nlgreyestOptions

Option set for nlgreyest

Syntax

opt = nlgreyestOptions

opt = nlgreyestOptions(Name,Value)

Description

opt = nlgreyestOptions creates the default option set for nlgreyest. Use dot notation to customize the option set, if needed.

opt = nlgreyestOptions(Name,Value) creates an option set with options specified by one or more Name,Value pair arguments. The options that you do not specify retain their default value.

Examples

Create Default Option Set for Nonlinear Grey-Box Model Estimation

opt = nlgreyestOptions;

Estimate a Nonlinear Grey-Box Model Using Specific Options

Create estimation option set for nlgreyest to view estimation progress, and to set the maximum iteration steps to 50.

opt = nlgreyestOptions;
opt.Display = 'on';
opt.SearchOptions.MaxIterations = 50;

Load data.

load dcmotordata
z = iddata(y,u,0.1,'Name','DC-motor');

The data is from a linear DC motor with one input (voltage), and two outputs (angular position and angular velocity). The structure of the model is specified by dcmotor_m.m file.

Create a nonlinear grey-box model.

file_name = 'dcmotor_m';
Order = [2 1 2];
Parameters = [1;0.28];
InitialStates = [0;0];

init_sys = idnlgrey(file_name,Order,Parameters,InitialStates,0, ...
    'Name','DC-motor');

Estimate the model parameters using the estimation options.

sys = nlgreyest(z,init_sys,opt);

Specify Options for Nonlinear Grey-Box Model Estimation

Create an option set for nlgreyest where:

• Parameter covariance data is not generated.

• Subspace Gauss-Newton least squares method is used for estimation.

opt = nlgreyestOptions('EstimateCovariance',false,'SearchMethod','gn');

Input Arguments

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: nlgreyestOptions('Display','on')

GradientOptions — Options for computing Jacobians and gradients

structure

Options for computing Jacobians and gradients, specified as the comma-separated pair consisting of 'GradientOptions' and a structure with fields:

Field Name	Description	Default
MaxDifference	Largest allowed parameter perturbation when computing numerical derivatives. Specified as a positive real value > 'MinDifference'.	Inf
MinDifference	Smallest allowed parameter perturbation when computing numerical derivatives. Specified as a positive real value <'MaxDifference'.	0.01*sqrt(eps)
DifferencingScheme	Method for computing numerical derivatives with respect to the components of the parameters and/or the initial state(s) to form the Jacobian. Specified as one of the following: 'Auto' - Automatically chooses from the following methods. 'Central approximation' 'Forward approximation' 'Backward approximation'	'Auto'
Type	Method used when computing derivatives (Jacobian) of the parameters or the initial states to be estimated. Specified as one of the following: 'Auto' — Automatically chooses from the following methods. 'Basic' — Individually computes all numerical derivatives required to form each column of the Jacobian. 'Refined' — Simultaneously computes all numerical derivatives required to form each column of the Jacobian.	'Auto'

To specify field values in GradientOptions, create a default nlgreyestOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlgreyestOptions;
opt.GradientOptions.Type = 'Basic';

EstimateCovariance — Parameter covariance data generation setting

1 or true (default) | 0 or false

Controls whether parameter covariance data is generated, specified as true (1) or false (0).

Display — Estimation progress display setting

'off' (default) | 'on'

Estimation progress display setting, specified as the comma-separated pair consisting of 'Display' and one of the following:

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

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

Regularization — Options for regularized estimation of model parameters

structure

Options for regularized estimation of model parameters, specified as the comma-separated pair consisting of 'Regularization' and a structure with fields:

Field Name	Description	Default
Lambda	Bias versus variance trade-off constant, specified as a nonnegative scalar.	0 — Indicates no regularization.
R	Weighting matrix, specified as a vector of nonnegative scalars or a square positive semi-definite matrix. The length must be equal to the number of free parameters in the model, np. Use the nparams command to determine the number of model parameters.	1 — Indicates a value of eye(np).
Nominal	The nominal value towards which the free parameters are pulled during estimation specified as one of the following: 'zero' — Pull parameters towards zero. 'model' — Pull parameters towards pre-existing values in the initial model.	'zero'

