System Identification:
from open-loop and closed-loop systems
to dynamic networks
Paul M.J. Van den Hof
Inauguration speech,
Hungarian Academy of Sciences, October 2, 2017, Budapest, Hungary
System identification
• Estimating dynamic models on the
basis of noisy observations over time
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u
G
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y
• Dynamic cause-effect relationships described by
(linear) ordinary differential equations (ODE’s)
• Models in physical structure or “black-box”
System identification
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G
• Omnipresent/ubiquitous in many branches of
science and technology
• from econometrics to mechatronics, and
• from medicine / disease treatment to robotics
• from automotive systems to industrial processes
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y
System identification
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• Use of models, for
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understanding
prediction of future behaviour
r
simulation
indirect measurement / monitoring
control
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• Model-based control and optimization is the leading
paradigm for the optimal operation of dynamical
systems
• Model = knowledge base,
stored structured information from the past
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y
A “man-on-the-moon” example
ASML Wafer scanner
• Moving mass 90 kg
• Scan a wafer in 13 sec,
0.13 sec per chip.
• Overlay of around 2 nm.
https://youtu.be/jH6Urfqt_d4?t=2m29s
System identification – the birth
Proc. IFAC Symp. Self-Adaptive Control Systems,
Teddington, England, 1965
Karl J. Åström
Rudolf Kalman
Torsten Bohlin
Effective construction of linear state-variable models from
input-output functions.
Regelungstechnik, Vol. 14 (1966), 545-548.
System identification
Pieter Eykhoff
1974
Graham Goodwin
Goodwin and Payne (1977)
System identification – Prediction Error Approach
Lennart Ljung
(1987)
(1999)
System identification
Rik Pintelon and Johan Schoukens
(2000,2012), Frequency domain approach
My own entrance into the field
Tibor Vamos
Janos Gertler Laszlo Keviczky
Contents
• Introduction
• Developments and some highlights
•
•
•
•
From SISO to MIMO
Orthogonal basis funcitons
Closed-loop identification
Identification for control
• The role in future technology
• Towards dynamic network identification
Developments and some highlights
• From SISO to MIMO (multi-input multi-output)
u
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Just technicalities and added complexity?
For black-box models:
How to parsemoneously and uniquely parametrize models through
a real-valued vector to be estimated from data?
For number of outputs p > 1 this is a nontrivial problem
From SISO to MIMO
Options:
State space models:
For p>1, there exists no continuous parametrization that covers all models,
with a predefined order (state space dimension)
[Hazewinkel and Kalman, 1976]
Matrix fractions / Vector difference equations:
with
matrix polynomials in the forward and backward shift operators
Focus of many contributions in the 1980s, on the construction of canonical and
pseudo-canonical (overlapping) forms.
From SISO to MIMO
Set of all models with order n
Focus of many contributions in the 1980s, among which Gevers, Wertz, Guidorzi,
Bokor and Keviczky, Correa and Glover, Rissanen, ....
Important insights into the structural properties of linear MIMO systems
After 1990s in identification
• succeeded by subspace and other techniques,
• less sensitive to lack of uniqueness of the parameters – models mapping
Orthogonal basis functions (OBFs)
0.3
Pulse response representation:
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
10
20
30
40
with
complete set of orthogonal basis functions
of the function space
(all stable models)
As a parametrized model set:
with possibly large values of
Are there appropriate generalizations of the set of basis functions
that allow a fast convergence of the series?
