polyestOptions
Option set for polyest
Description
Use an polyestOptions
object to specify options for estimating
polynomial models through the polyest
function. You can specify options such as
the handling of initial conditions or weighting prefilter to be used in
estimation.
Creation
Properties
InitialCondition
— Handling of initial conditions
'auto'
(default) | 'zero'
| 'estimate'
| 'backcast'
Handling of initial conditions during estimation, specified as one of the following values:
'zero'
— The initial condition is set to zero.'estimate'
— The initial state is treated as an independent estimation parameter.'backcast'
— The initial state is estimated using the best least squares fit.'auto'
— The software chooses the method to handle initial states based on the estimation data.
Focus
— Error to be minimized
'prediction'
(default) | 'simulation'
Error to be minimized in the loss function during estimation,
specified as the comma-separated pair consisting of 'Focus'
and
one of the following values:
'prediction'
— The one-step ahead prediction error between measured and predicted outputs is minimized during estimation. As a result, the estimation focuses on producing a good predictor model.'simulation'
— The simulation error between measured and simulated outputs is minimized during estimation. As a result, the estimation focuses on making a good fit for simulation of model response with the current inputs.
The Focus
option can be interpreted as a
weighting filter in the loss function. For more information, see Loss Function and Model Quality Metrics.
WeightingFilter
— Weighting prefilter
[]
(default) | vector | matrix | cell array | linear system
Weighting prefilter applied to the loss function to be minimized
during estimation. To understand the effect of WeightingFilter
on
the loss function, see Loss Function and Model Quality Metrics.
Specify WeightingFilter
as one of the following
values:
[]
— No weighting prefilter is used.Passbands — Specify a row vector or matrix containing frequency values that define desired passbands. You select a frequency band where the fit between estimated model and estimation data is optimized. For example,
[wl,wh]
wherewl
andwh
represent lower and upper limits of a passband. For a matrix with several rows defining frequency passbands,[w1l,w1h;w2l,w2h;w3l,w3h;...]
, the estimation algorithm uses the union of the frequency ranges to define the estimation passband.Passbands are expressed in
rad/TimeUnit
for time-domain data and inFrequencyUnit
for frequency-domain data, whereTimeUnit
andFrequencyUnit
are the time and frequency units of the estimation data.SISO filter — Specify a single-input-single-output (SISO) linear filter in one of the following ways:
A SISO LTI model
{A,B,C,D}
format, which specifies the state-space matrices of a filter with the same sample time as estimation data.{numerator,denominator}
format, which specifies the numerator and denominator of the filter as a transfer function with same sample time as estimation data.This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function.
Weighting vector — Applicable for frequency-domain data only. Specify a column vector of weights. This vector must have the same length as the frequency vector of the data set,
Data.Frequency
. Each input and output response in the data is multiplied by the corresponding weight at that frequency.
EnforceStability
— Control whether to enforce stability of model
false
(default) | true
Control whether to enforce stability of estimated model, specified
as the comma-separated pair consisting of 'EnforceStability'
and
either true
or false
.
This option is not available for multi-output models with a non-diagonal A polynomial array.
Data Types: logical
EstimateCovariance
— Option to generate parameter covariance data
true
(default) | false
Option to generate parameter covariance data, specified as true
or
false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Option to display estimation progress
'off'
(default) | 'on'
Option to display the estimation progress, specified as one of the following values:
'on'
— Information on model structure and estimation results are displayed in a progress-viewer window.'off'
— No progress or results information is displayed.
InputOffset
— Removal of offset from time-domain input data during estimation
[]
(default) | vector of positive integers | matrix
Removal of offset from time-domain input data during estimation, specified as one of the following:
A column vector of positive integers of length Nu, where Nu is the number of inputs.
[]
— Indicates no offset.Nu-by-Ne matrix — For multi-experiment data, specify
InputOffset
as an Nu-by-Ne matrix. Nu is the number of inputs and Ne is the number of experiments.
Each entry specified by InputOffset
is
subtracted from the corresponding input data.
OutputOffset
— Removal of offset from time-domain output data during estimation
[]
(default) | vector | matrix
Removal of offset from time-domain output data during estimation, specified as one of the following:
A column vector of length Ny, where Ny is the number of outputs.