To specify field values in Regularization, create a default nlgreyestOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlgreyestOptions;
opt.Regularization.Lambda = 1.2;
opt.Regularization.R = 0.5*eye(np);

Regularization is a technique for specifying model flexibility constraints, which reduce uncertainty in the estimated parameter values. For more information, see Regularized Estimates of Model Parameters.

SearchMethod — Numerical search method used for iterative parameter estimation

'auto' (default) | 'gn' | 'gna' | 'lm' | 'grad' | 'lsqnonlin'

Numerical search method used for iterative parameter estimation, specified as the comma-separated pair consisting of 'SearchMethod' and one of the following:

• 'auto' — If Optimization Toolbox™ is available, 'lsqnonlin' is used. Otherwise, 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 Gauss-Newton least squares search. Singular values of the Jacobian matrix less than GnPinvConstant*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated by J^TJ. If there is no improvement in this direction, the function tries the gradient direction.

• 'gna' — Adaptive subspace Gauss-Newton search. Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv are the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitialGnaTolerance (see Advanced in 'SearchOptions' 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' — Levenberg-Marquardt 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' — Trust-region-reflective algorithm of lsqnonlin (Optimization Toolbox). Requires Optimization Toolbox software.

• 'fmincon' — Constrained nonlinear solvers. You can use the sequential quadratic programming (SQP) and trust-region-reflective algorithms of the fmincon solver. If you have Optimization Toolbox software, you can also use the interior-point and active-set algorithms of the fmincon (Optimization Toolbox) solver. Specify the algorithm in the SearchOptions.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.

  • Multi-output model estimation. A determinant loss function is minimized by default for MIMO model estimation. fmincon algorithms are able to minimize such loss functions directly. The other available 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 multi-output model estimations.

SearchOptions — Option set for the search algorithm

search option set

Option set for the search algorithm, specified as the comma-separated pair consisting of 'SearchOptions' and a search option set with fields that depend on the value of SearchMethod.

SearchOptions Structure When SearchMethod Is Specified as 'lsqnonlin' or 'auto', When Optimization Toolbox Is Available

Field Name	Description	Default
FunctionTolerance	Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The value of FunctionTolerance is the same as that of opt.SearchOptions.Advanced.TolFun.	1e-5
StepTolerance	Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of StepTolerance is the same as that of opt.SearchOptions.Advanced.TolX.	1e-6
MaxIterations	Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance. The value of MaxIterations is the same as that of opt.SearchOptions.Advanced.MaxIter.	20

SearchOptions Structure When SearchMethod Is Specified as 'gn', 'gna', 'lm', 'grad', or 'auto', When Optimization Toolbox Is Not Available