Orthogonal basis functions (OBFs)
0.8
Consider
0.6
0.4
where the functions have dynamics
(prior info)
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0
Examples:
Laguerre:
Orthogonalized version of
Takenake/Malmquist:
Orthogonalized version of
GOBF’s: use repeated set of poles
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0
10
20
30
40
Orthogonal basis functions (OBFs)
Generalization of tapped delay line:
With all-pass functions
Analysis and completeness:
Built on the clasic work of a.o. Otto Sász (1955) and Gábor Szegő (1939,1958)
Orthogonal basis functions (OBFs)
GOBFs: very effective model structure for identification:
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identification properties fully analyzed (VdH, Heuberger, Bokor, 1995)
simple (linear regression) algorithms
appropriate handling of prior info
fit for large scale problems
used for uncertainty quantification
for nonlinear (LPV) modeling
and in system (realization) theory
Orthogonal basis functions (OBFs)
GOBFs: very effective model structure for identification:
Hambo
Transform
Closed-loop identification
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• Many systems operate under the
presence of feedback (control)
• Intrinsic problem that input and
disturbances are correlated
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• Plant input u is only partly under control of
a designed experiment r
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r, u and y are measured
Classical approach:
• Direct parametric method, based on u,y, (Swedish school, 1970s)
• Consistent and minimum variance (CRLB), under perfect conditions
No well-interpretable results in case of approximations
Closed-loop identification
e
Projection/two-stage/IV method
[Van den Hof & Schrama, 1993]
H0
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Use measured excitation signal
to generate ,
the signal projected onto
,
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u
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Estimate the dynamics between
and
Plant representation
white noise
and
uncorrelated
y
Closed-loop identification
1. Direct method
e
[Ljung, 1987]
Consistent estimate of
provided that u is sufficiently exciting
Estimate achieves minimum variance
(CRLB)
H0
v
r -
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u
G0
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Implicit approximation properties
C
2. Projection/two-stage/IV method
[Van den Hof & Schrama, 1993]
Plant representation
Consistent estimate of
provided that
is sufficiently exciting
No minimum variance properties
Tunable approximation properties
white noise
and
uncorrelated
y
Identification for control
Model-based control
10
disturbance
10
Data
Model
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output
input
2
amplitude
0
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-4
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process
process
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-1
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fase
-200
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frequency
Identification
Feedback
control system
Feedback
Feedbackcontrol
control system
system
disturbance
Model
Controller
reference
input +
output
controller
controller
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process
process
Identification for control
• High interest from control community in 1990s
Gevers, Bitmead, Anderson, Schrama, de Callafon, Keviczky, Banyasz, Lee,
Skelton, Kosut, Hansen, Mareels, Bombois
• Primal result:
Optimal models for control are identified under
closed-loop conditions, with the to-be-designed
controller in the loop
disturbance
reference
input +
output
controller
controller
-
process
process
Identification for control
experiment design
Experiment
Experiment
data
Identification
Identificatie
model
Solution through iterative
procedure
Modelling for control is
learning
(Gevers, 1993; Schrama, 1992;
Lee, Anderson et al, 1992,1993)
Control design
Regelaarontwerp
controller
Implementation
Implementatie
evaluation
Modern version of
adaptive control
Identification for control
• In process control, experiments are typically expensive
Reaching the highest performance for an
expensive experiment
Designing the most economic experiment that
reaches the performance requirements
Least-costly experiment design
(Bombois et al., 2006)
Identification for control - Autoprofit
Advanced Autonomous Model-Based
Operation of Industrial Process Systems
Goal of the project:
Improved lifetime performance of model-based (MPC)
controllers by autonomous cost efficient maintenance.
EU-STREP 2010-2013 – 2.5M€ www.fp7-autoprofit.eu
Developments focused on:
• Performance monitoring and
diagnostics
• Autonomous testing:
• Autonomous MPC tuning:
• Extension to non-linear systems
• LPV modeling
economic criterion based decisions
Identification for control - Autoprofit
Performance
monitoring & diagnosis
Degradation detected
selection of appropriate action
Model structure
assessment
least-costly
re-identification
Retuning of
model-based
application
Prototype testing on industrial
FT depropanizor (Sasol)
Autonomous maintenance for linear
model-based operation
Contents
• Introduction
• Developments and some highlights
•
•
•
•
From SISO to MIMO
Orthogonal basis funcitons
Closed-loop identification
Identification for control
• The role in future technology
• Towards dynamic network identification
Industry 4.0 – process operations aspects
From isolated (statically) optimized units to
• integrated chains/networks of production units,
• fully automated, high level of sensing/actuation,
• data and product flows across classical
(company) borders (suppliers,customers,
energy grid)
• modular build-up
• continuously monitored for control,
optimization, (predictive) maintenance,
analysis, ......
