A Basis-Function Canonical Piecewise-Linear Approximation

This paper proposes a basis-function canonical piecewise-linear (BF-CPWL) function, which can approximate any continuous function using a weighted sum of PWL BFs. The BF-CPWL approximation integrates Breiman's hinging hyperplane model and Julian's high-level canonical PWL approximation int...

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Vydáno v:IEEE transactions on circuits and systems. I, Regular papers Ročník 55; číslo 5; s. 1328 - 1334
Hlavní autoři: Chengtao Wen, Chengtao Wen, Xiaoyan Ma, Xiaoyan Ma
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.06.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Approximation
Approximation algorithms
Canonical piecewise-linear representation (CPWL)
Circuit synthesis
Circuits
Control system synthesis
Control systems
Convergence
Dynamical systems
Iterative algorithms
Least squares methods
Mathematical analysis
Mathematical models
Newton method
nonlinear approximation
nonlinear circuit synthesis
Nonlinear circuits
Piecewise linear techniques
PWL basis function (BF)
Recursive estimation
Canonical Piecewise-linear representation
PWL basis function
Nonlinear approximation
nonlinear circuit synthesis
ISSN:1549-8328, 1558-0806
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Popis
Shrnutí:This paper proposes a basis-function canonical piecewise-linear (BF-CPWL) function, which can approximate any continuous function using a weighted sum of PWL BFs. The BF-CPWL approximation integrates Breiman's hinging hyperplane model and Julian's high-level canonical PWL approximation into a common theoretical framework. Moreover, an approximation algorithm is developed, which fits and adds the PWL BFs iteratively using a modified Gauss-Newton method. This algorithm guarantees a local convergence, while achieving a good tradeoff between computational simplicity and approximation accuracy. The BF-CPWL approximation can find applications in nonlinear circuit synthesis, dynamic system identification and control.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2008.916552