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Option set for greyest
opt = greyestOptions
opt = greyestOptions(Name,Value)
creates
the default options set for opt
= greyestOptionsgreyest
.
creates
an option set with the options specified by one or more opt
= greyestOptions(Name,Value
)Name,Value
pair
arguments.
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside single quotes (' '
). You can
specify several name and value pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
'InitialState'
— Handling of initial states'auto'
(default)  'model'
 'zero'
 'estimate'
 'backcast'
Handling of initial states during estimation, specified as one of the following values:
'model'
— The initial state
is parameterized by the ODE file used by the idgrey
model.
The ODE file must return 6 or more output arguments.
'zero'
— The initial state
is set to zero. Any values returned by the ODE file are ignored.
'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.
Vector of doubles — Specify a column vector of length Nx, where Nx is the number of states. For multiexperiment data, specify a matrix with Ne columns, where Ne is the number of experiments. The specified values are treated as fixed values during the estimation process.
'DisturbanceModel'
— Handling of disturbance component'auto'
(default)  'model'
 'fixed'
 'none'
 'estimate'
Handling of the disturbance component (K) during estimation, specified as one of the following values:
'model'
— K values
are parameterized by the ODE file used by the idgrey
model.
The ODE file must return 5 or more output arguments.
'fixed'
— The value of the K
property
of the idgrey
model is fixed to its original
value.
'none'
— K is
fixed to zero. Any values returned by the ODE file are ignored.
'estimate'
— K is
treated as an independent estimation parameter.
'auto'
— The software chooses
the method to handle how the disturbance component is handled during
estimation. The software uses the 'model'
method
if the ODE file returns 5 or more output arguments with a finite value
for K. Else, the software uses the 'fixed'
method.
Noise model cannot be estimated using frequency domain data.
'Focus'
— Error to be minimized'prediction'
(default)  'simulation'
Error to be minimized in the loss function during estimation,
specified as the commaseparated pair consisting of 'Focus'
and
one of the following values:
'prediction'
— The onestep
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
timedomain data and in FrequencyUnit
for frequencydomain
data, where TimeUnit
and FrequencyUnit
are
the time and frequency units of the estimation data.
SISO filter — Specify a singleinputsingleoutput (SISO) linear filter in one of the following ways:
A SISO LTI model
{A,B,C,D}
format, which specifies
the statespace 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 frequencydomain
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 modelfalse
(default)  true
Control whether to enforce stability of estimated model, specified
as the commaseparated pair consisting of 'EnforceStability'
and
either true
or false
.
Data Types: logical
'EstCovar'
— Control whether to generate parameter covariance datatrue
(default)  false
Controls whether parameter covariance data is generated, specified
as true
or false
.
If EstCovar
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 progressviewer
window.
'off'
— No progress or results
information is displayed.
'InputOffset'
— Removal of offset from timedomain input data during estimation[]
(default)  vector of positive integers  matrixRemoval of offset from timedomain input data during estimation,
specified as the commaseparated 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.
NubyNe matrix
— For multiexperiment data, specify InputOffset
as
an NubyNe 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 timedomain output data during estimation[]
(default)  vector  matrixRemoval of offset from timedomain output data during estimation,
specified as the commaseparated 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.
NybyNe matrix
— For multiexperiment data, specify OutputOffset
as
a NybyNe 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.
'OutputWeight'
— Weighting of prediction errors in multioutput estimations[]
(default)  'noise'
 positive semidefinite symmetric matrixWeighting of prediction errors in multioutput estimations, specified as one of the following values:
'noise'
— Minimize $$\mathrm{det}(E\text{'}*E/N)$$, where E represents
the prediction error and N
is the number of data
samples. This choice is optimal in a statistical sense and leads to
maximum likelihood estimates if nothing is known about the variance
of the noise. It uses the inverse of the estimated noise variance
as the weighting function.
OutputWeight
must not be 'noise'
if SearchMethod
is 'lsqnonlin'
.
Positive semidefinite symmetric matrix (W
)
— Minimize the trace of the weighted prediction error matrix trace(E'*E*W/N)
where:
E is the matrix of prediction errors, with one column for each output, and W is the positive semidefinite symmetric matrix of size equal to the number of outputs. Use W to specify the relative importance of outputs in multipleoutput models, or the reliability of corresponding data.
N
is the number of data samples.
[]
— The software chooses
between the 'noise'
or using the identity matrix
for W
.
This option is relevant for only multioutput models.
'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 semidefinite matrix. The length must be equal to the number of free parameters of the model.
For blackbox models, using the default value is recommended.
For structured and greybox 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 commaseparated 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 GaussNewton
least squares search. Singular values of the Jacobian matrix less
than GnPinvConst*eps*max(size(J))*norm(J)
are discarded
when computing the search direction. J is the Jacobian
matrix. The Hessian matrix is approximated as 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 contains the
singular values of the Hessian. The GaussNewton direction is computed
in the remaining subspace. gamma has the initial
value InitGnaTol
(see Advanced
in 'SearchOption'
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 SearchOption.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 multioutput 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 multioutput model estimations.
'SearchOption'
— Option set for the search algorithmOption set for the search algorithm, specified as the commaseparated
pair consisting of 'SearchOption'
and a search
option set with fields that depend on the value of SearchMethod
.
SearchOption
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  
MaxIter  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:

SearchOption
Structure When SearchMethod
is
Specified as 'lsqnonlin'
Field Name  Description  Default 

TolFun  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 
TolX  Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of  1e6 
MaxIter  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. 
SearchOption
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' 
TolFun  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.  1e6 
TolX  Termination tolerance on the estimated parameter values, specified as a positive scalar.  1e6 
MaxIter  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, 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 frequencydomain data, the software sets ErrorThreshold
to
zero. For timedomain data that contains outliers, try setting ErrorThreshold
to 1.6
.
Default: 0
MaxSize
— Specifies the
maximum number of elements in a segment when inputoutput 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 rightmost pole to test the stability of continuoustime models.
A model is considered stable when its rightmost pole is to the left
of s
.
Default: 0
z
— Specifies the maximum
distance of all poles from the origin to test stability of discretetime
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 state.
The initial state is estimated when
$$\frac{\Vert {y}_{p,z}{y}_{meas}\Vert}{\Vert {y}_{p,e}{y}_{meas}\Vert}>\text{AutoInitThreshold}$$
y_{meas} is the measured output.
y_{p,z} is the predicted output of a model estimated using zero initial states.
y_{p,e} is the predicted output of a model estimated using estimated initial states.
Applicable when InitialState
is 'auto'
.
Default: 1.05
opt
— Options set for greyest
greyestOptions
option setOption set for greyest
,
returned as an greyestOptions
option set.
opt = greyestOptions;
Create an options set for greyest
using the 'backcast'
algorithm to initialize the state. Specify Display
as 'on'
.
opt = greyestOptions('InitialState','backcast','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = greyestOptions; opt.InitialState = 'backcast'; opt.Display = 'on';
[1] Wills, Adrian, B. Ninness, and S. Gibson. “On GradientBased 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: PrenticeHall PTR, 1999.
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