A nonparametric kernel-based approach to Hammerstein system identification

Risuleo, Riccardo Sven; Bottegal, Giulio; Hjalmarsson, Håkan

doi:10.1016/j.automatica.2017.07.055

Cited by 47 publications

(31 citation statements)

References 46 publications

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“…The concept of exact decomposition will be made clear throughout the paper. We also demonstrate strong connections with our recently proposed method [25], effectively proving that, although the two approaches are inherently different, the estimates obtained with the two methods are equivalent. Finally, we show, through several numerical experiments, that the proposed method outperforms both the algorithm proposed in [2] and the standard matlab system identification toolbox function for Hammerstein system identification.…”

Section: Introductionsupporting

confidence: 55%

A new kernel-based approach to overparameterized Hammerstein system identification

Risuleo

Bottegal

Hjalmarsson

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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The object of this paper is the identification of Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of p basis functions. We model the system dynamics by means of an np-dimensional vector. This vector, usually referred to as overparameterized vector, contains all the combinations between the nonlinearity coefficients and the first n samples of the impulse response of the linear block. The estimation of the overparameterized vector is performed with a new regularized kernel-based approach. To this end, we introduce a novel kernel tailored for overparameterized models, which yields estimates that can be uniquely decomposed as the combination of an impulse response and p coefficients of the static nonlinearity. As part of the work, we establish a clear connection between the proposed identification scheme and our recently developed nonparametric method based on the stable spline kernel.

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Section: Introductionsupporting

confidence: 55%

A new kernel-based approach to overparameterized Hammerstein system identification

Risuleo

Bottegal

Hjalmarsson

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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“…Consider the complete-data likelihood (39). From (32) we have that log q w = E log p(y, v, g, w; τ ) , where the expectation is taken with respect to q g .…”

Section: A3 Proof Of Theoremmentioning

confidence: 99%

Modeling and identification of uncertain-input systems

2019

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In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about the input or the linear system, we use Gaussian-process models. We estimate the model from data using the empirical Bayes approach: the input and the impulse responses of the linear system are estimated using the posterior means of the Gaussian-process models given the data, and the hyperparameters that characterize the Gaussian-process models are estimated from the marginal likelihood of the data. We propose an iterative algorithm to find the hyperparameters that relies on the EM method and results in simple update steps. In the most general formulation, neither the marginal likelihood nor the posterior distribution of the unknowns is tractable. Therefore, we propose two approximation approaches, one based on Markov-chain Monte Carlo techniques and one based on variational Bayes approximation. We also show special model structures for which the distributions are treatable exactly. Through numerical simulations, we study the application of the uncertain-input model to the identification of Hammerstein systems and cascaded linear systems. As part of the contribution of the paper, we show that this model structure encompasses many classical problems in system identification such as classical PEM, Hammerstein models, errors-in-variables problems, blind system identification, and cascaded linear systems. This allows us to build a systematic procedure to apply the algorithms proposed in this work to a wide class of classical problems.

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“…In order to employ EMtype algorithms, one has to define a latent variable; in our problem, a natural choice is s 11 . Then, a (local) solution to (22) is achieved by iterating over the following steps: (E-step) Given an estimateη (k) (computed at the k-th iteration of the algorithm), compute…”

Section: Computation Of the Solution Of The Marginal Likelihood Cmentioning

confidence: 99%

“…The effectiveness of the proposed method is demonstrated through numerical experiment. The method proposed in this paper is close in spirit to some recently proposed kernelbased techniques for blind system identification [21] and Hammerstein system identification [22].…”

Section: Introductionmentioning

confidence: 99%

Identification of modules in dynamic networks: An empirical Bayes approach

Everitt

Bottegal

Rojas

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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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 ExpectationMaximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method.

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A nonparametric kernel-based approach to Hammerstein system identification

Cited by 47 publications

References 46 publications

A new kernel-based approach to overparameterized Hammerstein system identification

A new kernel-based approach to overparameterized Hammerstein system identification

Modeling and identification of uncertain-input systems

Identification of modules in dynamic networks: An empirical Bayes approach

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