 Ingår i: Proceedings of the 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes. ; , s. 652-658 Konferensbidrag (refereegranskat)abstract In this paper the asymptotic normality of a large class of prediction error estimators is established. (Prediction error identification methods were introduced in [1] and further developed in [2] and [3].) The observed processes in this paper are assumed to be stationary and ergodic and the parameterized process models are taken to be non-linear regression models. In the gaussian case the results presented in this paper constitute substantial generalizations of previous results concerning the asymptotic normality of maximum likelihood estimators for (i) processes of independent random variables [9,4] and (ii) Markov processes [5]; these results also generalize previous results on the asymptotic normality of least squares estimators for autoregressive moving average processes [6,7]. The asymptotic normality theorem gives formulae for the covariances of the asymptotic distributions of the parameter estimation errors arising from the specified class of prediction error identification methods. Employing these formulae it is demonstrated that the prediction error method using the determinant of the residual error covariance matrix as loss function is asymptotically efficient with respect to the specified class of prediction error estimators regardless of the distribution of the observed processes.
26.	Carrette, Pierre, et al. (författare) Efficient Computation of Cramer-Rao Bounds for the Transfer Functions of MIMO State-Space Systems 1998 Rapport (övrigt vetenskapligt/konstnärligt)abstract The present contribution deals with the accuracy of the transfer function of state-space parametric models estimated under the prediction error identification framework. More precisely, we intend to propagate the Cramer-Rao bound usually available on the covariance matrix of the state-space parameter estimates to that of the coefficients of the corresponding input-to-output transfer function. A natural way to solve this problem is to take advantage of the Jacobian matrix of the state-space to transfer function transformation while applying Gauss' formula for evaluating the covariance of the transfer function coefficients. Here, we focus on the computational aspects of the evaluation of this Jacobian matrix. In doing so, we show that the most computationally efficient way to access this matrix is to evaluate it as the product of the Jacobian matrices associated to the two following transformations: firstly, from the original state-space model to a state-space representation where the state-feedback matrix is diagonal and, secondly, from this latter state-space representation to the model transfer function. Note that the elements of these two Jacobian matrices are evaluated analytically.
27.	Cassasco, Diego S., et al. (författare) On the Accuracy of Parameter Estimation for Continuous Time Nonlinear Systems from Sampled Data 2011 Ingår i: Proceedings of the 50th IEEE Conference on Decision and Control. - 9781612847993 - 9781612848006 ; , s. 4308-4311 Konferensbidrag (refereegranskat)abstract This paper deals with the issue of estimating the parameters in a continuous-time nonlinear dynamical model from sampled data. We focus on the issue of bias-variance trade-offs. In particular, we show that the bias error can be significantly reduced by using a particular form of sampled data model based on truncated Taylor series. This model retains the conceptual simplicity of models based on Euler integration but has much improved accuracy as a function of the sampled period.
28.	Chen, Tianshi, et al. (författare) Decentralization of Particle Filters Using Arbitrary State Decomposition 2010 Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control. - 9781424477456 ; , s. 7383-7388 Konferensbidrag (refereegranskat)abstract In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has an advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and thus can be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results from a numerical example indicates that the DPF has a potential to achieve the same level of performance as the regular PF, in a shorter execution time.
29.	Chen, Tianshi, et al. (författare) Decentralized Particle Filter with Arbitrary State Decomposition 2011 Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 59:2, s. 465-478 Tidskriftsartikel (refereegranskat)abstract In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.
30.	Chen, Tianshi, et al. (författare) Impulse Response Estimation with Binary Measurements : A Regularized FIR Model 2012 Ingår i: Proceedings of the 16th IFAC Symposium on System Identification. - 9783902823069 ; , s. 113-118 Konferensbidrag (refereegranskat)abstract FIR (finite impulse response) model is widely used in tackling the problem of the impulse response estimation with quantized measurements. Its use is, however, limited, in the case when a high order FIR model is required to capture a slowly decaying impulse response. This is because the high variance for high order FIR models would override the low bias and thus lead to large MSE (mean square error). In this contribution, we apply the recently introduced regularized FIR model approach to the problem of the impulse response estimation with binary measurements. We show by Monte Carlo simulations that the proposed approach can yield both better accuracy and better robustness than a recently introduced FIR model based approach.
31.	Chen, Tianshi, et al. (författare) Kernel Selection in Linear System Identification : Part II: A Classical Perspective 2011 Ingår i: Proceedings of the 50th IEEE Conference on Decision and Control. - 9781612847993 - 9781612848006 ; , s. 4326-4331 Konferensbidrag (refereegranskat)abstract In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed. The ideas are tested on the same data bank as used in Part I of the companion papers. The resulting findings and conclusions in the two papers are very similar despite the different perspectives.
