findstates
Estimate initial states of model
Syntax
Description
estimates the initial states x0
= findstates(sys
,data
)x0
of an identified model
sys
to maximize the fit between the model response and
the output signal in the estimation data data
.
data
can be a timetable, a commaseparated input/output
matrix pair, or a timedomain or frequencydomain iddata
object.
For timetables and data objects, findstates
matches the
input/output channels based on the channel names in sys
and
ignores nonmatching channels.
Examples
Estimate Initial States of a Model
Create a nonlinear greybox model. The model is 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.
FileName = 'dcmotor_m'; Order = [2 1 2]; Parameters = [0.24365;0.24964]; nlgr = idnlgrey(FileName,Order,Parameters); nlgr = setinit(nlgr, 'Fixed', false(2,1)); % set initial states free
Load data for initial state estimation.
load dcmotordata
z = iddata(y,u,0.1);
Estimate the initial states such that the model's response using the estimated states X0 and measured input u is as close as possible to the measured output y.
X0 = findstates(nlgr,z,Inf);
Estimate Initial States of StateSpace Model
Estimate an idss
model and simulate it such that the response of the estimated model matches the estimation data's output signal as closely as possible.
Load sample data.
load iddata1 z1;
Estimate a linear model from the data.
model = ssest(z1,2);
Estimate the value of the initial states to best fit the measured output z1.y
.
x0est = findstates(model,z1,Inf);
Simulate the model.
opt = simOptions('InitialCondition',x0est);
sim(model,z1(:,[],:),opt);
Selectively Estimate Initial States of a Model
Estimate the initial states of a model selectively by fixing the first state and allowing the second state of the model to be estimated.
Create a nonlinear greybox model.
FileName = 'dcmotor_m';
Order = [2 1 2];
Parameters = [0.24365;0.24964];
nlgr = idnlgrey(FileName,Order,Parameters);
The model is 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.
Load the estimation data.
load dcmotordata
z = iddata(y,u,0.1);
Hold the first state fixed at zero, and estimate the value of the second.
x0spec = idpar('x0',[0;0]);
x0spec.Free(1) = false;
opt = findstatesOptions;
opt.InitialState = x0spec;
[X0,Report] = findstates(nlgr,z,Inf,opt)
X0 = 2×1
0
0.0061
Report = Status: 'Estimated by simulation error minimization' Method: 'lsqnonlin' Covariance: [2x2 double] DataUsed: [1x1 struct] Termination: [1x1 struct]
Estimate Initial States by Specifying an Initial State Vector
Create a nonlinear greybox model.
FileName = 'dcmotor_m';
Order = [2 1 2];
Parameters = [0.24365;0.24964];
nlgr = idnlgrey(FileName,Order,Parameters);
The model is 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.
Load the estimation data.
load dcmotordata
z = iddata(y,u,0.1);
Specify an initial guess for the initial states.
x0spec = idpar('x0',[10;10]);
x0spec.Free
is true by default
Estimate the initial states
opt = findstatesOptions; opt.InitialState = x0spec; x0 = findstates(nlgr,z,Inf,opt)
x0 = 2×1
0.0362
0.1322
Estimate Initial States Using MultiExperiment Data
Create a nonlinear greybox model.
FileName = 'dcmotor_m'; Order = [2 1 2]; Parameters = [0.24365;0.24964]; nlgr = idnlgrey(FileName,Order,Parameters); set(nlgr, 'InputName','Voltage','OutputName', ... {'Angular position','Angular velocity'});
The model is 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.
Load the estimation data.
load dcmotordata z = iddata(y,u,0.1,'Name','DCmotor',... 'InputName','Voltage','OutputName',... {'Angular position','Angular velocity'});
Create a threeexperiment data set.
z3 = merge(z,z,z);
Choose experiment for estimating the initial states:
Estimate initial state 1 for experiments 1 and 3
Estimate initial state 2 for experiment 1
The fixed initial states have zero values.
x0spec = idpar('x0',zeros(2,3));
x0spec.Free(1,2) = false;
x0spec.Free(2,[2 3]) = false;
opt = findstatesOptions;
opt.InitialState = x0spec;
Estimate the initial states.
[X0,EstInfo] = findstates(nlgr,z3,Inf,opt);
Input Arguments
sys
— Identified model
idss
object  idgrey
object  idnlarx
object  idnlhw
object  idnlgrey
object
Identified model whose initial states are estimated, represented
as a linear statespace (idss
or idgrey
)
or nonlinear model (idnlarx
, idnlhw
,
or idnlgrey
).
data
— Estimation data
timetable  matrices  cell array  iddata object
Estimation data, specified as a uniformly sampled timetable, pair of
input/output matrices, cell array, or iddata
data object. The
input/output dimensions of data
must match
sys
. The specification for
data
depends on the data type.
Timetable
For SISO, MISO, and MIMO systems, specify data
as
a timetable
that uses a
regularly spaced time vector. For the timetable
data
type, data
contains variables representing the
input and output channels.
data
must have the same variable names as the
original data from which each model sys
was
estimated. The model properties include the names of the input and
output variables. You therefore do not need to explicitly specify which
channels to use in the timetable.
For multiexperiment data, specify data
as a
1byNe cell array, where Ne
is the number of experiments. The sample times of all the experiments
must match.
Matrices
For SISO, MISO, and MIMO systems, specify data as a pair of matrices
with dimensions NsbyNu for the
input matrix and NsbyNy for the
output matrix. The software uses the sample period in the
Ts
property of sys
.
For multiexperiment data, specify data
as a pair
of 1byNe cell arrays, where Ne
is the number of experiments. The sample times of all the experiments
must match the sample time of sys
.
iddata
Object
For all model types, data
can be a timedomain
iddata
object.
If sys
is a linear model,
data
can also be a frequencydomain
iddata
object. For easier interpretation of
initial conditions, make the frequency vector of
data
be symmetric about the origin. For
converting timedomain data into frequencydomain data, use fft
with the
'compl'
input argument, and ensure that there is
sufficient zero padding. Scale your data appropriately when you compare
x0
between the timedomain and
frequencydomain. Since for an Npoint FFT, the
input/output signals are scaled by 1/sqrt(N)
, the
estimated x0
vector is also scaled by this factor.
For more information about working with estimation data types, see Data Domains and Data Types in System Identification Toolbox.
Horizon
— Prediction horizon for computing model response
1
(default)  positive integer between 1
and Inf
Prediction horizon for computing the response of sys
,
specified as a positive integer between 1
and Inf
.
The most common values used are:
Horizon = 1
— Minimizes the 1step prediction error. The 1–step ahead prediction response ofsys
is compared to the output signals indata
to determinex0
. Seepredict
for more information.Horizon = Inf
— Minimizes the simulation error. The difference between measured output,data.y
, and simulated response ofsys
to the measured input data,data.u
is minimized. Seesim
for more information.
Specify Horizon
as any positive integer
between 1 and Inf
, with the following restrictions:
Scenario  Horizon 

