nlarxOptions
Option set for nlarx
Description
creates
an option set with options specified by one or more opt
= nlarxOptions(Name,Value
)Name,Value
pair
arguments.
Examples
Create Default Option Set for Nonlinear ARX Estimation
opt = nlarxOptions;
Create and Modify Default Nonlinear ARX Option Set
Create a default option set for nlarx
, and use dot notation to modify specific options.
opt = nlarxOptions;
Turn on the estimation progress display.
opt.Display = 'on';
Minimize the norm of the simulation error.
opt.Focus = 'simulation';
Use a subspace GaussNewton least squares search with a maximum of 25 iterations.
opt.SearchMethod = 'gn';
opt.SearchOptions.MaxIterations = 25;
Specify Options for Nonlinear ARX Estimation
Create an option set for nlarx
specifying the following options:
Turn off iterative estimation for the default wavelet network estimation.
Turn on the estimation progressviewer display.
opt = nlarxOptions('IterativeWavenet','off','Display','on');
Input Arguments
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'Focus','simulation','SearchMethod','grad'
specifies
that the norm of the simulation error is minimized using a steepest
descent least squares search.
Focus
— Minimization objective
'prediction'
(default)  'simulation'
Minimization objective, specified as the commaseparated pair
consisting of 'Focus'
and one of the following:
'prediction'
— Minimize the norm of the prediction error, which is defined as the difference between the measured output and the onestep ahead predicted response of the model.'simulation'
— Minimize the norm of the simulation error, which is defined as the difference between the measured output and simulated response of the model.
Display
— Estimation progress display setting
'off'
(default)  'on'
Estimation progress display setting, specified as the commaseparated
pair consisting of 'Display'
and one of the following:
'off'
— No progress or results information is displayed.'on'
— Information on model structure and estimation results are displayed in a progressviewer window.
OutputWeight
— Weighting of prediction error in multioutput estimations
'noise'
(default)  positive semidefinite matrix
Weighting of prediction error in multioutput model estimations,
specified as the commaseparated pair consisting of 'OutputWeight'
and
one of the following:
'noise'
— Optimal weighting is automatically computed as the inverse of the estimated noise variance. This weighting minimizesdet(E'*E)
, whereE
is the matrix of prediction errors. This option is not available when using'lsqnonlin'
as a'SearchMethod'
.A positive semidefinite matrix,
W
, of size equal to the number of outputs. This weighting minimizestrace(E'*E*W/N)
, whereE
is the matrix of prediction errors andN
is the number of data samples.
Normalize
— Option to normalize estimation data
true
(default)  false
Option to normalize estimation data, specified as
true
or false
. If
Normalize
is true
, then the
algorithm uses the method specified in
NormalizationOptions
to normalize the
data.
NormalizationOptions
— Option set for configuring normalization
option set
Option set for configuring normalization, specified as the options
shown in the following table. The first option,
NormalizationMethod
, determines which method
the algorithm uses. The default option is 'auto'
. For
idnlarx
models, a setting of
'auto'
is equivalent to a setting of
'center'
. Except for
'medianiqr'
, each specific method in
NormalizationMethod
has an associated
configuration option, such as CenterMethodType
when
you specify the 'center'
method. For more
information about these methods, see the MATLAB^{®} function normalize
.
Method or Method Option  Value  Description  Default 

NormalizationMethod  'auto'  Set method automatically. 
(equivalent
to 
'center'  Center data to have mean 0.  
'zscore'  zscore with mean 0 and standard deviation 1.  
'norm'  2norm.  
'scale'  Scale by standard deviation.  
'range'  Rescale range of data to [min,max].  
'medianiqr'  Center and scale data to have median 0 and interquartile scale of 1.  
 'mean'  Center to have mean 0.  'mean' 
'median'  Center to have median 0.  
 'std'  Center and scale to have mean 0 and standard deviation 1.  'std' 
'robust'  Center and scale to have median 0 and median absolute deviation 1.  
 'std'  Scale by standard deviation.  'std' 
'mad'  Scale by median absolute deviation.  
'iqr'  Scale by interquartile range.  
'first'  Scale by first element of data.  
 Positive real value  pnorm, where p is a positive integer.  2 
 2element row vector  Rescale range of data to an interval of the form
[a b] , where a
< b .  [0 1] 
SearchMethod
— Numerical search method used for iterative parameter estimation
'auto'
(default)  'gn'
 'gna'
 'lm'
 'grad'
 'lsqnonlin'
 'fmincon'
Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.
SearchMethod  Description 