32.	Chen, Tianshi, et al. (författare) On the Estimation of Transfer Functions, Regularizations and Gaussian Processes – Revisited 2010 Ingår i: Proceedings of the 18th IFAC World Congress. - 9783902661937 ; , s. 2303-2308 Konferensbidrag (refereegranskat)abstract Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements.We formulate a classical regularization approach, focused on ﬁnite impulse response (FIR) models, and ﬁnd that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression.
33.	Chen, Tianshi, et al. (författare) On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited 2012 Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 48:8, s. 1525-1535 Tidskriftsartikel (refereegranskat)abstract Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.
34.	Egardt, Bo, et al. (författare) Adaptive Systems Performance in the Frequency Domain 1991 Rapport (övrigt vetenskapligt/konstnärligt)
35.	Enqvist, Martin, 1976-, et al. (författare) Approximation of Non-Linear Systems in a Neighborhood of LTI Systems 2002 Ingår i: Proceedings of Reglermöte 2002. ; , s. 289-291 Konferensbidrag (övrigt vetenskapligt/konstnärligt)
36.	Enqvist, Martin, 1976-, et al. (författare) Estimating Nonlinear Systems in a Neighborhood of LTI-approximants 2002 Ingår i: Proceedings of the 41st IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780375165 ; , s. 1005-1010 vol.1 Konferensbidrag (refereegranskat)abstract The estimation of Linear Time Invariant (LTI) models is a standard procedure in system identification. Any real-life system will however be nonlinear and time-varying, and the estimated model will converge to the LTI second order equivalent (LTI-SOE) of the true system. In this paper we consider some aspects of this convergence and the distance between the true system and its LTI-SOE. We show that there may be cases where even the slightest nonlinearity may cause big differences in the LTI-SOE. We also show a result that gives conditions that guarantee that the LTI-SOE is close to "the natural" LTI approximant. Finally, an upper bound on the distance between the LTI-SOE of a nonlinear FIR system with a white input signal and the linear part of the system is derived.
37.	Enqvist, Martin, 1976-, et al. (författare) Linear Approximations of Nonlinear FIR Systems for Separable Input Processes 2005 Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 41:3, s. 459-473 Tidskriftsartikel (refereegranskat)abstract Nonlinear systems can be approximated by linear time-invariant (LTI) models in-many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the in ut should be separable of a certain order, i.e., that certain conditional expectations should be,P linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.
38.	Enqvist, Martin, 1976-, et al. (författare) LTI Approximations of Slightly Nonlinear Systems : Some Intriguing Examples 2004 Ingår i: Proceedings of Reglermöte 2004. ; , s. 639- Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied here, it seems that LTI approximations for inputs with distributions that are Gaussian or almost Gaussian are less sensitive to small nonlinearities.
39.	Enqvist, Martin, 1976-, et al. (författare) LTI Approximations of Slightly Nonlinear Systems : Some Intriguing Examples 2005 Rapport (övrigt vetenskapligt/konstnärligt)abstract Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied here, it seems that LTI approximations for inputs with distributions that are Gaussian or almost Gaussian are less sensitive to small nonlinearities.
40.	Falck, Tillmann, et al. (författare) Segmentation of Time Series from Nonlinear Dynamical Systems 2011 Ingår i: Proceedings of the 18th IFAC World Congress. - 9783902661937 ; , s. 13209-13214 Konferensbidrag (refereegranskat)abstract Segmentation of time series data is of interest in many applications, as for example in change detection and fault detection. In the area of convex optimization, the sum-of-norms regularization has recently proven useful for segmentation. Proposed formulations handle linear models, like ARX models, but cannot handle nonlinear models. To handle nonlinear dynamics, we propose integrating the sum-of-norms regularization with a least squares support vector machine (LS-SVM) core model. The proposed formulation takes the form of a convex optimization problem with the regularization constant trading off the fit and the number of segments.
41.	Fnaiech, Farhat, et al. (författare) On the Identification and Adaptive Control of Bilinear Systems 1985 Ingår i: Proceedings of the JTEA'85, 6eme Journées Tunisiennes d ' Electrotechnique et d'Automatique. - Linköping : Linköping University. ; , s. Paper 19- Rapport (övrigt vetenskapligt/konstnärligt)
42.	Fnaiech, Farhat, et al. (författare) Recursive Identification of Bilinear Systems 1985 Rapport (övrigt vetenskapligt/konstnärligt)abstract Methods of identifying bilinear systems from recorded input-output data are discussed in this article. A short survey of the existing literature on the topic is given. ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation. Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem.
43.	Fnaiech, Farhat, et al. (författare) Recursive Identification of Bilinear Systems 1987 Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 45:2, s. 453-470 Tidskriftsartikel (refereegranskat)abstract Methods of identifying bilinear systems from recorded input-output data are discussed in this article. A short survey of the existing literature on the topic is given. ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation. Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem.
44.	Forsman, Krister, et al. (författare) Merging 'Reasoning' and Filtering in a Bayesian Framework : Some Sensitivity and Optimality Aspects 1989 Ingår i: Proceedings of the 28th Conference on Decision and Control. - Linköping : Linköping University. ; , s. 1427-1429 Konferensbidrag (refereegranskat)abstract It is shown how to incorporate symbolic or logical knowledge into a conventional framework of noisy observations in dynamical systems. The idea is based on approximating the optimal solution that could, theoretically, be computed if a complete Bayesian framework were known (and infinite computational power were available). The nature of the approximations, the deviations from optimality and the sensitivity to ad hoc parameters are specifically addressed.
45.	Forsman, Krister, et al. (författare) Merging 'Reasoning' and Filtering in a Bayesian Framework - Some Sensitivity and Optimality Aspects 1991 Ingår i: International journal of adaptive control and signal processing (Print). - : Wiley. - 0890-6327 .- 1099-1115. ; 5:2, s. 93-106 Tidskriftsartikel (refereegranskat)abstract An approach is described how to incorporate knowledge of symbolic/logic character into a conventional framework of noisy observations in dynamical systems. The idea is based on approximating the optimal solution that could theoretically be computed if a complete Bayesian framework were known (and infinite computational power were available). The nature of the approximations, the deviations from optimality and the sensitivity to ad hoc parameters are specifically addressed. This merging of logic and numerics is essential in many problems of adaptation in control and signal processing.
46.	Forsman, Krister, et al. (författare) On the Dead-Zone in System Identification 1991 Ingår i: Proceedings of the 9th IFAC Symposium on System Identification and System Parameter Estimation. - Linköping : Linköping University. ; , s. 1410-1414 Rapport (övrigt vetenskapligt/konstnärligt)abstract A prediction error method for parameter estimation in a dynamical system is studied.The following problems are treated in this paper:When is the DZ estimate inconsistent, and what is the set of parameters which minimizes the criterion in the case of inconsistency?What happens to the variance of the estimate as the DZ is introduced?Does the deadzone give a better estimate than LS when there are unmodelled deterministic disturbances present?What are the relations between identification with a deadzone criterion and so called set membership identification?
47.	Forssell, Urban, et al. (författare) A Projection Method for Closed-Loop Identification 1998 Rapport (övrigt vetenskapligt/konstnärligt)abstract A new method for closed-loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed. Just as the direct method, this new method is applicable to systems with arbitrary feedback mechanisms. This is in contrast to other methods, such as the indirect method and the two-stage method, that assume linear feedback. The finite sample behavior of the proposed method is illustrated in a simulation study.
48.	Forssell, Urban, et al. (författare) A Projection Method for Closed-Loop Identification 1997 Rapport (övrigt vetenskapligt/konstnärligt)abstract A new method for closed-loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed. Just as the direct method, this new method is applicable to systems with arbitrary feedback mechanisms. This is in contrast to other methods, such as the indirect method and the two-stage method, that assume linear feedback. The finite sample behavior of the proposed method is illustrated in a simulation study.
49.	Forssell, Urban, et al. (författare) An Alternative Motivation for the Indirect Approach to Closed-Loop Identification 1999 Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 44:11, s. 2206-2209 Tidskriftsartikel (refereegranskat)abstract Direct prediction error identification of systems operating in closed loop may lead to biased results due to the correlation between the input and the output noise. The authors study this error, what factors affect it, and how it may be avoided. In particular, the role of the noise model is discussed and the authors show how the noise model should be parameterized to avoid the bias. Apart from giving important insights into the properties of the direct method, this provides a nonstandard motivation for the indirect method.
50.	Forssell, Urban, et al. (författare) Closed-Loop Identification Revisited 1997 Rapport (övrigt vetenskapligt/konstnärligt)abstract Identification of systems operating in closed loop has long been of prime interest in industrial applications. The problem offers many possibilities, and also some fallacies, and a wide variety of approaches have been suggested, many quite recently. The purpose of the current contribution is to place most of these approaches in a coherent framework, thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates. The common framework is created by the basic prediction error method, and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models. The so-called indirect methods, e.g., are indeed “direct” methods employing noise models that contain the regulator. The asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations. We also study a new projection approach to closed-loop identification with the advantage of allowing approximation of the open-loop dynamics in a given, and user-chosen frequency domain norm, even in the case of an unknown, nonlinear regulator.

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