• adapting to changing circumstances (process
and market conditons), and learning
• economically optimized
• supervised by new-generation HMI technology
and operators
[Boston Consulting Group report: “Industry
4.0, The Future of Production & Growth in
Manufacturing Industries“, 2015]
Cyber-physical systems of systems
Similar developments in other domains of technology
Proposal of a European Research and Innovation Agenda on Cyber-Physical Systems of Systems, 2016-2025
Role in future technology
Future requirements on engineering systems:
Handling of highly complex
interacting
distributed
systems that
operate
autonomously
with variable objectives
in a ``learning’’ mode
adapting to changing circumstances
and maintain a verifiable high performance
Role in future technology
Some required capabilities of models
1. Accuracy assessment
on-line assessment of model validity
2. Adaptability
flexible on-line updating of models (dynamics and
interconnection structure)
3. Active data-driven learning
demands on accuracy, autonomy, robustness
 active probing for information
all relating to phenomena of data-driven modeling
Data-driven modeling becomes an integral part in
virtually all complex engineering systems
Information-driven operations
From model-based control to information-driven operations
First principles
Models
Optimal proces operations
Process data
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Monitoring
Indirect measurements
Control
(Predictive) maintenance
Optimization
Scheduling
From single loops to interconnected systems
Networked and distributed systems:
• collection of dynamical subsystems
• local control capability,
• physically interacting
Examples: smart power grids, intelligent traffic
networks, sensor networks & process plants
and their supply chain.
Contents
• Introduction
• Developments and some highlights
•
•
•
•
From SISO to MIMO
Orthogonal basis funcitons
Closed-loop identification
Identification for control
• The role in future technology
• Towards dynamic network identification
Dynamic network identification
Example decentralized MPC; 2 interconnected MPC loops
Target:
Identify interaction dynamics
G10
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C1
u1
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G1
y1
Addressed by
Gudi & Rawlings (2006)
for the situation
(no cycles)
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G21
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C2
u2
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G2
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y2
v2
Gudi, R. D. and Rawlings, J. B. (2006). Identification for decentralized model predictive control.
AIChE Journal, 52(6):2198-2210.
Dynamic network identification
Example decentralized MPC; 2 interconnected MPC loops
Target:
Identify interaction dynamics
G10
r1
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C1
u1
v1
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y1
Structural aspects
need to be addressed.
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Dynamic network identification
ri external excitation
vi process noise
wi node signal
Some modules may be known (e.g. controllers)
Dynamic network identification
ri external excitation
vi process noise
wi node signal
Some modules may be known (e.g. controllers)
Dynamic network identification
ri external excitation
vi process noise
wi node signal
Some modules may be known (e.g. controllers)
Dynamic network identification
ri external excitation
vi process noise
wi node signal
Some modules may be known (e.g. controllers)
Dynamic network identification
Relevant identification questions that appear:
How to perform local identification?
which signals to measure?
Dynamic network identification
Relevant identification questions that appear:
Where to optimally locate sensors and actuators?
Dynamic network identification
Relevant identification questions that appear:
How to identify a subnetwork?
which signals to measure?
Dynamic network identification
Relevant identification questions that appear:
How can we benefit from known (orange) modules?
Dynamic network identification
Relevant identification questions that appear:
Can we (on-line) identify the topology?
(notion of identifiability)
Dynamic network identification
Relevant identification questions that appear:
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Fault detection and isolation?
Detect/identify/handle nonlinear elements
Dynamic network identification
• Attractive and rich domain
of research
• Many challenges ahead
• Relation to distributed
control / optimization
(multi-agent systems)
• Relate to developments in
machine learning / data
analytics
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An exciting area with lots of new questions to be explored
Acknowledgements
• My teachers and supervisors:
Ad Damen, Pieter Eykhoff, Okko Bosgra and Jan Willems
• My co-authors, PhD students and postdocs, and
colleagues from TU Delft and TU Eindhoven
• International colleagues in the control community
• My Hungarian colleagues and co-authors from SZTAKI,
Jozsef Bokor, Laszlo Keviczky, Szoltan Szabo
• My sponsors, among which EU (FP7, ERC).
Acknowledgements
Köszönöm nagyrabecsülésüket és a megtiszteltetést,
amit e rangos cím jelent számomra!
THE END