Lecture 14 #7B A Perspectiveon
Adaptive Control
Theme,How does adaptive control relate to
adaptive signal processing and other systems
with "intelligent features".
1,Introduction
2,Adaptive Signal Processing
3,Intelligent Systems
4,Neural Networks
5,Expert Control - Hybrid Systems
6,Conclusions
Control and SignalProcessing
#0F Signal processing and control
#7B Similarities
#03 Same methodology
#03 Similarproblems
#7B Di#0Berences
#03 Time delays
#03 Sampling rates
#7B Di#0Berent market places
#7B Silly to have separate communities
#0F Relations to recursive estimation
#0F Output error estimation
#0F Adaptive noise cancellation
#0F Adaptive pulse code modulation
Adaptive SignalProcessing
Filter
e
- 1 S
y
x
y
x#28t#29=s#28t#29+n#28t#29 and y#28t#29=s#28t+#1C#29
Introduce
#0F s signal
#0F n disturbance
#0F x = s + n measurement
Let the desired output be y#28t#29=s#28t+#1C#29,Three
problems
#0F smoothing #1C#3C0
#0F#0Cltering #1C =0
#0Fprediction #1C#3E0
Adaptive versions,adaptive smoothing etc!
A recursive estimator is an adaptive predictor!!
Adaptive FilteringFIR
Process model
y#28t#29=b
1
u#28t,1#29+b
2
u#28t,2#29+#01#01#01+b
n
u#28t,n#29
Standard form
y#28t#29='
T
#28t,1#29#12
#12
T
=#28b
1
::,b
n
#29
'
T
#28t,1#29 = #28u#28t,1#29,:,u#28t,n#29#29
The adaptive #0Clter
^y#28t#29=
^
b
1
#28t,1#29u#28t,1#29+#01#01#01+
^
b
n
#28t,1#29u#28t,n#29
Estimate given by the standard RLS
Block diagram
e
FIR filter
Adjustment
mechanism
q
y
u
S
y
- 1
y
c#0D K,J,#C5str#F6m and B,Wittenmark 1
Adaptive FilteringARMA
Equation error models
y#28t#29+a
1
y#28t,1#29 +#01#01#01+a
n
y#28t,n#29
=b
1
u#28t+m,n,1#29 +#01#01#01+b
m
u#28t,n#29
Hence
#12
T
=#28a
1
::,a
n
b
1
::,b
m
#29
'
T
#28t,1#29 =
#10
,y#28t,1#29:::,y#28t,n#29
u#28t+m,n,1#29:::u#28t,n#29
#11
#12#28t+1#29=#12#28t#29+P#28t#29'#28t#29#0F#28t+1#29
#0F#28t+1#29=y#28t+1#29,#12
T
#28t#29'#28t#29
Output Error Estimation
Model
^y#28t#29+a
1
^y#28t,1#29 +#01#01#01+a
n
^y#28t,n#29
=b
1
u#28t+m,n,1#29 +#01#01#01+b
m
u#28t,n#29
Estimator
'
T
#28t,1#29 =
#10
,^y#28t,1#29^y#28t,2#29:::,^y#28t,n#29
u#28t+m,n,1#29:::u#28t,n#29
#11
"#28t#29=y#28t#29,'
T
#28t,1#29
^
#12#28t,1#29
Filter
Adjustment
mechanism
e
q
- 1 S
y
(a)
x
S
y
x
-
q
(b)
e
y
y
Block Diagrams
Equation error estimation
Output error estimation
Adaptive Noise Cancellation
#0F The Fenton Silencer #28A,C,Clarke,1957#29
#0F B,Widrow
#0F Lots of applications
#0F Hands free car phone
-
q
Microphone for
ambient noise
Driver's microphone
S
Filtered voice
signal
Traditional estimation based on RMS #28a
gradient algorithm#29
#12#28t +1#29=#12#28t#29+#0D
'#28t,1#29
#0B + '
T
#28t,1#29'#28t,1#29
#0F#28t +1#29
c#0D K,J,#C5str#F6m and B,Wittenmark 2
Adaptive Di#0Berential Pulse Code
Modulation#28ADPCM#29
Transmission of telephone signals.
