Subspace identification of Hammerstein systems using least squares support vector machines (original) (raw)
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IET Control Theory & Applications, 2009
A recursive scheme for the identification of SIMO Hammerstein models is presented. In the proposed scheme, first the Markov parameters of the system are determined, by a least squares support vector machines regression through an over-parameterisation technique. Then, a state-space realisation of the system is retrieved using a recursive subspace identification method. Simulation results are provided to demonstrate the effectiveness of the algorithm.
NARX Identification of Hammerstein Systems Using Least-Squares Support Vector Machines
Lecture Notes in Control and Information Sciences, 2010
This chapter describes a method for the identification of a SISO and MIMO Hammerstein systems based on Least Squares Support Vector Machines (LS-SVMs). The aim of this chapter is to give a practical account of the works and , adding to this material new insights published since. The identification method presented in this chapter gives estimates for the parameters governing the linear dynamic block represented as an ARX model, as well as for the unknown static nonlinear function. The method is essentially based on Bai's overparameterization technique, and combines this with a regularization framework and a suitable model description which fits nicely within the LS-SVM framework with primal and dual model representations. This technique is found to cope effectively (i) with the ill-conditioning typically occurring in overparameterization approaches, and (ii) with cases where no stringent assumptions can be made about the nature of the nonlinearity except for a certain degree of smoothness.
Hammerstein system identification using LS-SVM and steady state time response
2016 European Control Conference (ECC), 2016
In this paper a new system identification approach for Hammerstein systems is proposed. A straightforward estimation of the nonlinear block through the use of LS-SVM is done by making use of the behavior of Hammerstein systems in steady state. Using the estimated nonlinear block, the intermediate variable is calculated. Using the latter and the known output, the linear block can be estimated. The results indicate that the method can effectively identify Hammerstein systems also in the presence of a considerable amount of noise. The well-known capabilities of LS-SVM for the representation of nonlinear functions play an important role in the generalization capabilities of the method allowing to work with a wide range of model classes. The proposed method's main strength lies precisely in the identification of the nonlinear block of the Hammerstein system. The relevance of these findings resides in the fact that a very good estimation of the inner workings of a Hammerstein system can be achieved.
An identification algorithm for Hammerstein systems using subspace method
Proceedings of the 2011 American Control Conference, 2011
This paper describes a new algorithm for the identification of single-input single-output Hammerstein systems using the multivariable output error state space (MOESP) class of subspace identification algorithms. The algorithm consists of three main steps. First, the MOESP algorithm is used to determine the system order and estimate two of the state space model matrices. Second, a least squares problem is solved to minimize the prediction error. Finally, the global search optimization is needed to be used to estimate optimal values for the remaining parameters. Performance of the model was evaluated by simulating a model of ankle joint reflex stiffness, a well known Hammerstein system. The results demonstrate that the algorithm estimated the model parameters very accurately in the presence of additive, output noise.
Hammerstein system identification through best linear approximation inversion and regularisation
International Journal of Control, 2017
Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.
Identification of MIMO Hammerstein models using least squares support vector machines
Automatica, 2005
This paper studies a method for the identification of Hammerstein models based on Least Squares Support Vector Machines (LS-SVMs). 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.
Least-Squares Support Vector Machines for the identification of Wiener–Hammerstein systems
Control Engineering Practice, 2012
This paper considers the identification of Wiener-Hammerstein systems using Least-Squares Support Vector Machines based models. The power of fully black box NARX-type models is evaluated and compared with models including information about the structure of the systems. For the NARX models it is shown how to extend the kernel based estimator to large data sets. For the structured model the emphasis is on preserving the convexity of the estimation problem through a suitable relaxation of the original problem. To develop an empirical understanding of the implications of the different model design choices, all considered models are compared on an artificial system under a number of different experimental conditions. The obtained results are then validated on the Wiener-Hammerstein benchmark data set and the final models are presented. It is illustrated that black box models are a suitable technique for the identification of Wiener-Hammerstein systems. The incorporation of structural information as well as using large data sets give rise to significant improvements in modeling performance.
An Iterative Algorithm for the Subspace Identification of SISO Hammerstein Systems
IFAC Proceedings Volumes, 2011
This paper describes an algorithm to identify state-space models for single input single output (SISO) Hammerstein structures based on input-output measurements. The algorithm consists of two main steps. First, a subspace algorithm is used to determine the system order and estimate the A and C system matrices. Estimation of the other state space matrices as well as the nonlinearity is then formulated as nonlinear optimization problem in which the state space model of the linear component and the coefficients of the basis function expansion of the nonlinear component are distinct. This formulation minimizes the number of parameters to estimate; moreover any one parameter is related to either the linear dynamics or the static nonlinearity. The unknown parameters are then estimated using an iterative procedure that solves a least square problem at each step. Simulation studies using a well known model of ankle joint reflex stiffness demonstrate that the algorithm is accurate and performs well in the non-ideal conditions that prevail during practical experiments.
Identification of Wiener-Hammerstein systems by means of Support Vector Machines for Regression
2007
Wiener-Hammerstein models are flexible, well known and often studied. The main challenge in identifying a Wiener-Hammerstein model is to distinguish the linear time invariant (LTI) blocks at the front and the back. This paper presents a nonparametric approach to separate the front and back dynamics starting from the best linear approximation (BLA). Next, the nonparametric estimates of the LTI blocks in the model can be parametrized, taking into account a phase shift degeneration. Once the dynamics are known, the estimation of the static nonlinearity boils down to a simple linear least squares problem. The consistency of the proposed approach is discussed and the method is validated on the Wiener-Hammerstein benchmark that was presented at the IFAC SYSID conference in 2009.
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 function-approximation and allows to determine the memoryless static nonlinearity as well as the linear model parameters. As the technique is non-parametric by nature, no assumptions about the static nonlinearity need to be made.