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Option set for `ssregest`

options = ssregestOptions;

Create an option set for `ssregest`

that fixes the value of the initial states to `'zero'`

. Also, set the `Display`

to `'on'`

.

opt = ssregestOptions('InitialState','zero','Display','on');

Alternatively, use dot notation to set the values of `opt`

.

opt = ssregestOptions; opt.InitialState = 'zero'; opt.Display = 'on';

Specify optional comma-separated 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`

.

`opt = ssregestOptions('InitialState','zero')`

fixes
the value of the initial states to zero.`'InitialState'`

— Handling of initial states`'estimate'`

(default) | `'zero'`

Handling of initial states during estimation, specified as one of the following values:

`'zero'`

— The initial state is set to zero.`'estimate'`

— The initial state is treated as an independent estimation parameter.

`'ARXOrder'`

— ARX model orders`'auto'`

(default) | matrix of nonnegative integersARX model orders, specified as a matrix of nonnegative integers ```
[na
nb nk]
```

. The `max(ARXOrder)+1`

must be greater
than the desired state-space model order (number of states). If you
specify a value, it is recommended that you use a large value for `nb`

order.
To learn more about ARX model orders, see `arx`

.

`'RegulKernel'`

— Regularizing kernel`'TC'`

(default) | `'SE'`

| `'SS'`

| `'HF'`

| `'DI'`

| `'DC'`

Regularizing kernel used for regularized estimates of the underlying ARX model, specified as one of the following values:

`'TC'`

— Tuned and correlated kernel`'SE'`

— Squared exponential kernel`'SS'`

— Stable spline kernel`'HF'`

— High frequency stable spline kernel`'DI'`

— Diagonal kernel`'DC'`

— Diagonal and correlated kernel

For more information, see [1].

`'Reduction'`

— Options for model order reductionstructure

Options for model order reduction, specified as a structure with the following fields:

`StateElimMethod`

State elimination method. Specifies how to eliminate the weakly coupled states (states with smallest Hankel singular values). Specified as one of the following values:

`'MatchDC'`

Discards the specified states and alters the remaining states to preserve the DC gain. `'Truncate'`

Discards the specified states without altering the remaining states. This method tends to product a better approximation in the frequency domain, but the DC gains are not guaranteed to match. **Default:**`'Truncate'`

`AbsTol, RelTol`

Absolute and relative error tolerance for stable/unstable decomposition. Positive scalar values. For an input model

*G*with unstable poles, the reduction algorithm of`ssregest`

first extracts the stable dynamics by computing the stable/unstable decomposition*G*→*GS*+*GU*. The`AbsTol`

and`RelTol`

tolerances control the accuracy of this decomposition by ensuring that the frequency responses of*G*and*GS*+*GU*differ by no more than`AbsTol`

+`RelTol`

*abs(*G*). Increasing these tolerances helps separate nearby stable and unstable modes at the expense of accuracy. See`stabsep`

for more information.**Default:**`AbsTol = 0; RelTol = 1e-8`

`Offset`

Offset for the stable/unstable boundary. Positive scalar value. In the stable/unstable decomposition, the stable term includes only poles satisfying

`Re(s) < -Offset * max(1,|Im(s)|)`

(Continuous time)`|z| < 1 - Offset`

(Discrete time)

Increase the value of

`Offset`

to treat poles close to the stability boundary as unstable.**Default:**`1e-8`

`'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.

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.

`'EstCovar'`

— Control whether to generate parameter covariance data`true`

(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 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.

`'OutputWeight'`

— Weight of prediction errors in multi-output estimation`[]`

(default) | positive semidefinite, symmetric matrixWeight of prediction errors in multi-output estimation, specified as one of the following values:

Positive semidefinite, symmetric matrix (

`W`

). The software minimizes 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 multiple-output models, or the reliability of corresponding data.`N`

is the number of data samples.

`[]`

— No weighting is used. Specifying as`[]`

is the same as`eye(Ny)`

, where`Ny`

is the number of outputs.

This option is relevant only for multi-output models.

`'Advanced'`

— Advanced estimation optionsstructure

Advanced options for regularized estimation, specified as a structure with the following fields:

`MaxSize`

— Maximum allowable size of Jacobian matrices formed during estimation, specified as a large positive number.**Default:**`250e3`

`SearchMethod`

— Search method for estimating regularization parameters, specified as one of the following values:`'gn'`

: Quasi-Newton line search.`'fmincon'`

: Trust-region-reflective constrained minimizer. In general,`'fmincon'`

is better than`'gn'`

for handling bounds on regularization parameters that are imposed automatically during estimation. Requires Optimization Toolbox™ software.

**Default:**`'gn'`

If you have the Optimization Toolbox software, the default is

`'fmincon'`

.

`options`

— Option set for `ssregest`

`ssregestOptions`

options setEstimation options for `ssregest`

, returned
as an `ssregestOptions`

option
set.

[1] T. Chen, H. Ohlsson, and L. Ljung. "On
the Estimation of Transfer Functions, Regularizations and Gaussian
Processes - Revisited", *Automatica*,
Volume 48, August 2012.

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