Option set for armax
opt = armaxOptions
opt = armaxOptions(Name,Value)
opt = armaxOptionsarmax.
opt = armaxOptions(Name,Value)Name,Value pair
arguments.
Specify optional
comma-separated 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.
'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 conditions
are set to zero.
'estimate' — The initial
conditions are treated as independent estimation parameters.
'backcast' — The initial
conditions are estimated using the best least squares fit.
'auto' — The software chooses
the method to handle initial conditions 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 systemWeighting 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], where wl and wh 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 in FrequencyUnit for frequency-domain
data, where TimeUnit and FrequencyUnit 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.
'EnforceStability' — Control whether to enforce stability of modelfalse (default) | trueControl 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' — Control whether to generate parameter covariance datatrue (default) | falseControls whether parameter covariance data is generated, specified as
true or false.
If EstimateCovariance is true, then use
getcov to fetch the covariance matrix
from the estimated model.
'Display' — Specify whether to display the estimation progress'off' (default) | 'on'Specify whether 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 | matrixRemoval of offset from time-domain input data during estimation,
specified as the comma-separated pair consisting of 'InputOffset' and
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 | matrixRemoval of offset from time-domain output data during estimation,
specified as the comma-separated pair consisting of 'OutputOffset' and
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 parametersOptions for regularized estimation of model parameters. For more information on regularization, see Regularized Estimates of Model Parameters.
Regularization is a structure with the following
fields:
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 zero implies no regularization.
Default: 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 np positive numbers such that each entry denotes
the confidence in the value of the associated parameter.
The default value of 1 implies a value of eye(npfree),
where npfree is the number of free parameters.
Default: 1
Nominal — The nominal value
towards which the free parameters are pulled during estimation.
The default value of zero implies that the parameter values
are pulled towards zero. If you are refining a model, you can set
the value to 'model' to pull the parameters towards
the parameter values of the initial model. The initial parameter values
must be finite for this setting to work.
Default: 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 comma-separated 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 Gauss-Newton 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
JTJ. If there is no
improvement in this direction, the function tries the gradient direction.
'gna' — Adaptive subspace Gauss-Newton search.
Eigenvalues less than gamma*max(sv) of the Hessian are
ignored, where sv contains the singular values of the
Hessian. The Gauss-Newton 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' — 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 of lsqnonlin (Optimization Toolbox). Requires Optimization Toolbox™ software.
'fmincon' — Constrained nonlinear solvers. You can
use the sequential quadratic programming (SQP) and trust-region-reflective
algorithms of the fmincon (Optimization Toolbox) solver. If you have
Optimization Toolbox software, you can also use the interior-point and active-set
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.
Multi-output model estimation. A determinant loss function
is minimized by default for multi-output 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 multi-output model estimations.
'SearchOptions' — Option set for the search algorithmOption 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 '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 |
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. | 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 optionsAdditional 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 and divided
by 0.7. 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 sets ErrorThreshold to
zero. For time-domain data that contains outliers, try setting ErrorThreshold to 1.6.
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
of s.
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 distance z 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 conditions.
yp,e is the predicted output of a model estimated using estimated initial conditions.
Applicable when InitialCondition is 'auto'.
Default: 1.05
opt — Options set for armaxarmaxOptions option setOption set for armax,
returned as an armaxOptions option set.
opt = armaxOptions;
Create an option set for armax to use the 'simulation' Focus and to set the Display to 'on'.
opt = armaxOptions('Focus','simulation','Display','on');
Alternatively, use dot notation to set the values of opt.
opt = armaxOptions; opt.Focus = 'simulation'; opt.Display = 'on';
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.
[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.
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