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 Grey-Box Model Estimation
opt = nlgreyestOptions;
Estimate a Nonlinear Grey-Box 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','DC-motor');
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 grey-box 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','DC-motor');
Estimate the model parameters using the estimation options.
sys = nlgreyest(z,init_sys,opt);
Specify Options for Nonlinear Grey-Box Model Estimation
Create an option set for nlgreyest
where:
Parameter covariance data is not generated.
Subspace Gauss-Newton least squares method is used for estimation.
opt = nlgreyestOptions('EstimateCovariance',false,'SearchMethod','gn');
Input Arguments
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value 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 comma-separated 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 comma-separated
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 progress-viewer window.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified
as the comma-separated pair consisting of 'Regularization'
and
a structure with fields:
Field Name | Description | Default |
---|---|---|
Lambda | Bias versus variance trade-off constant, specified as a nonnegative scalar. | 0 — Indicates no regularization. |
R | Weighting matrix, specified as a vector of nonnegative scalars
or a square positive semi-definite 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 comma-separated 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 Gauss-Newton 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 JTJ. If there is no improvement in this direction, the function tries the gradient direction.'gna'
— Adaptive subspace Gauss-Newton search. Eigenvalues less thangamma*max(sv)
of the Hessian are ignored, where sv are the singular values of the Hessian. The Gauss-Newton 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'
— Levenberg-Marquardt 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'
— Trust-region-reflective algorithm oflsqnonlin
(Optimization Toolbox). Requires Optimization Toolbox software.'fmincon'
— Constrained nonlinear solvers. You can use the sequential quadratic programming (SQP) and trust-region-reflective algorithms of thefmincon
solver. If you have Optimization Toolbox software, you can also use the interior-point and active-set 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.
Multi-output 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 multi-output model estimations.
SearchOptions
— Option set for the search algorithm
search option set
Option set for the search algorithm, specified as the comma-separated
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
| 1e-5 |
StepTolerance | Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of
| 1e-6 |
MaxIterations | Maximum number of iterations during
loss-function 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
| 1e-5 | ||||||||||||||||||||||||||||||
MaxIterations | Maximum number of iterations during
loss-function 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. | 1e-6 |
StepTolerance | Termination tolerance on the estimated parameter values, specified as a positive scalar. | 1e-6 |
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 multi-output estimations
[]
(default) | 'noise'
| matrix
Weighting of prediction error in multi-output model estimations,
specified as the comma-separated 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 comma-separated
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.
See Also
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)