'auto'  Automatic method selection A combination of the
line search algorithms, 
'gn'  Subspace GaussNewton leastsquares search Singular
values of the Jacobian matrix less than

'gna'  Adaptive subspace GaussNewton search Eigenvalues
less than 
'lm'  LevenbergMarquardt least squares search Each
parameter value is 
'grad'  Steepest descent leastsquares search 
'lsqnonlin'  Trustregionreflective algorithm of This algorithm requires Optimization Toolbox™ software. 
'fmincon'  Constrained nonlinear solvers You can use the
sequential quadratic programming (SQP) and trustregionreflective
algorithms of the

SearchOptions
— Option set for search algorithm
search option set
Option set for the search algorithm, specified as the commaseparated
pair consisting of 'SearchOptions'
and a search
option set with fields that depend on the value of
SearchMethod
:
SearchOptions
Structure When SearchMethod
is Specified
as 'gn'
, 'gna'
, 'lm'
,
'grad'
, or 'auto'
Field Name  Description  Default  

Tolerance  Minimum percentage difference between the current value
of the loss function and its expected improvement after the next iteration,
specified as a positive scalar. When the percentage of expected improvement
is less than  1e5  
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when Setting
Use
 20  
Advanced  Advanced search settings, specified as a structure with the following fields:

SearchOptions
Structure When SearchMethod
is Specified
as 'lsqnonlin'
Field Name  Description  Default 

FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The
value of  1e5 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of  1e6 
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when The value of
 20 
SearchOptions
Structure When SearchMethod
is Specified
as 'fmincon'
Field Name  Description  Default 

Algorithm 
For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).  'sqp' 
FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.  1e6 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar.  1e6 
MaxIterations  Maximum number of iterations during loss function minimization, specified as a positive
integer. The iterations stop when  100 
To specify field values in SearchOptions
, create a
default nlarxOptions
set and modify the fields using
dot notation. Any fields that you do not modify retain their default
values.
opt = nlarxOptions; opt.SearchOptions.MaxIter = 15; opt.SearchOptions.Advanced.RelImprovement = 0.5;
SparsifyRegressors
— Option to remove sparse regressors
0
or
false
(default)  1
or true
Option to remove sparse regressors from the nonlinear ARX model,
specified as logical 0
(false
) or
logical 1
(true
).
Set this option to true
to use a sparsification
algorithm in the nlarx
function to identify
sparse regressors. The function removes these regressors from the
nonlinear mapping function of the output idnlarx
model, leaving
only the optimal subset of regressors. To see which regressors are
removed, enter sys.RegressorUsage
at the command
line, where sys
is the idnlarx
model.
To configure the sparsification algorithm, use the option SparsificationOptions
.
The sparsification algorithm, also known as structured pruning, is similar to the lasso (least absolute shrinkage and selection operator) technique.
SparsificationOptions
— Option set for configuring sparsification
option set
Option set for configuring sparsification, specified as one or more of the options shown in this table.
Option  Description  Default 

SparsityMeasure  Form of the sparsification penalty added to the prediction error minimization objective, specified as one of these values:
If several parameters multiply a certain regressor in different parts of the nonlinear mapping function, interpret the sparsification penalty in the group sense.  "logsum" 
GroupNorm  Norm used to measure the contribution of each
parameter group to the sparsification penalty,
specified as The default of


