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Option set for findstates
opt = findstatesOptions
opt = findstatesOptions(Name,Value)
creates
the default option set for opt
= findstatesOptionsfindstates
. Use dot
notation to customize the option set, if needed.
creates
an option set with options specified by one or more opt
= findstatesOptions(Name,Value
)Name,Value
pair
arguments. The options that you do not specify retain their default
value.
Create an option set for findstates
by configuring a specification object for the initial states.
Identify a fourthorder statespace model from data.
load iddata8 z8; sys = ssest(z8,4);
z8
is an iddata
object containing timedomain system response data. sys
is a fourthorder 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);
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 GaussNewton search is used for estimation.
opt = findstatesOptions('InitialState','d','SearchMethod','gna');
Specify optional
commaseparated 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
.
findstatesOptions('InitialState','d')
'InitialState'
— Estimation of initial states'e'
(default)  'd'
 vector or matrix  idpar
object x0Obj
Estimation of initial states, specified as the commaseparated
pair consisting of 'InitialState'
and one of the
following:
'e'
— The initial states
are estimated such that the norm of prediction error is minimized.
For nonlinear greybox models, only those initial states i
that
are designated as free in the model (sys.InitialStates(i).Fixed
= false
) are estimated. To estimate all the states of the
model, first specify all the Nx
states of the idnlgrey
model sys
as
free.
for i = 1:Nx sys.InitialStates(i).Fixed = false; end
Similarly, to fix all the initial states to values specified
in sys.InitialStates
, first specify all the states
as fixed in the sys.InitialStates
property of the
nonlinear greybox model.
'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 discretetime 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 multiexperiment
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 greybox models
and linear statespace 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 timedomain input data during estimation[]
(default)  vector of positive integers  matrixRemoval of offset from timedomain input data during estimation,
specified as the commaseparated 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.
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  matrixRemoval of offset from timedomain output data during estimation,
specified as the commaseparated 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.
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 when using multioutput data[]
(default)  'noise'
 matrixWeighting of prediction errors when using multioutput data,
specified as the commaseparated 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'
— Inverse of the
noise variance stored with the model is used for weighting during
estimation of initial states.
Positive semidefinite matrix, W
,
of size NybyNy — This
weighting minimizes trace(E'*E*W)
for estimation
of initial states, where E
is the matrix of prediction
errors.
'SearchMethod'
— Numerical search method used for iterative parameter estimation'auto'
(default)  'gn'
 'gna'
 'lm'
 'grad'
 'lsqnonlin'
 'fmincon'
Numerical search method used for iterative parameter estimation,
specified as the commaseparated 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 in sequence at each
iteration. The first descent direction leading to a reduction in estimation
cost is used.
'gn'
— Subspace GaussNewton
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 as J^{T}J.
If there is no improvement in this direction, the function tries the
gradient direction.
'gna'
— Adaptive subspace
GaussNewton search. Eigenvalues less than gamma*max(sv)
of
the Hessian are ignored, where sv contains the
singular values of the Hessian. The GaussNewton 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 fewer
than five bisections. This value is decreased by the factor 2*LMStep
each
time a search is successful without any bisections.
'lm'
— LevenbergMarquardt
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'
— Trustregionreflective
algorithm of lsqnonlin
. Requires Optimization
Toolbox™ software.
'fmincon'
— Constrained
nonlinear solvers. You can use the sequential quadratic programming
(SQP) and trustregionreflective algorithms of the fmincon
solver. If you have Optimization
Toolbox software,
you can also use the interiorpoint and activeset algorithms of the fmincon
solver.
Specify the algorithm in the SearchOption.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.
Multioutput model estimation. A determinant loss function is
minimized by default for multioutput model estimation. fmincon
algorithms
are able to minimize such loss functions directly. The other 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 multioutput model estimations.
'SearchOption'
— Option set for the search algorithmOption set for the search algorithm, specified as the commaseparated
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 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  0.01  
MaxIter  Maximum number of iterations during lossfunction minimization,
specified as a positive integer. The iterations stop when Setting Use  20  
Advanced  Advanced search settings, specified as a structure with the following fields:

SearchOption
Structure When SearchMethod
is
Specified as 'lsqnonlin'
Field Name  Description  Default 

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  1e5 
TolX  Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of  1e6 
MaxIter  Maximum number of iterations during lossfunction minimization,
specified as a positive integer. The iterations stop when The
value of  20 
Advanced  Advanced search settings, specified as an option set
for For more information, see the Optimization Options table in Optimization Options (Optimization Toolbox).  Use optimset('lsqnonlin') to create a default
option set. 
SearchOption
Structure When SearchMethod
is
Specified as 'fmincon'
Field Name  Description  Default 

Algorithm 
For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).  'sqp' 
TolFun  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.  1e6 
TolX  Termination tolerance on the estimated parameter values, specified as a positive scalar.  1e6 
MaxIter  Maximum number of iterations during loss function minimization,
specified as a positive integer. The iterations stop when  100 
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;
opt
— Option set for findstates
findstatesOptions
option setOption set for findstates
, returned as
an findstatesOptions
option set.
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