# Documentation

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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.

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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.

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

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

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.

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] 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.

Control whether to enforce stability of estimated model, specified as the comma-separated pair consisting of 'EnforceStability' and either true or false.

Data Types: logical

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.

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.

Removal 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.

Removal 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.

Weighting of prediction errors in multi-output estimations, specified as one of the following values:

• 'noise' — Minimize $\mathrm{det}\left(E\text{'}*E/N\right)$, 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 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/N) where:

• 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-output 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 only for multi-output models.

Additional advanced options, specified as 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

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Option set for n4sid, returned as an n4sidOptions option set.

## Examples

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opt = n4sidOptions;

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.

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