Option set for findstates
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);
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 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.
'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 time domain 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 error in multioutput estimations[]
(default)  'noise'
 matrixWeighting of prediction error in multioutput model estimations,
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'
— 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 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 at each iteration.
The descent direction leading to the largest 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 by 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 less
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'
— 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 setOption 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.  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;
opt
— Option set for findstates
findstatesOptions
option setOption set for findstates
, returned as
an findstatesOptions
option set.