System Identification Toolbox™

sigmoidnet

Class representing sigmoid network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models

Syntax

s=sigmoidnet('NumberOfUnits',N) s=sigmoidnet(Property1,Value1,...PropertyN,ValueN)

Description

sigmoidnet is an object that stores the sigmoid network nonlinear estimator for estimating nonlinear ARX and Hammerstein-Wiener models.

You can use the constructor to create the nonlinearity object, as follows:

s=sigmoidnet('NumberOfUnits',N) creates a sigmoid nonlinearity estimator object with N terms in the sigmoid expansion.

s=sigmoidnet(Property1,Value1,...PropertyN,ValueN) creates a sigmoid nonlinearity estimator object specified by properties in sigmoidnet Properties.

Use evaluate(s,x) to compute the value of the function defined by the sigmoidnet object s at x.

Remarks

Use sigmoidnet to define a nonlinear function , where y is scalar and x is an m-dimensional row vector. The sigmoid network function is based on the following expansion:

where f is the sigmoid function, given by the following equation:

P and Q are m-by-p and m-by-q projection matrices. The projection matrices P and Q are determined by principal component analysis of estimation data. Usually, p=m. If the components of x in the estimation data are linearly dependent, then p<m. The number of columns of Q, q, corresponds to the number of components of x used in the sigmoid function.

When used in a nonlinear ARX model, q is equal to the size of the NonlinearRegressors property of the idnlarx object. When used in a Hammerstein-Wiener model, m=q=1 and Q is a scalar.

r is a 1-by-m vector and represents the mean value of the regressor vector computed from estimation data.

d, a_k, and c_k are scalars.

L is p-by-1 vector.

b_k are q-by-1 vectors.

sigmoidnet Properties

You can include property-value pairs in the constructor to specify the object.

After creating the object, you can use get or dot notation to access the object property values. For example:

% List all property values
get(s)
% Get value of NumberOfUnits property
s.NumberOfUnits

You can also use the set function to set the value of particular properties. For example:

set(s, 'LinearTerm', 'on')

The first argument to set must be the name of a MATLAB^® variable.

Property Name Description

Property Name	Description
`NumberOfUnits`	Integer specifies the number of nonlinearity units in the expansion. Default=`10`. For example: sigmoidnet(H,'NumberOfUnits',5)
`LinearTerm`	Can have the following values: `'on'`—Estimates the vector L in the expansion. `'off'`—Fixes the vector L to zero. For example: sigmoidnet(H,'LinearTerm','on')
`Parameters`	A structure containing the parameters in the nonlinear expansion, as follows: `RegressorMean`: 1-by-`m` vector containing the means of `x` in estimation data, `r`. `NonLinearSubspace`: `m`-by-`q` matrix containing Q. `LinearSubspace`: `m`-by-`p` matrix containing P. `LinearCoef`: `p`-by-1 vector L. `Dilation`: `q`-by-`n` matrix containing the values `b_k`. `Translation`: 1-by-`n` vector containing the values `c_k`. `OutputCoef`: `n`-by-1 vector containing the values `a_k`. `OutputOffset`: scalar `d`. Typically, the values of this structure are set by estimating a model with a `sigmoidnet` nonlinearity.

NumberOfUnits

Integer specifies the number of nonlinearity units in the expansion.
Default=10.

For example:

sigmoidnet(H,'NumberOfUnits',5)

LinearTerm

Can have the following values:

'on'—Estimates the vector L in the expansion.
'off'—Fixes the vector L to zero.

For example:

sigmoidnet(H,'LinearTerm','on')

Parameters

A structure containing the parameters in the nonlinear expansion, as follows:

RegressorMean: 1-by-m vector containing the means of x in estimation data, r.
NonLinearSubspace: m-by-q matrix containing Q.
LinearSubspace: m-by-p matrix containing P.
LinearCoef: p-by-1 vector L.
Dilation: q-by-n matrix containing the values b_k.
Translation: 1-by-n vector containing the values c_k.
OutputCoef: n-by-1 vector containing the values a_k.
OutputOffset: scalar d.

Typically, the values of this structure are set by estimating a model with a sigmoidnet nonlinearity.

Examples

Use sigmoidnet to specify the nonlinear estimator in nonlinear ARX and Hammerstein-Wiener models. For example: