Option set for nlhw
creates
the default option set for opt
= nlhwOptionsnlhw
. Use dot notation
to customize the option set, if needed.
creates
an option set with options specified by one or more opt
= nlhwOptions(Name,Value
)Name,Value
pair
arguments. The options that you do not specify retain their default
value.
Create estimation option set for nlhw
to view estimation progress, use the LevenbergMarquardt search method, and set the maximum iteration steps to 50
.
opt = nlhwOptions; opt.Display = 'on'; opt.SearchMethod = 'lm'; opt.SearchOptions.MaxIterations = 50;
Load data and estimate the model.
load iddata3
sys = nlhw(z3,[4 2 1],idSigmoidNetwork,idPiecewiseLinear,opt);
Create an options set for nlhw
where:
Initial conditions are estimated from the estimation data.
Subspace GaussNewton least squares method is used for estimation.
opt = nlhwOptions('InitialCondition','estimate','SearchMethod','gn');
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
nlhwOptions('InitialCondition','estimate')
InitialCondition
— Handling of initial conditions'zero'
(default)  'estimate'
Handling of initial conditions during estimation using nlhw
,
specified as the commaseparated pair consisting of InitialCondition
and
one of the following:
'zero'
— The initial conditions
are set to zero.
'estimate'
— The initial
conditions are treated as independent estimation parameters.
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 matrixWeighting 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 minimizes det(E'*E)
, where E
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 minimizes trace(E'*E*W/N)
,
where E
is the matrix of prediction errors and N
is
the number of data samples.
Regularization
— Options for regularized estimation of model parametersOptions 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 nlhwOptions
set and modify the
fields using dot notation. Any fields that you do not modify retain
their default values.
opt = nlhwOptions; 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.
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 commaseparated pair consisting of 'SearchMethod'
and
one of the following:
'auto'
— A combination of
the line search algorithms, 'gn'
, 'lm'
, 'gna'
,
and 'grad'
methods is tried in sequence at each
iteration. The first descent direction leading to a reduction in estimation
cost is used.
'gn'
— Subspace GaussNewton least squares search.
Singular values of the Jacobian matrix less than
GnPinvConstant*eps*max(size(J))*norm(J)
are discarded
when computing the search direction. J is the Jacobian
matrix. The Hessian matrix is approximated as
J^{T}J. If there is no
improvement in this direction, the function tries the gradient direction.
'gna'
— Adaptive subspace GaussNewton search.
Eigenvalues less than gamma*max(sv)
of the Hessian are
ignored, where sv contains the singular values of the
Hessian. The GaussNewton direction is computed in the remaining subspace.
gamma has the initial value
InitialGnaTolerance
(see Advanced
in
'SearchOptions'
for more information). This value is
increased by the factor LMStep
each time the search fails to
find a lower value of the criterion in fewer than five bisections. This value is
decreased by the factor 2*LMStep
each time a search is
successful without any bisections.
'lm'
— LevenbergMarquardt
least squares search, where the next parameter value is pinv(H+d*I)*grad
from
the previous one. H is the Hessian, I is
the identity matrix, and grad is the gradient. d is
a number that is increased until a lower value of the criterion is
found.
'grad'
— Steepest descent
least squares search.
'lsqnonlin'
— Trustregionreflective
algorithm of lsqnonlin
(Optimization Toolbox). Requires Optimization Toolbox™ software.
'fmincon'
— Constrained nonlinear solvers. You can
use the sequential quadratic programming (SQP) and trustregionreflective
algorithms of the fmincon
(Optimization Toolbox) solver. If you have
Optimization Toolbox software, you can also use the interiorpoint and activeset
algorithms of the fmincon
solver. Specify the algorithm in
the SearchOptions.Algorithm
option. The
fmincon
algorithms may result in improved estimation
results in the following scenarios:
Constrained minimization problems when there are bounds imposed on the model parameters.
Model structures where the loss function is a nonlinear or non smooth function of the parameters.
Multioutput model estimation. A determinant loss function
is minimized by default for multioutput model estimation.
fmincon
algorithms are able to minimize such loss
functions directly. The other search methods such as
'lm'
and 'gn'
minimize the
determinant loss function by alternately estimating the noise variance
and reducing the loss value for a given noise variance value. Hence, the
fmincon
algorithms can offer better efficiency
and accuracy for multioutput model estimations.
SearchOptions
— Option set for the search algorithmOption 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 
Advanced  Advanced search settings, specified as an option set
for For more information, see the Optimization Options table in Optimization Options (Optimization Toolbox).  Use optimset('lsqnonlin') to create a default
option set. 
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 nlhwOptions
set and modify the fields using
dot notation. Any fields that you do not modify retain their default
values.
opt = nlhwOptions; opt.SearchOptions.MaxIterations = 50; opt.SearchOptions.Advanced.RelImprovement = 0.5;
Advanced
— Additional advanced optionsAdditional 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 nlhwOptions
set and modify the fields
using dot notation. Any fields that you do not modify retain their
default values.
opt = nlhwOptions; opt.Advanced.ErrorThreshold = 1.2;
opt
— Option set for nlhw
nlhwOptions
option setOption set for nlhw
, returned as an nlhwOptions
option
set.
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.
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