SYSTEMS Identification

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SYSTEMSIdentification

• Ali Karimpour
• Assistant Professor
• Ferdowsi University of Mashhad

Reference System Identification Theory For The
User Lennart Ljung(1999) Practical Issues of
System Identification Lennart Ljung
(2007) Perspectives on System Identification
Lennart Ljung (2009)
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Lecture 1
Perspective on System Identification

• Topics to be covered include
• System Identification.
• Place System Identification on the global map.
  Who are our neighbors in this part of universe?
• Discuss some open areas in System Identification.

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System Identification
System Identification The art and science of
building mathematical models of dynamic systems
from observed input-output data.
System Identification is look for sustainable
description by proper decision on
Model complexity
Information contents in the data
Effective Validation
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Dynamic systems
System An object in which variables of different
kinds interact and produce observable signals.
Stimuli External signals that affects system.
Dynamic System A system that the current output
value depends not only on the current external
stimuli but also on their earlier value.
Time series A dynamic system whose external
stimuli are not observed.
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Dynamic systems
Stimuli
Input
Disturbance
It can be manipulated by the observer.
It can not be manipulated by the observer.
Measured
Unmeasured
Dynamic system
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A solar heated house
Dynamic system
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Speech generation
Dynamic system
Time series A dynamic system whose external
stimuli are not observed.
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Models
Model Relationship among observed signals.
1- Mental models
2- Graphical models
3- Mathematical (analytical) models
4- Software models

• Split up system into subsystems,

• Joined subsystems mathematically,

1- Modeling

• Does not necessarily involve any
  experimentation on the actual system.

• It is directly based on experimentation.

2- System identification

• Input and output signals from the system are
  recorded.

3- Combined
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The fiction of a true model
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The Core
The Core The core of estimating models is
statistical theory.

• Model m

• True Description S

• Model Class M

• Complexity (Flexibility) C

• Information Z

• Estimation

• Validation

• Model Fit F(m,Z)

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Estimation
A template problem Curve fitting
No more satisfaction
All data contains signal and noise.
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Estimation
The simplest explanation is usually the correct
one. So the conceptual process for estimation is
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The System Identification Problem
1- Select an input signal to apply to the process.
2- Collect the corresponding output data.
3- Scrutinize the corresponding output data to
find out if some preprocessing
4- Specify a model structure.
5- Find the best model in this structure.
6- Evaluate the property of model.
7- Test a new structure, go to step 4.
8- If the model is not adequate, go to step 3 or
1.
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The System Identification Problem
1- Choice of Input Signals.

• Filtered Gaussian White Noise.

• Random Binary Noise.

• Pseudo Random Binary Noise, PRBS.

• Multi-Sines.

• Chirp Signals or Swept Sinusoids.

• Periodic Inputs.

2- Preprocessing Data.

• Drifts and Detrending.

• Prefiltering.

3- Selecting Model Structures.

• Looking at the Data.

• Getting a Feel for the Difficulties.

• Examining the Difficulties.

• Fine Tuning Orders and Noise Structures .

• Accepting the Models .

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The Communities around the core
ML Methods, Bootstrap method,
1- Statistics.
2- Econometrics and time series analysis.
3- Statistical learning theory.
4- Machine learning.
5- Manifold learning.
6- Chemo metrics.
7- Data Mining.
8- Artificial Neural Network.
9- Fitting Ordinary Differential equation to data.
10- System Identification.
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Some Open Areas in System Identification

• Spend more time with neighbors.

• Model Reduction and System Identification.

• Issues in Identification of Non-linear
  Systems.

• Meet Demand from Industry.

• Convexification.

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Model Reduction
System identification is really system
approximation and therefore closely related to
model reduction.
Linear systems Linear models. Divide, conquer
and reunite.
Non-linear systems Linear models. Is it good
for control?
Non-linear systems nonlinear reduced models.
Much work remains.
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Linear Systems Linear ModelsDivide-Conquer-Reun
ite
Helicopter data 1 pulse input 8 outputs (only 3
shown here)
State space of order 20 wanted.
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Linear Systems Linear ModelsDivide-Conquer-Reun
ite
Next fit 8 SISO models of order 12, one for each
output
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Linear Systems Linear ModelsDivide-Conquer-Reun
ite
Reduce model from 96 to 20
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Convexification