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n4sidOptions

Option set for n4sid

Syntax

opt = n4sidOptions
opt = n4sidOptions(Name,Value)

Description

opt = n4sidOptions creates the default options set for n4sid.

opt = n4sidOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

Input Arguments

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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 single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'InitialState' — Specify handling of initial states during estimation'estimate' (default) | 'zero'

Specify handling of initial states during estimation, specified as one of the following strings:

• 'zero' — The initial state is set to zero.

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

'N4Weight' —

Weighting scheme used for singular-value decomposition by the N4SID algorithm.

'N4Weight' requires one of the following values:

• 'MOESP' — Uses the MOESP algorithm by Verhaegen [2].

• 'CVA' — Uses the Canonical Variable Algorithm by Larimore [1].

Estimation using frequency-domain data always uses 'CVA'.

• 'SSARX' — A subspace identification method that uses an ARX estimation based algorithm to compute the weighting.

Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see [4].

• 'auto' — The estimating function chooses between the MOESP, CVA and SSARX algorithms.

'N4Horizon' —

Forward- and backward-prediction horizons used by the N4SID algorithm.

'N4Horizon' requires one of the following values:

• A row vector with three elements —  [r sy su], where r is the maximum forward prediction horizon, using up to r step-ahead predictors. sy is the number of past outputs, and su is the number of past inputs that are used for the predictions. See pages 209 and 210 in [3] for more information. These numbers can have a substantial influence on the quality of the resulting model, and there are no simple rules for choosing them. Making 'N4Horizon' a k-by-3 matrix means that each row of 'N4Horizon' is tried, and the value that gives the best (prediction) fit to data is selected. k is the number of guesses of  [r sy su] combinations. If you specify N4Horizon as a single column, r = sy = su is used.

• 'auto' — The software uses an Akaike Information Criterion (AIC) for the selection of sy and su.

'Focus' —

Defines how the errors e between the measured and the modeled outputs are weighed at specific frequencies during the minimization of the prediction error.

Higher weighting at specific frequencies emphasizes the requirement for a good fit at these frequencies.

Focus requires one of the following values:

• 'simulation' — Estimates the model using the frequency weighting of the transfer function that is given by the input spectrum. Typically, this method favors the frequency range where the input spectrum has the most power.

This method provides a stable model.

• 'prediction' — Automatically calculates the weighting function as a product of the input spectrum and the inverse of the noise model. The weighting function minimizes the one-step-ahead prediction, which typically favors fitting small time intervals (higher frequency range). From a statistical-variance point of view, this weighting function is optimal. However, this method neglects the approximation aspects (bias) of the fit. Thus, the method may not result in a stable model. Specify Focus as 'stability' when you want to ensure a stable model.

• 'stability' — Same as 'prediction', but with model stability enforced.

• Passbands — Row vector or matrix containing frequency values that define desired passbands. For example:

```[wl,wh]
[w1l,w1h;w2l,w2h;w3l,w3h;...]```

where wl and wh represent upper and lower limits of a passband. For a matrix with several rows defining frequency passbands, the algorithm uses union of frequency ranges to define the estimation passband.

• SISO filter — Enter any SISO linear filter in any of the following ways:

• A single-input-single-output (SISO) linear system.

• The {A,B,C,D} format, which specifies the state-space matrices of the filter.

• The {numerator, denominator} format, which specifies the numerator and denominator of the filter transfer function

This format calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function. To obtain a good model fit for a specific frequency range, you must choose the filter with a passband in this range. The estimation result is the same if you first prefilter the data using idfilt.

• Weighting vector — For frequency-domain data only, enter a column vector of weights for 'Focus'. This vector must have the same size as length of 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 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 strings:

Display requires one of the following strings:

• 'on' — Information on model structure and estimation results are displayed in a progress-viewer window

• 'off' — No progress or results information is displayed

'InputOffset' — Remove offset from time-domain input data during estimation[] (default) | vector of positive integers

Removes offset from time-domain input data during estimation, specified as a vector of positive integers.

Specify as a column vector of length Nu, where Nu is the number of inputs.

Use [] to indicate no offset.

For multiexperiment data, specify InputOffset as a 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' — Remove offset from time-domain output data during estimation[] (default) | vector

Removes offset from time domain output data during estimation, specified as a vector of positive integers or [].

Specify as a column vector of length Ny, where Ny is the number of outputs.

Use [] to indicate no offset.

For multiexperiment 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' — Criterion used during minimization[] (default) | 'noise' | positive semidefinite symmetric matrix

Specifies criterion used during minimization, specified as one of the following:

• 'noise' — Minimize $\mathrm{det}\left(E\text{'}*E\right)$, where E represents the prediction error. This choice is optimal in a statistical sense and leads to the maximum likelihood estimates in case no data is available about the variance of the noise. This option uses the inverse of the estimated noise variance as the weighting function.

• Positive semidefinite symmetric matrix (W) — Minimize the trace of the weighted prediction error matrix trace(E'*E*W). E is the matrix of prediction errors, with one column for each output. 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-input, multiple-output models, or the reliability of corresponding data.

This option is relevant only for multi-input, multi-output models.

• [] — The software chooses between the 'noise' or using the identity matrix for W.

Advanced is a structure with the field MaxSize. 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

Output Arguments

 opt Option set containing the specified options for n4sid.

Examples

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Create Default Options Set for State-Space Estimation Using Subspace Method

```opt = n4sidOptions;
```

Specify Options for State-Space Estimation Using Subspace Method

Create an options set for n4sid using the 'zero' option to initialize the state. Set the Display to 'on'.

```opt = n4sidOptions('InitialState','zero','Display','on');
```

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

```opt = n4sidOptions;
opt.InitialState = 'zero';
opt.Display = 'on';
```

References

[1] Larimore, W.E. "Canonical variate analysis in identification, filtering and adaptive control." Proceedings of the 29th IEEE Conference on Decision and Control, pp. 596–604, 1990.

[2] Verhaegen, M. "Identification of the deterministic part of MIMO state space models." Automatica, Vol. 30, 1994, pp. 61–74.

[3] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.

[4] Jansson, M. "Subspace identification and ARX modeling." 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.