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Identification of MIMO Hammerstein Models using Least Squares Support Vector Machines
, 2004
"... This paper studies a method for the identification of Hammerstein models based on Least Squares Support Vector Machines (LSSVMs). The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic ARX part. The SISO as w ..."
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This paper studies a method for the identification of Hammerstein models based on Least Squares Support Vector Machines (LSSVMs). The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic ARX part. The SISO as well as the MIMO identification cases are elaborated. The technique can lead to significant improvements with respect to classical methods as illustrated on a number of examples as no stringent assumptions on the nature of the nonlinearity need to be imposed.
Subspace Identification of Hammerstein Systems using Least Squares Support Vector Machines
 IEEE Trans. on Automatic Control
, 2005
"... In this paper, a method for the identification of multiinput/multioutput Hammerstein systems is presented. The method extends the N4SID linear subspace identification algorithm, mainly by rewriting the oblique projection in the N4SID algorithm as a set of componentwise LSSVM regression problems. ..."
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In this paper, a method for the identification of multiinput/multioutput Hammerstein systems is presented. The method extends the N4SID linear subspace identification algorithm, mainly by rewriting the oblique projection in the N4SID algorithm as a set of componentwise LSSVM regression problems. The linear model and static nonlinearities are obtained from a rank 1 approximation of a matrix produced by this regression problem. Keywords: Subspace identification, Hammerstein models, Least Squares Support Vector Machines. 1
On the identification of nonlinear maps in a general interconnected system
 In Proceedings of the 1999 American Controls Conference
, 1999
"... This paper is concerned with the problem of identifying static nonlinear maps in a general, structured interconnected system. These static nonlinear maps are nonparametric in that they do not have a natural parameterization that is known or suggested from an analytical understanding of the underlyin ..."
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Cited by 4 (2 self)
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This paper is concerned with the problem of identifying static nonlinear maps in a general, structured interconnected system. These static nonlinear maps are nonparametric in that they do not have a natural parameterization that is known or suggested from an analytical understanding of the underlying process. Our technique involves selecting the nonlinear maps so as to maximize the “smoothness ” or “staticness ” of these maps while respecting the available inputoutput data and the noise model. These techniques avoid bias problems that arise when imposing artificial parameterizations on the nonlinearities. Computationally, these methods reduce to iterative least squares problems together with Kalman smoothing. Preliminary examples reveal the promise of these techniques. 1
Narx Identification of Hammerstein Models Using Least Squares Support Vector Machines
, 2004
"... In this paper we propose a new technique for the identification of NARX Hammerstein systems. The new technique is based on the theory of Least Squares Support Vector Machines functionapproximation and allows to determine the memoryless static nonlinearity as well as the linear model parameters. ..."
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In this paper we propose a new technique for the identification of NARX Hammerstein systems. The new technique is based on the theory of Least Squares Support Vector Machines functionapproximation and allows to determine the memoryless static nonlinearity as well as the linear model parameters. As the technique is nonparametric by nature, no assumptions about the static nonlinearity need to be made.
PARAMETRIC IDENTIFICATION OF STATIC NONLINEARITIES IN A GENERAL INTERCONNECTED SYSTEM
"... Abstract: We are concerned with the identification of static nonlinear maps in a structured interconnected system. Structural information is often neglected in nonlinear system identification methods. In this paper, we exploit a priori structural information and use parametric identification methods ..."
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Abstract: We are concerned with the identification of static nonlinear maps in a structured interconnected system. Structural information is often neglected in nonlinear system identification methods. In this paper, we exploit a priori structural information and use parametric identification methods. We focus on the case where the linear part of the interconnection is known and only the static nonlinear components require identification. We propose an identification algorithm and investigate its convergence properties. Copyright c○2005 IFAC
On the Identification of Hammerstein Systems Having Saturationlike Functions with Positive Slopes
, 2004
"... Abstract. The aim of the given paper is the development of an approach for parametric identification of Hammerstein systems with piecewise linear nonlinearities, i.e., when the saturationlike function with unknown slopes is followed by a linear part with unknown parameters. It is shown here that b ..."
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Abstract. The aim of the given paper is the development of an approach for parametric identification of Hammerstein systems with piecewise linear nonlinearities, i.e., when the saturationlike function with unknown slopes is followed by a linear part with unknown parameters. It is shown here that by a simple input data rearrangement and by a following data partition the problem of identification of a nonlinear Hammerstein system could be reduced to the linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of inputoutput data. A technique based on ordinary least squares is proposed here for the estimation of parameters of linear and nonlinear parts of the Hammerstein system, including the unknown threshold of the piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of inputoutput signals of a discretetime Hammerstein system with a piecewise nonlinearity with positive slopes by computer are given. Key words: nonlinear systems, system identification, Hammerstein systems, parameter estimation. 1.
SUMMARY
"... The paper deals with recovering nonlinearities in the Hammerstein systems by using multiresolution approximation a basic concept of wavelet theory. The systems are driven by random signals and are disturbed by additive, white or coloured, random noise. The a priori information about system compone ..."
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The paper deals with recovering nonlinearities in the Hammerstein systems by using multiresolution approximation a basic concept of wavelet theory. The systems are driven by random signals and are disturbed by additive, white or coloured, random noise. The a priori information about system components is nonparametric and a delay in the dynamical part of systems is admitted. A nonparametric identification algorithm for estimating nonlinear characteristics of static parts is proposed and investigated. The algorithm is based on the Haar multiresolution approximation. The pointwise convergence and pointwise asymptotic rate of convergence of the algorithm are established. It is shown that neither the form nor the convergence conditions of the algorithm need any modification for the noise being not white but correlated. Also the asymptotic rate of convergence is the same for white and coloured noise. The theoretical results are confirmed by computer simulations. KEY WORDS: Hammerstein system; nonlinearity recovering; nonparametric identification; multiresolution approximation
Nonparametric Hammerstein Model Based Model Predictive Control for Heart Rate Regulation
"... Abstract — This paper proposed a novel nonparametric model based model predictive control approach for the regulation of heart rate during treadmill exercise. As the model structure of human cardiovascular system is often hard to determine, nonparametric modelling is a more realistic manner to desc ..."
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Abstract — This paper proposed a novel nonparametric model based model predictive control approach for the regulation of heart rate during treadmill exercise. As the model structure of human cardiovascular system is often hard to determine, nonparametric modelling is a more realistic manner to describe complex behaviours of cardiovascular system. This paper presents a new nonparametric Hammerstein model identification approach for heart rate response modelling. Based on the pseudorandom binary sequence experiment data, we decouple the identification of linear dynamic part and input nonlinearity of the Hammerstein system. Correlation analysis is applied to acquire step response of linear dynamic component. Support Vector Regression is adopted to obtain a nonparametric description of the inverse of input static nonlinearity that is utilized to form an approximate linear model of the Hammerstein system. Based on the established model, a model predictive controller under predefined speed and acceleration constraints is designed to achieve safer treadmill exercise. Simulation results show that the proposed control algorithm can achieve optimal heart rate tracking performance under predefined constraints.