[]
— Indicates no offset.Ny-by-Ne matrix — For multi-experiment data, specify
OutputOffset
as a Ny-by-Ne matrix. Ny is the number of outputs, and Ne is the number of experiments.
Each entry specified by OutputOffset
is
subtracted from the corresponding output data.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified as a structure with the fields in the following table. For more information on regularization, see Regularized Estimates of Model Parameters.
Field Name | Description | Default |
---|---|---|
Lambda | Constant that determines the bias versus variance tradeoff. Specify a positive scalar to add the regularization term to the estimation cost. The default value of 0 implies no regularization. | 0 |
R | Weighting matrix. Specify a vector of nonnegative numbers or a square positive semi-definite matrix. The length must be equal to the number of free parameters of the model. For black-box models, using the default value is
recommended. For structured and grey-box models, you can also
specify a vector of The default value of 1 implies a value of
| 1 |
Nominal | The nominal value towards which the free parameters are pulled during estimation. The default value of 0 implies that
the parameter values are pulled towards zero. If you are refining a
model, you can set the value to | 0 |
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 Gauss-Newton least-squares search Singular
values of the Jacobian matrix less than
|
'gna' | Adaptive subspace Gauss-Newton search Eigenvalues
less than |
'lm' | Levenberg-Marquardt least squares search Each
parameter value is |
'grad' | Steepest descent least-squares search |
'lsqnonlin' | Trust-region-reflective algorithm of This algorithm requires Optimization Toolbox™ software. |
'fmincon' | Constrained nonlinear solvers You can use the
sequential quadratic programming (SQP) and trust-region-reflective
algorithms of the
|
SearchOptions
— Option set for search algorithm
search option set
Option set for the search algorithm, specified as 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 | 0.01 | ||||||||||||||||||||||||||||||
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 '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 | 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 '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 |
Advanced
— Additional advanced options
structure
Additional advanced options, specified as a structure with the following fields:
ErrorThreshold
— Specifies when to adjust the weight of large errors from quadratic to linear.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 by0.7
. For more information on robust norm choices, see section 15.2 of [2].ErrorThreshold = 0
disables robustification and leads to a purely quadratic loss function. When estimating with frequency-domain data, the software setsErrorThreshold
to zero. For time-domain data that contains outliers, try settingErrorThreshold
to1.6
.Default: 0
MaxSize
— Specifies the maximum number of elements in a segment when input-output data is split into segments.MaxSize
must be a positive integer.Default: 250000
StabilityThreshold
— Specifies thresholds for stability tests.StabilityThreshold
is a structure with the following fields:s
— Specifies the location of the right-most pole to test the stability of continuous-time models. A model is considered stable when its right-most pole is to the left ofs
.Default: 0
z
— Specifies the maximum distance of all poles from the origin to test stability of discrete-time models. A model is considered stable if all poles are within the distancez
from the origin.Default:
1+sqrt(eps)
AutoInitThreshold
— Specifies when to automatically estimate the initial condition.The initial condition is estimated when
ymeas is the measured output.
yp,z is the predicted output of a model estimated using zero initial states.
yp,e is the predicted output of a model estimated using estimated initial states.
Applicable when
InitialCondition
is'auto'
.Default:
1.05
Examples
Create Default Option Set for Polynomial Estimation
opt = polyestOptions;
Specify Options for Polynomial Estimation
Create an option set for polyest
where you enforce model stability and set the Display
to 'on'
.
opt = polyestOptions('EnforceStability',true,'Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = polyestOptions;
opt.EnforceStability = true;
opt.Display = 'on';
References
[1] Wills, Adrian, B. Ninness, and S. Gibson. “On Gradient-Based Search for Multivariable System Estimates”. Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, July 3–8, 2005. Oxford, UK: Elsevier Ltd., 2005.
[2] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.
Version History
Introduced in R2010bR2018a: Renaming of Estimation and Analysis Options
The names of some estimation and analysis options were changed in R2018a. Prior names still work.
Commande MATLAB
Vous avez cliqué sur un lien qui correspond à cette commande MATLAB :
Pour exécuter la commande, saisissez-la dans la fenêtre de commande de MATLAB. Les navigateurs web ne supportent pas les commandes MATLAB.
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)