Continuoustime model with timedomain data  1 or Inf 
Continuoustime frequencydomain data (  Inf 
Output Error models (trivial noise component):

Irrelevant Any value of 
Nonlinear ARX (idnlarx )  1 or Inf 
Options
— Estimation options for findstates
findstates
Option set
Estimation options for findstates
, specified
as an option set created using findstatesOptions
Output Arguments
x0
— Estimated initial states
vector  matrix
Estimated initial states of model sys
,
returned as a vector or matrix. For multiexperiment data, x0
is
a matrix with one column for each experiment.
Report
— Initial state estimation information
structure
Initial state estimation information, returned as a structure. Report
contains
information about the data used, state covariance, and results of
any numerical optimization performed to search for the initial states. Report
has
the following fields:
Report Field  Description  

Status  Summary of how the initial state were estimated.  
Method  Search method used.  
Covariance  Covariance of state estimates, returned as a NsbyNs matrix, where Ns is the number of states.  
DataUsed  Attributes of the data used for estimation, returned as a structure with the following fields.
 
Termination  Termination conditions for the iterative search used for initial state estimation of nonlinear models. Structure with the following fields:

Version History
Introduced in R2015aR2022b: Timedomain estimation data is accepted in the form of timetables and matrices
Most estimation, validation, analysis, and utility functions now accept timedomain
input/output data in the form of a single timetable that contains both input and output data
or a pair of matrices that contain the input and output data separately. These functions
continue to accept iddata
objects as a data source as well, for
both timedomain and frequencydomain data.
R2018a: Advanced Options are deprecated for SearchOptions
when SearchMethod
is 'lsqnonlin'
Specification of lsqnonlin
 related advanced options are deprecated,
including the option to invoke parallel processing when estimating using the
lsqnonlin
search method, or solver, in Optimization Toolbox™.
See Also
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