n4sidOptions
Option set for n4sid
Description
Use an n4sidOptions
object to specify options for estimating
statespace models using the n4sid
function. You can specify options such as
the handling of initial states, stability enforcement, and the weighting prefilter to be used
in estimation.
Creation
Properties
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.
N4Weight
— Weighting scheme used for singularvalue decomposition by the N4SID algorithm
'auto'
(default)  'MOESP'
 'CVA'
 'SSARX'
 'all'
Weighting scheme used for singularvalue decomposition by the N4SID algorithm, specified as one of the following values:
'MOESP'
— Uses the MOESP algorithm by Verhaegen [2].'CVA'
— Uses the Canonical Variate Algorithm by Larimore [1].Estimation using frequencydomain 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 closedloop operation. For more information about the algorithm, see [4].
'all'
—n4sid
performs separate estimations for'MOESP'
,'CVA'
, and'SSARX'
and returns the estimation results for the weighting scheme that provides the best fit.'auto'
—n4sid
automatically selects the algorithm.
N4Horizon
— Forward and backwardprediction horizons used by the N4SID
algorithm
'auto'
(default)  vector [r sy su]
 k
by3 matrix
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]
, wherer
is the maximum forward prediction horizon. The algorithm uses up tor
stepahead predictors.sy
is the number of past outputs, andsu
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. MakingN4Horizon
a kby3 matrix means that each row ofN4Horizon
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 specifyN4Horizon
as a single column,r = sy = su
is used.'auto'
— The software uses an Akaike Information Criterion (AIC) for the selection ofsy
andsu
.
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 system
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 values in the following
table.
Value  Description 

[]  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, specify
Passbands are expressed in
rad/ 
SISO filter  Specify a singleinputsingleoutput (SISO) linear filter in one of the following ways:

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, 
EnforceStability
— Control whether to enforce stability of model
false
(default)  true
Control whether to enforce stability of estimated model, specified
as the commaseparated pair consisting of 'EnforceStability'
and
either true
or false
.
EstimateCovariance
— Option to generate parameter covariance data
true
(default)  false
Option to generate parameter covariance data, specified as true
or
false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Option to display estimation progress
'off'
(default)  'on'
Option 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.
InputInterSample
— Inputchannel intersample behavior
'auto'
 'zoh'
 'foh'
 'bl'
Inputchannel intersample behavior for transformations between discrete time and continuous time, specified as 'auto'
, 'zoh'
,'foh'
, or 'bl'
.
The definitions of the three behavior values are as follows:
'zoh'
— Zeroorder hold maintains a piecewiseconstant input signal between samples.'foh'
— Firstorder hold maintains a piecewiselinear input signal between samples.'bl'
— Bandlimited behavior specifies that the continuoustime input signal has zero power above the Nyquist frequency.
iddata
objects have a similar property,
data.InterSample
, that contains the same behavior value options.
When the InputInterSample
value is 'auto'
and
the estimation data is in an iddata
object data
, the
software uses the data.InterSample
value. When the estimation data
is instead contained in a timetable or a matrix pair, with the 'auto'
option, the software uses 'zoh'
.
The software applies the same option value to all channels and all experiments.
InputOffset
— Removal of offset from timedomain input data during estimation
[]
(default)  vector of positive integers  matrix
Removal of offset from timedomain input data during estimation, specified as 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  matrix
Removal of offset from timedomain output data during estimation, specified as 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 matrix
Weighting 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 andN
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.Positive semidefinite symmetric matrix (
W
) — Minimize the trace of the weighted prediction error matrixtrace(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'noise'
and using the identity matrix forW
.
This option is relevant for only multioutput models.
Advanced
— Additional advanced options
structure with field MaxSize
of 250000 (default)  structure
Additional advanced options, specified as a structure with the field
MaxSize
. MaxSize
specifies the maximum number of
elements in a segment when inputoutput data is split into segments.
MaxSize
must be a positive integer.
Examples
Create Default Options Set for StateSpace Estimation Using Subspace Method
opt = n4sidOptions;
Specify Options for StateSpace 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, Wallace 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, Michel. "Identification of the deterministic part of MIMO state space models given in innovations form from inputoutput data." Automatica, Vol. 30, No. 1, 1994, pp. 61–74. https://doi.org/10.1016/00051098(94)902291
[3] Ljung, Lennart. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
[4] Jansson, Magnus. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, 2003.
Version History
Introduced in R2012aR2022b: InputInterSample
option allows intersample behavior specification for continuous models estimated from timetables or matrices.
iddata
objects contain an InterSample
property that
describes the behavior of the signal between sample points. The
InputInterSample
option implements a version of that property in
n4sidOptions
so that intersample behavior can be specified also when
estimation data is stored in timetables or matrices.
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