Documentation

findstatesOptions

Option set for findstates

Syntax

  • opt = findstatesOptions example
  • opt = findstatesOptions(Name,Value) example

Description

example

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

example

opt = findstatesOptions(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

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Identify Initial States Using Option Set

Create an option set for findstates by configuring a specification object for the initial states.

Identify a fourth-order state-space model from data.

load iddata8 z8;
sys = ssest(z8,4);

z8 is an iddata object containing time-domain system response data. sys is a fourth-order idss model that is identified from the data.

Configure a specification object for the initial states of the model.

x0obj = idpar([1;nan(3,1)]);
x0obj.Free(1) = false;
x0obj.Minimum(2) = 0;
x0obj.Maximum(2) = 1;

x0obj specifies estimation constraints on the initial conditions. The value of the first state is specified as 1 when x0obj is created. x0obj.Free(1) = false specifies the first initial state as a fixed estimation parameter. The second state is unknown. But, x0obj.Minimum(2) = 0 and x0obj.Maximum(2) = 1 specify the lower and upper bounds of the second state as 0 and 1, respectively.

Create an option set for findstates to identify the initial states of the model.

opt = findstatesOptions;
opt.InitialState = x0obj;

Identify the initial states of the model.

x0_estimated = findstates(sys,z8,Inf,opt);

Specify Option Set for Estimating Initial States Using findstates

Create an option set for findstates where:

  • Initial states are estimated such that the norm of prediction error is minimized. The initial values of the states corresponding to nonzero delays are also estimated.

  • Adaptive subspace Gauss-Newton search is used for estimation.

opt = findstatesOptions('InitialState','d','SearchMethod','gna');

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.

Example: findstatesOptions('InitialState','d')

'InitialState' — Estimation of initial states'e' (default) | 'd' | vector or matrix | idpar object x0Obj

Estimation of initial states, specified as the comma-separated pair consisting of 'InitialState' and one of the following:

  • 'e' — The initial states are estimated such that the norm of prediction error is minimized.

  • 'd' — Similar to 'e', but absorbs nonzero delays into the model coefficients. The delays are first converted to explicit model states, and the initial values of those states are also estimated and returned.

    Use this option for discrete-time linear models only.

  • Vector or Matrix — Initial guess for state values, when using nonlinear models. Specify a column vector of length equal to the number of states. For multi-experiment data, use a matrix with Ne columns, where Ne is the number of experiments.

    Use this option for nonlinear models only.

  • x0obj — Specification object created using idpar. Use x0obj to impose constraints on the initial states by fixing their value or specifying minimum or maximum bounds.

    Use x0obj only for nonlinear grey-box models and linear state-space models ( idss or idgrey ). This option is applicable only for prediction horizon equal to 1 or Inf. See findstates for more details about the prediction horizon.

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

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 multiexperiment 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 | matrix

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 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' — 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), where E is the matrix of prediction errors. 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), where E is the matrix of prediction errors.

'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' — A combination of the line search algorithms, 'gn', 'lm', 'gna', and 'grad' methods is tried at each iteration. The descent direction leading to the largest reduction in estimation cost is used.

  • 'gn' — Subspace Gauss-Newton least squares search. Singular values of the Jacobian matrix less than GnPinvConst*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated by JTJ. 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 contains the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitGnaTol (see Advanced in 'SearchOption' 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 less 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 provided by Optimization Toolbox™. This method cannot be used with the 'OutputWeight' option'noise'. See lsqnonlin for more information.

'SearchOption' — Option set for the search algorithmsearch option set

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

SearchOption Structure When SearchMethod Is Specified as 'gn', 'gna', 'lm', 'grad', or 'auto'

Field NameDescriptionDefault
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.

0.01
MaxIter

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIter is reached or another stopping criterion is satisfied, such as Tolerance.

Setting MaxIter = 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.

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Advanced

Advanced search settings, specified as a structure with the following fields:

Field NameDescriptionDefault
GnPinvConst

Jacobian matrix singular value threshold, specified as a positive scalar. Singular values of the Jacobian matrix that are smaller than GnPinvConst*max(size(J)*norm(J)*eps) are discarded when computing the search direction. Applicable when SearchMethod is 'gn'.

10000
InitGnaTol

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
MaxFunEvals

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
MinParChange

Smallest parameter update allowed per iteration, specified as a nonnegative scalar.

0
RelImprovement

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 MaxBisections tries are completed or a lower value of the criterion function is obtained.

StepReduction is not applicable for SearchMethod 'lm' (Levenberg-Marquardt method).

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SearchOption Structure When SearchMethod Is Specified as 'lsqnonlin'

Field NameDescriptionDefault
TolFun

Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.

The value of TolFun is the same as that of opt.SearchOption.Advanced.TolFun.

1e-5
TolX

Termination tolerance on the estimated parameter values, specified as a positive scalar.

The value of TolX is the same as that of opt.SearchOption.Advanced.TolX.

1e-6
MaxIter

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIter is reached or another stopping criterion is satisfied, such as TolFun.

The value of MaxIter is the same as that of opt.SearchOption.Advanced.MaxIter.

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Advanced

Advanced search settings, specified as an option set for lsqnonlin.

For more information, see the Optimization Options table in Optimization Options.

Use optimset('lsqnonlin') to create a default option set.

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

opt = findstatesOptions;
opt.SearchOption.Tolerance = 0.02;
opt.SearchOption.Advanced.MaxBisections = 30;

Output Arguments

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opt — Option set for findstatesfindstatesOptions option set

Option set for findstates, returned as an findstatesOptions option set.

See Also

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Introduced in R2012a

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