nlgreyestOptions
Option set for nlgreyest
Description
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.
Examples
Create Default Option Set for Nonlinear GreyBox Model Estimation
opt = nlgreyestOptions;
Estimate a Nonlinear GreyBox Model Using Specific Options
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 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);
Specify Options for Nonlinear GreyBox Model Estimation
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');
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: nlgreyestOptions('Display','on')
GradientOptions
— Options for computing Jacobians and gradients
structure
Options 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) 
DifferencingScheme  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 setting
1
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 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 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 thanGnPinvConstant*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 thangamma*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 valueInitialGnaTolerance
(seeAdvanced
in'SearchOptions'
for more information). This value is increased by the factorLMStep
each time the search fails to find a lower value of the criterion in fewer than five bisections. This value is decreased by the factor2*LMStep
each time a search is successful without any bisections.'lm'
— LevenbergMarquardt least squares search, where the next parameter value ispinv(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 oflsqnonlin
(Optimization Toolbox). Requires Optimization Toolbox software.'fmincon'
— Constrained nonlinear solvers. You can use the sequential quadratic programming (SQP) and trustregionreflective algorithms of thefmincon
solver. If you have Optimization Toolbox software, you can also use the interiorpoint and activeset algorithms of thefmincon
(Optimization Toolbox) solver. Specify the algorithm in theSearchOptions.Algorithm
option. Thefmincon
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, thefmincon
algorithms can offer better efficiency and accuracy for multioutput model estimations.
SearchOptions
— Option set for the 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
'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 
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'
 matrix
Weighting 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 aseye(Ny)
, whereNy
is the number of outputs.'noise'
— Optimal weighting is automatically computed as the inverse of the estimated noise variance. This weighting minimizesdet(E'*E/N)
, whereE
is the matrix of prediction errors andN
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 minimizestrace(E'*E*W/N)
, whereE
is the matrix of prediction errors andN
is the number of data samples.
Advanced
— Additional advanced options
structure
Additional 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;
Output Arguments
opt
— Option set for nlgreyest
nlgreyestOptions
option set
Option set for nlgreyest
, returned as an nlgreyestOptions
option
set.
Version History
Introduced in R2015aR2018a: Renaming of Estimation and Analysis Options
The names of some estimation and analysis options were changed in R2018a. Prior names still work.
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