| 1. |
- Iouditski, Anatoli, et al.
(författare)
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Adaptive DWO Estimator of a Regression Function
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.
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| 2. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Adaptive DWO Estimator of a Regression Function
- 2004
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Ingår i: Proceedings of the 2004 IFAC Symposium on Nonlinear Control Systems.
-
Konferensbidrag (refereegranskat)abstract
- We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.
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| 3. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
An Integrated System Identification Toolbox for Linear and Nonlinear Models
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 931-936
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Konferensbidrag (refereegranskat)abstract
- The paper describes additions to the MATLAB system identification toolbox, that handle also the estimation of nonlinear models. Both structured grey-box models and general, flexible black-box models are covered. The idea is that the look and feel of the syntax, and the graphical user interface should be as close as possible to the linear case.
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| 4. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
An Integrated System Identification Toolbox for Linear and Nonlinear Models
- 2007
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The paper describes additions to the MATLAB system identification toolbox, that handle also the estimation of nonlinear models. Both structured grey-box models and general, flexible black-box models are covered. The idea is that the look and feel of the syntax, and the graphical user interface should be as close as possible to the linear case.
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| 5. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Estimation of Grey Box and Black Box Models for Non-Linear Circuit Data
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Identification of non-linear systems is a challenge, due to the richness of both model structures and estimation approaches. As a case study, in this paper we test a number of methods on a data set collected from an electrical circuit at the Free University of Brussels. These methods are based on black box and grey box model structures or on a mixture of them, which are all implemented in a forthcoming Matlab toolbox. The results of this case study illustrate the importance of the use of custom (user defined) regressors in a black box model. Based on physical knowledge or on insights gained through experience, such custom regressors allow to build efficient models with a relatively simple model structure.
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| 6. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Identification of Wiener System with Monotonous Nonlinearity
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 166-171
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Konferensbidrag (refereegranskat)abstract
- A Wiener system is composed of a linear dynamic subsystem followedby a static nonlinearity. It is well known in the literature that the identifcationof the linear subsystem of a Wiener system can be separated from that of theoutput nonlinearity, if the input signal is a Gaussian noise. In order to deal withthe non Gaussian input case, two new algorithms are proposed in this paper fordirect identifcation of the linear subsystem, regardless of any parametrization ofthe output nonlinearity. The essential assumption required in this paper is thestrict monotonousness of the output nonlinearity.
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| 7. |
- Zhang, Qinghua, et al.
(författare)
-
Identification of Wiener Systems with Monotonous Nonlinearity
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A Wiener system is composed of a linear dynamic subsystem followed by a static nonlinearity. It is well known in the literature that the identification of the linear subsystem of a Wiener system can be separated from that of the output nonlinearity, if the input signal is Gaussian distributed. In order to deal with the non Gaussian input case, two new algorithms are proposed in this paper for direct identification of the linear subsystem, regardless of any parametrization of the output nonlinearity. The essential assumption required in this paper is the strict monotonousness of the output nonlinearity.
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