Lambda  Sparsification penalty, λ, specified as a positive scalar. The sparsification penalty is the cost, c, of a regressor being identified as sparse in the minimization objective, defined as c = λ × f + p, where:
 1 
MaxIterations  Maximum number of Alternating Direction Method of Multipliers (ADMM) iterations to run to sparsify the regressor selection, specified as a positive integer.  20 
When configuring the sparsification algorithm, keep these points in mind:
Getting the best results can require trying various solver and sparsification options. The options with the most significant effect on the results are the:
Choice of sparsification measure (
=SparsificationOptions
.SparsityMeasure'logsum'
,'l1'
, or'l2'
)Search method (
SearchMethod
='lm'
,'lsqnonlin'
, and so on)Value of the
option, which describes the strength of the sparsification penalty in the minimization objectiveSparsificationOptions
.Lambda
Sparsification with the
Focus
property set to'prediction'
can be significantly faster than specification withFocus
='simulation'
, but the results might not lead to good simulation models. To balance these approaches, consider performing sparsification withFocus
='prediction'
first. Then, perform a followup estimation using the selected regressors andFocus
='simulation'
.
Dependencies
To enable these options, set SparsifyRegressors
to
true
.
IterativeWavenet
— Iterative idWaveletNetwork
estimation setting
'auto'
(default)  'on'
 'off'
Iterative idWaveletNetwork
estimation setting, specified as the commaseparated pair consisting of
'IterativeWavenet'
and one of the
following:
'auto'
— First estimation is noniterative and subsequent estimations are iterative.'on'
— Perform iterative estimation only.'off'
— Perform noniterative estimation only.
This option applies only when using an idWaveletNetwork
nonlinearity estimator.
InputInterSample
— Inputchannel intersample behavior
'auto'
 'zoh'
 'foh'
 'bl'
Inputchannel intersample behavior for transformations between discrete time and continuous time, specified as 'auto'
, 'zoh'
,'foh'
, or 'bl'
.
The definitions of the three behavior values are as follows:
'zoh'
— Zeroorder hold maintains a piecewiseconstant input signal between samples.'foh'
— Firstorder hold maintains a piecewiselinear input signal between samples.'bl'
— Bandlimited behavior specifies that the continuoustime input signal has zero power above the Nyquist frequency.
iddata
objects have a similar property,
data.InterSample
, that contains the same behavior value options.
When the InputInterSample
value is 'auto'
and
the estimation data is in an iddata
object data
, the
software uses the data.InterSample
value. When the estimation data
is instead contained in a timetable or a matrix pair, with the 'auto'
option, the software uses 'zoh'
.
The software applies the same option value to all channels and all experiments.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified as
the commaseparated pair consisting of
'Regularization'
and a structure with
fields:
Field Name  Description  Default 

Lambda  Bias versus variance tradeoff constant, specified as a nonnegative scalar.  0 — Indicates no regularization. 
R  Weighting matrix, specified as a vector of nonnegative scalars
or a square positive semidefinite matrix. The length must be equal
to the number of free parameters in the model, np .
Use the nparams command to determine
the number of model parameters.  1 — Indicates a value of eye(np) . 
Nominal 
The nominal value towards which the free parameters are pulled during estimation, specified as one of the following:
 'zero' 
To specify field values in Regularization
, create a
default nlarxOptions
set and modify the fields using
dot notation. Any fields that you do not modify retain their default
values.
opt = nlarxOptions; opt.Regularization.Lambda = 1.2; opt.Regularization.R = 0.5*eye(np);
Regularization is a technique for specifying model flexibility constraints, which reduce uncertainty in the estimated parameter values. For more information, see Regularized Estimates of Model Parameters.
Advanced
— Additional advanced options
structure
Additional advanced options, specified as the commaseparated
pair consisting of 'Advanced'
and a structure with
fields:
Field Name  Description  Default 

ErrorThreshold  Threshold for when to adjust the weight of large errors from
quadratic to linear, specified as a nonnegative scalar. Errors larger
than ErrorThreshold times the estimated standard
deviation have a linear weight in the loss function. The standard
deviation is estimated robustly as the median of the absolute deviations
from the median of the prediction errors, divided by 0.7. If your
estimation data contains outliers, try setting ErrorThreshold to 1.6 .  0 — Leads to a purely quadratic loss
function. 
MaxSize  Maximum number of elements in a segment when inputoutput data is split into segments, specified as a positive integer.  250000 
To specify field values in Advanced
, create
a default nlarxOptions
set and modify the fields
using dot notation. Any fields that you do not modify retain their
default values.
opt = nlarxOptions; opt.Advanced.ErrorThreshold = 1.2;
Output Arguments
opt
— Option set for nlarx
command
nlarxOptions
option set
Option set for nlarx
command, returned
as an nlarxOptions
option set.
Version History
Introduced in R2015aR2022b: InputInterSample
option allows intersample behavior specification for continuous models estimated from timetables or matrices.
iddata
objects contain an InterSample
property that
describes the behavior of the signal between sample points. The
InputInterSample
option implements a version of that property in
nlarxOptions
so that intersample behavior can be specified also when
estimation data is stored in timetables or matrices.
R2018a: Renaming of Estimation and Analysis Options
The names of some estimation and analysis options were changed in R2018a. Prior names still work. For details, see the R2018a release note Renaming of Estimation and Analysis Options.
See Also
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