Adaptive nonlinear digital filter with canonical piecewise-linear structure

Lin, Ji-Nan; Unbehauen, R.

doi:10.1109/31.52728

Cited by 61 publications

(30 citation statements)

References 11 publications

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“…The problems associated with the determination of these regions and the CPWL approximations have been extensively studied in the literature. For example, Lin and Unbehahuen [12] proved that CPWL models can approximate as much as it is desired a continuous non-linear function on a compact set of variables. Lin and Unbehahuen [13] proposes an algorithm for adjust a CPWL model of one variable, this method could be applied in conjunction with the algorithm due to Yamamura [14] that allows the representation of a general non-linear function as a superposition of non-linear terms of one variable.…”

Section: Appendix A: Canonical Piecewise Linear Functionsmentioning

confidence: 98%

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Dynamic ‘back‐off’ analysis: use of piecewise linear approximations

Figueroa

Desages

2003

Optim Control Appl Methods

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SUMMARYThe operating point of a process is usually computed by optimizing an objective function, e.g. the profit, subject to some plant characteristics. Typically, the resulting point lies on the boundary of the operating region. At this point, the presence of disturbances can easily cause constraint violations and make the process move to the unfeasible region. Then, it is necessary to move the operating point away into the feasible region by considering the effect that the expected disturbances will have on the operation of the plant. The purpose of this paper is to present an efficient algorithm to modify the operating point in order to keep feasibility (both in steady-state and along transitory) in the process operation against the disturbances.

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Section: Appendix A: Canonical Piecewise Linear Functionsmentioning

confidence: 98%

“…Introducing this expression in (12), the objective function constrained to the kth sector could be written as…”

Section: Solution To the Dynamic Back-off Problemmentioning

confidence: 99%

Dynamic ‘back‐off’ analysis: use of piecewise linear approximations

Figueroa

Desages

2003

Optim Control Appl Methods

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“…Related to this work, in [23] the researchers proposed the use of a canonical piecewise linear representation using a structure similar to that discussed in [4]. We call this realization the Lin-Unbehauen piecewise linear (LUPWL) represen- tation.…”

Section: Introductionmentioning

confidence: 99%

“…We present in this work a CPWL filter, the simplicial canonical piecewise linear (SPWL) filter, in the context of nonlinear Wiener models aiming to put in evidence the simple way in which this realization can describe these kind of models (if compared for example with [34]) and, also, to put in evidence the advantages of the resulting filter in terms of low complexity due to the reduced number of parameters (with respect to [23]). …”

Section: Introductionmentioning

confidence: 99%

A Simplicial Canonical Piecewise Linear Adaptive Filter

Figueroa

Cousseau

Figueiredo

2004

Circuits Syst Signal Process

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A new adaptive nonlinear filter realization is presented based on a canonical piecewise linear (CPWL) approach. This filter realization consists of a linear part represented by a finite impulse response filter and a zero-memory nonlinear part implemented as a CPWL map. The resultant structure requires fewer parameters than other realizations found in the literature with comparable modeling capabilities. As a consequence, the proposed nonlinear filter, in addition to its simple description, has low computation and implementation costs. Some results related to convergence properties and implementation of the adaptive algorithm associated to this new realization are presented. The performance of the proposed filter is illustrated through simulation examples.

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“…The main object of the analysis is to compare the filter network properties with the classical adaptive filters [l], the filters from [2] and [3] and the well known 3-layer feed-forward neural networks [4]. The filter network has a structural relationship to a 3-layer feed-forward neural network, where the filter network parameters: N , t h r and thn, are related to the feedforward neural network parameters: The number of input nodes, the number of nodes in the hidden layer and the connectivity between the hidden layer and the output layer.…”

Section: Initial Investigationmentioning

confidence: 99%

A family of quantization based piecewise linear filter networks

Sorensen

1992

[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing

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A family of quantization based piecewise linear filter networks is proposed. For stationary signals a filter network from this family is a generalization of the classical Wiener filter with an input signal and a desired response. The construction of the filter network is based on the following elements: Quantization of the input signal x(n) into quantization classes. To each quantization class is associated a linear filter. The filtering at time n is carried out by the filter belonging to the actual quantization class of x(n) and the filters belonging to the neighbor quantization classes of x(n) (regularization). This construction leads to a 3-layer filter network. The first layer consists of the quantization class filters for the input signal. The second layer carry out the regularization between neighbor quantization classes and the third layer constitutes a decision of quantization class from where the resulting output is obtained.

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Adaptive nonlinear digital filter with canonical piecewise-linear structure

Cited by 61 publications

References 11 publications

Dynamic ‘back‐off’ analysis: use of piecewise linear approximations

Dynamic ‘back‐off’ analysis: use of piecewise linear approximations

A Simplicial Canonical Piecewise Linear Adaptive Filter

A family of quantization based piecewise linear filter networks

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