Custom nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
C=customnet(H)
C=customnet(H,PropertyName,PropertyValue)
customnet is an object that stores a custom
nonlinear estimator with a user-defined unit function. This custom
unit function uses a weighted sum of inputs to compute a scalar output.
C=customnet(H) creates a nonlinearity estimator
object with a user-defined unit function using the function handle H. H must
point to a function of the form [f,g,a] = function_name(x),
where f is the value of the function, g
= df/dx, and a indicates the unit function
active range. g is significantly nonzero in the
interval [-a a]. Hammerstein-Wiener models require
that your custom nonlinearity have only one input and one output.
C=customnet(H, creates
a nonlinearity estimator using property-value pairs defined in customnet Properties.PropertyName,PropertyValue)
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(C) % Get value of NumberOfUnits property C.NumberOfUnits
You can also use the set function to set
the value of particular properties. For example:
set(C, 'LinearTerm', 'on')
set must be the name of a MATLAB® variable.| Property Name | Description |
|---|---|
NumberOfUnits | Integer specifies the number of nonlinearity units in
the expansion. For example: customnet(H,'NumberOfUnits',5) |
LinearTerm | Can have the following values:
For example: customnet(H,'LinearTerm','on') |
Parameters |
A structure containing the parameters in the nonlinear expansion, as follows:
Typically, the values of this structure are set by estimating a model with a
|
UnitFcn | Stores the function handle that points to the unit function. |
Define custom unit function and save it in gaussunit.m:
function [f, g, a] = GAUSSUNIT(x) % x: unit function variable % f: unit function value % g: df/dx % a: unit active range (g(x) is significantly % nonzero in the interval [-a a]) % The unit function must be "vectorized": for % a vector or matrix x, the output arguments f and g % must have the same size as x, % computed element-by-element. % GAUSSUNIT customnet unit function example [f, g, a] = gaussunit(x) f = exp(-x.*x); if nargout>1 g = - 2*x.*f; a = 0.2; end
Use custom networks in nlarx and nlhw model estimation commands:
% Define handle to example unit function. H = @gaussunit; % Estimate nonlinear ARX model using % Gauss unit function with 5 units. m = nlarx(Data,Orders,customnet(H,'NumberOfUnits',5));
Use customnet to define a nonlinear function , where y is
scalar and x is an m-dimensional
row vector. The unit function is based on the following function expansion
with a possible linear term L:
where f is a unit function that you define using the function handle H.
P and Q are m-by-p and m-by-q projection
matrices, respectively. 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 unit
function.
When used to estimate nonlinear ARX models, q is
equal to the size of the NonlinearRegressors property
of the idnlarx object. When
used to estimate Hammerstein-Wiener models, 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, and c are scalars.
L is a p-by-1
vector.
b represents q-by-1
vectors.
The function handle of the unit function of the custom net must
have the form [f,g,a] = function_name(x). This
function must be vectorized, which means that for a vector or matrix x,
the output arguments f and g must
have the same size as x and be computed element-by-element.
customnet uses an iterative search technique
for estimating parameters.