Nonlinear systems can be approximated by linear time-invariant (LTI) models in many ways. Here, LTI models that are optimal approximations in the meansquare 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 input should be separable of a certain order, i.e., that certain conditional expectations should be 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 identification of generalized Wiener-Hammerstein systems.Keywords: System identification, Mean-square error, Nonlinear systems, Linearization Linear Approximations of Nonlinear FIR Systems for Separable Input ProcessesMartin Enqvist, Lennart Ljung 2005-12-29 AbstractNonlinear 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 input should be separable of a certain order, i.e., that certain conditional expectations should be 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 identification of generalized Wiener-Hammerstein systems.
A common issue with many system identification problems is that the true input to the system is unknown. This paper extends a previously presented indirect modeling framework that deals with identification of systems where the input is partially or fully unknown. In this framework, unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs. The resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties. Since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output, estimation of the indirect model has similar challenges as a closed-loop estimation problem. In fact, due to the generality of the indirect modeling framework it unifies a number of already existing system identification problems that are contained as special cases. For completeness, the paper is concluded with one method that can be used to estimate the indirect model as well as an experimental verification to show the applicability of the framework.
Van den, P. M. J. (2009). Order and structural dependence selection of LPV-ARX models using a nonnegative Garrote approach. In Proceedings of the 48th IEEE Conference on Decision and Control (CDC 2009), 16-18 December 2009 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. Abstract-In order to accurately identify Linear ParameterVarying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.
Abstract-This paper presents a behavioral model structure and a model-based phase-only predistortion method suitable for outphasing RF amplifiers. The predistortion method is based on a model of the amplifier with a constant gain factor and phase rotation for each outphasing signal, and a predistorter with phase rotation only. The method has been used for EDGE and WCDMA signals applied to a Class-D outphasing RF amplifier with an on-chip transformer used for power combining in 90nm CMOS. The measured peak power at 2 GHz was +10.3 dBm with a drain efficiency and power-added efficiency of 39 % and 33 %, respectively. For an EDGE 8-PSK signal with a phase error of 3• between the two input outphasing signals, the measured power at 400 kHz offset was -65.9 dB with predistortion, compared to -53.5 dB without predistortion. For a WCDMA signal with the same phase error between the input signals, the measured ACLR at 5 MHz offset was -50.2 dBc with predistortion, compared to -38.0 dBc without predistortion.
The prediction-error approach to parameter estimation of linear models often involves solving a non-convex optimization problem. In some cases, it is therefore difficult to guarantee that the global optimum will be found. A common way to handle this problem is to find an initial estimate, hopefully lying in the region of attraction of the global optimum, using some other method. The prediction-error estimate can then be obtained by a local search starting at the initial estimate. In this paper, a new approach for finding an initial estimate of certain linear models utilizing structure and the subspace method is presented. The polynomial models are first written on the observer canonical state-space form, where the specific structure is later utilized, rendering least-squares estimation problems with linear equality constraints.Keywords: System identification, Subspace method, Black-box models. Handling Certain Structure Information in Subspace IdentificationC. Lyzell * M. Enqvist * L. Ljung * * Division of Automatic Control, Department of Electrical Engineering, Linköpings Universitet, SE -581 83, Linköping, Sweden.(E-mail: {lyzell,maren,ljung}@isy.liu.se)Abstract: The prediction-error approach to parameter estimation of linear models often involves solving a non-convex optimization problem. In some cases, it is therefore difficult to guarantee that the global optimum will be found. A common way to handle this problem is to find an initial estimate, hopefully lying in the region of attraction of the global optimum, using some other method. The prediction-error estimate can then be obtained by a local search starting at the initial estimate. In this paper, a new approach for finding an initial estimate of certain linear models utilizing structure and the subspace method is presented. The polynomial models are first written on the observer canonical state-space form, where the specific structure is later utilized, rendering least-squares estimation problems with linear equality constraints.
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