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Option set for nlgreyest
opt = nlgreyestOptions
opt = nlgreyestOptions(Name,Value)
creates
the default option set for opt
= nlgreyestOptionsnlgreyest
. Use dot
notation to customize the option set, if needed.
creates
an option set with options specified by one or more opt
= nlgreyestOptions(Name,Value
)Name,Value
pair
arguments. The options that you do not specify retain their default
value.
opt = nlgreyestOptions;
Create estimation option set for nlgreyest
to view estimation progress, and to set the maximum iteration steps to 50.
opt = nlgreyestOptions;
opt.Display = 'on';
opt.SearchOptions.MaxIterations = 50;
Load data.
load(fullfile(matlabroot,'toolbox','ident','iddemos','data','dcmotordata')); z = iddata(y,u,0.1,'Name','DCmotor');
The data is from a linear DC motor with one input (voltage), and two outputs (angular position and angular velocity). The structure of the model is specified by dcmotor_m.m
file.
Create a nonlinear greybox model.
file_name = 'dcmotor_m'; Order = [2 1 2]; Parameters = [1;0.28]; InitialStates = [0;0]; init_sys = idnlgrey(file_name,Order,Parameters,InitialStates,0, ... 'Name','DCmotor');
Estimate the model parameters using the estimation options.
sys = nlgreyest(z,init_sys,opt);
Create an option set for nlgreyest
where:
Parameter covariance data is not generated.
Subspace GaussNewton least squares method is used for estimation.
opt = nlgreyestOptions('EstimateCovariance',false,'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
.
nlgreyestOptions('Display','on')
'GradientOptions'
— Options for computing Jacobians and gradientsOptions for computing Jacobians and gradients, specified as
the commaseparated pair consisting of 'GradientOptions'
and
a structure with fields:
Field Name  Description  Default 

MaxDifference  Largest allowed parameter perturbation when computing numerical derivatives. Specified
as a positive real value >
 Inf 
MinDifference  Smallest allowed parameter perturbation when computing numerical derivatives. Specified
as a positive real value
<  0.01*sqrt(eps) 
DifferenceScheme  Method for computing numerical derivatives with respect to the components of the parameters and/or the initial state(s) to form the Jacobian. Specified as one of the following:
 'Auto' 
Type  Method used when computing derivatives (Jacobian) of the parameters or the initial states to be estimated. Specified as one of the following:
 'Auto' 
To specify field values in GradientOptions
,
create a default nlgreyestOptions
set and modify
the fields using dot notation. Any fields that you do not modify retain
their default values.
opt = nlgreyestOptions;
opt.GradientOptions.Type = 'Basic';
'EstimateCovariance'
— Parameter covariance data generation setting1
or
true
(default)  0
or false
Controls whether parameter covariance data is generated, specified as
true
(1
) or
false
(0
).
'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.
'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 nlgreyestOptions
set and modify
the fields using dot notation. Any fields that you do not modify retain
their default values.
opt = nlgreyestOptions; 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'
Numerical search method used for iterative parameter estimation,
specified as the commaseparated pair consisting of 'SearchMethod'
and
one of the following:
'auto'
— If Optimization
Toolbox™ is
available, 'lsqnonlin'
is used. Otherwise, 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 by
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 are 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
. Requires Optimization
Toolbox software.
'fmincon'
— Constrained nonlinear
solvers. You can use the sequential quadratic programming (SQP)
and trustregionreflective algorithms of the
fmincon
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 MIMO
model estimation. fmincon
algorithms
are able to minimize such loss functions directly. The
other available 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
'lsqnonlin'
or 'auto'
,
When Optimization
Toolbox Is Available
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
'gn'
, 'gna'
,
'lm'
, 'grad'
, or
'auto'
, When Optimization
Toolbox Is Not Available
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 '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 nlgreyestOptions
set and modify the fields
using dot notation. Any fields that you do not modify retain their
default values.
opt = nlgreyestOptions('SearchMethod','gna'); opt.SearchOptions.MaxIterations = 50; opt.SearchOptions.Advanced.RelImprovement = 0.5;
'OutputWeight'
— Weighting of prediction error in multioutput estimations[]
(default)  'noise'
 matrixWeighting of prediction error in multioutput model estimations,
specified as the commaseparated pair consisting of 'OutputWeight'
and
one of the following:
[]
— No weighting is used.
Specifying as []
is the same as eye(Ny)
,
where Ny
is the number of outputs.
'noise'
— Optimal weighting
is automatically computed as the inverse of the estimated noise variance.
This weighting minimizes det(E'*E/N)
, where E
is
the matrix of prediction errors and N
is the number
of data samples. 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.
'Advanced'
— Additional advanced optionsAdditional advanced options, specified as the commaseparated
pair consisting of 'Advanced'
and a structure with
field:
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. 
To specify field values in Advanced
, create
a default nlgreyestOptions
set and modify the fields
using dot notation. Any fields that you do not modify retain their
default values.
opt = nlgreyestOptions; opt.Advanced.ErrorThreshold = 1.2;
opt
— Option set for nlgreyest
nlgreyestOptions
option setOption set for nlgreyest
, returned as an nlgreyestOptions
option
set.
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