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 Tolerance, the iterations stop. The estimate of the expected loss-function improvement at the next iteration is based on the Gauss-Newton vector computed for the current parameter value.	1e-5
MaxIterations	Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as Tolerance. Setting MaxIterations = 0 returns the result of the start-up procedure. Use sys.Report.Termination.Iterations to get the actual number of iterations during an estimation, where sys is an idtf model.	20
Advanced	Advanced search settings, specified as a structure with the following fields: Field Name Description Default GnPinvConstant Jacobian matrix singular value threshold, specified as a positive scalar. Singular values of the Jacobian matrix that are smaller than GnPinvConstant*max(size(J)*norm(J)*eps) are discarded when computing the search direction. Applicable when SearchMethod is 'gn'. 10000 InitialGnaTolerance Initial value of gamma, specified as a positive scalar. Applicable when SearchMethod is 'gna'. 0.0001 LMStartValue Starting value of search-direction length d in the Levenberg-Marquardt method, specified as a positive scalar. Applicable when SearchMethod is 'lm'. 0.001 LMStep Size of the Levenberg-Marquardt step, specified as a positive integer. The next value of the search-direction length d in the Levenberg-Marquardt method is LMStep times the previous one. Applicable when SearchMethod is 'lm'. 2 MaxBisections Maximum number of bisections used for line search along the search direction, specified as a positive integer. 25 MaxFunctionEvaluations Maximum number of calls to the model file, specified as a positive integer. Iterations stop if the number of calls to the model file exceeds this value. Inf MinParameterChange Smallest parameter update allowed per iteration, specified as a nonnegative scalar. 0 RelativeImprovement Relative improvement threshold, specified as a nonnegative scalar. Iterations stop if the relative improvement of the criterion function is less than this value. 0 StepReduction Step reduction factor, specified as a positive scalar that is greater than 1. The suggested parameter update is reduced by the factor StepReduction after each try. This reduction continues until either MaxBisections tries are completed or a lower value of the criterion function is obtained. StepReduction is not applicable for SearchMethod 'lm' (Levenberg-Marquardt method). 2

SearchOptions Structure When SearchMethod Is Specified as 'fmincon'

Field Name	Description	Default
Algorithm	fmincon optimization algorithm, specified as one of the following: 'sqp' — Sequential quadratic programming algorithm. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. It is not a large-scale algorithm. For more information, see Large-Scale vs. Medium-Scale Algorithms (Optimization Toolbox). 'trust-region-reflective' — Subspace trust-region method based on the interior-reflective Newton method. It is a large-scale algorithm. 'interior-point' — Large-scale algorithm that requires Optimization Toolbox software. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. 'active-set' — Requires Optimization Toolbox software. The algorithm can take large steps, which adds speed. It is not a large-scale algorithm. For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).	'sqp'
FunctionTolerance	Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.	1e-6
StepTolerance	Termination tolerance on the estimated parameter values, specified as a positive scalar.	1e-6
MaxIterations	Maximum number of iterations during loss function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.	100

To specify field values in SearchOptions, create a default nlgreyestOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlgreyestOptions('SearchMethod','gna');
opt.SearchOptions.MaxIterations = 50;
opt.SearchOptions.Advanced.RelImprovement = 0.5;

OutputWeight — Weighting of prediction error in multi-output estimations

[] (default) | 'noise' | matrix

Weighting of prediction error in multi-output model estimations, specified as the comma-separated pair consisting of 'OutputWeight' and one of the following:

• [] — No weighting is used. Specifying as [] is the same as eye(Ny), where Ny is the number of outputs.

• 'noise' — Optimal weighting is automatically computed as the inverse of the estimated noise variance. This weighting minimizes det(E'*E/N), where E is the matrix of prediction errors and N is the number of data samples. This option is not available when using 'lsqnonlin' as a 'SearchMethod'.

• A positive semidefinite matrix, W, of size equal to the number of outputs. This weighting minimizes trace(E'*E*W/N), where E is the matrix of prediction errors and N is the number of data samples.

Advanced — Additional advanced options

structure

Additional advanced options, specified as the comma-separated pair consisting of 'Advanced' and a structure with field:

Field Name	Description	Default
ErrorThreshold	Threshold for when to adjust the weight of large errors from quadratic to linear, specified as a nonnegative scalar. 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. If your estimation data contains outliers, try setting ErrorThreshold to 1.6.	0 — Leads to a purely quadratic loss function.

To specify field values in Advanced, create a default nlgreyestOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlgreyestOptions;
opt.Advanced.ErrorThreshold = 1.2;

Output Arguments

opt — Option set for nlgreyest

nlgreyestOptions option set

Option set for nlgreyest, returned as an nlgreyestOptions option set.

Version History

Introduced in R2015a

R2018a: Renaming of Estimation and Analysis Options

The names of some estimation and analysis options were changed in R2018a. Prior names still work.