#0F Standard sampling and AD conversion,8
kHz and 12 bit gives 96 kbit#2Fs
#0F Signal compression,8 kHz and 8 bit gives
64 kbit#2Fs
#0F Transmit only the innovation,8kHz and 4
bit gives 32 kbit#2Fs
Di#0Berential pulse code modulation #28DPCM#29
Filter
e
- 1 S
y
Transmis-
sion line
Filter
e
y
y
ADPCM standard
Filter
e
- 1
S
y
Transmis-
sion line
Filter
Adjustment
mechanism
q
q
Adjustment
mechanism
e
y
y
ADPCM Details
Filter
e
- 1
S
y
Transmis-
sion line
Filter
Adjustment
mechanism
q
q
Adjustment
mechanism
e
y
y
The need for standardization CCITT
Filter
H#28z#29=
b
0
z
5
+b
1
z
4
+:::+b
5
z
4
#28z
2
+a
1
z+a
2
Parameter estimator
^
b
i
#28t#29=#281,2
,8
#29
^
b
i
#28t,1#29 + 2
,7
signe#28t,i#29signe#28t#29
Fix point calculations
IntelligentSystems
#0F Semantics
#7B Adapt adjust to new conditions
#7B Learn to acquire knowledge or skill by
study,instruction or experience
#7B Intelligence capacityfor reasoning,
understandign and similarforms of
mental activity,Ability to adapt,
learn,recognize,abstract,bene#0Ct from
experience,cope with new situations
#0F Intelligent Control
#0F An Historical Perspective
#0F Mindsets
IntelligentSystems
#0F Technical & Biological Systems
#7B Understand
#7B Imitate
#0F Cybernetics
#7B Wiener 1948
#7B Ashby 1956
#0F Neural Systems
#7B Mc Culloch Pitts 1943
#7B Rosenblatt 1957
#0F Adaptive Systems
#7B Flight Control 1955
#0F Arti#0Ccial Intelligence
#7B Dartmouth Conference 1956
#7B Fuzzy Logic 1970
#0F Mind and Matter
c#0D K,J,#C5str#F6m and B,Wittenmark 3
Examples
#0F Adaptive systems
#0F Learning systems
#0F Arti#0Ccial intelligence
#0F Expert systems
#0F Neural networks
#0F Neuro-Fuzzy systems
Neural Networks
#0F The beginning
#7B McCulloch and Pitts 1943
#7B Wiener 1948
#7B Hebb 1949
#0F First successes
#7B Rosenblatt 1958
#7B Widrow-Ho#0B 1961
#0F Into the Doldrums
#7B Minsky and Papert 1969
#7B Survivors Andersson,Grossberg,
Kohonen
#0F A Revival
#7B Hop#0Celd 1982
#7B The Parallel Distributed Process Group
#7B The Snowbird Conference
#0F Cult Status
#7B Neuro Fuzzy
Neural Networks
#0F Real Neurons
#0F A simple arti#0Ccial neuron
y#28t#29=f
,
X
a
i
u
i
#28t#29
#01
#0F Arti#0Ccial neural systems
Mindsets
#0F Theory versus Experiments
#0F Analytic versus Heuristic
#0F The role of prior information
#7B White boxes
#7B Grey boxes
#7B Black boxes
c#0D K,J,#C5str#F6m and B,Wittenmark 4
Neural Paradigms
#0F A simple arti#0Ccial neuron
y#28t#29=g
,
X
a
i
u
i
#28t#29
#01
#0F Types of networks
#7B Feedforward nets
#03 Rosenblatts Perceptron
#03 Multilayer nets
#03 Radial basis functions
#7B Nets with feedback
#03 Boltzmann nets
#03 Kohonen nets
#7B Nets with feedback and dynamics
#03 Boltzmann
#03 NACHT Networks
#0F Silicon neurons
Applicationsof Neural Nets
#0F Nonlinear function with training mecha-
nism
#0F Pattern recognition
#0F Classi#0Ccation
#0F Optimization
#0F Content adressable memory
#0F Soft sensing
#0F Prediction
#0F Control
#0F Building complex systems from simple
components
#0F New computing architectures?
#0F New hardware - silicon neurons?
Feedforward Networks
#0F The perceptron
#0F Multilayer nets
#0F Representation power #28Kolmogorov#29
#0F f#28x
1;x
2;:::;x
n
#29=
P
n
i=1
b
i
g#28
P
m
j=1
a
ij
x
j
#29
#0F Locality
#0F Parameterization
#0F "Overtraining"
#0F Similarity to fuzzy
KohonensNetwork
#0F Lateral inhibition
#0F Learning with and without teacher
#0F Self-organizing map
#0F Applications
#7B Competitive learning
#7B Automatic classi#0Ccation
#7B The phonetic typewriter
c#0D K,J,#C5str#F6m and B,Wittenmark 5
The PhoneticTypewriter
Hop#0Celds Networks
#0F Arbitrary connections
#0F Dynamics in neurons
#03
dx
dt
=,x+ Ay; y
i
= f#28x
i
#29
#0F Steady state y
i
= f
,P
a
ij
x
j
#01
#0F Applications
#7B Optimization
#7B Associative memory
Neural Networks for Control
Replace
dx
dt
= Ax+ Bu; y = Cx
by
dx
dt
= f#28x;u#29; y = g#28x#29
where f and g are feedforward networks
a)
x
B
A
C
uy
Neural
network
u
yx
b)
Neural
network
1
s
1
s
Traininga Network
Process
Neural
network
Input
-
+
Desired response
e
Input
Desired response
Neural
network
-
+
M
e
Desired response
Neural
network
-
+
e
M
Process
model
Setpoint
a) Modeling/identification
b) Inverse modeling
c) Control design
Compare with MRAS
c#0D K,J,#C5str#F6m and B,Wittenmark 6
SiliconNeurons
#0F DeWeerth,Nielsen,Mead and #C5str#F6m:
A Simple Neuron Servo,IEEE Trans on
Neural Networks,1991:2.
#0F Pulsed operation
#0F Integration of sensing,actuating and
control
#0F Interesting possibilities
#0F Chip area
#0F Power consumption
#0F Reliability
Experiments
Network implemented in analog VLSI
Comparison with PI Control
Issues in Neural Networks
#0F Properties of individual neuron
#0F Network structure
#0F Parameterization
#0F "Learning" issues
#7B Algorithms
#7B With or without teacher
#7B Self-organization
#7B Overtraining
#0F Representation power
#0F The MISO paradigm
c#0D K,J,#C5str#F6m and B,Wittenmark 7
Summary of Neural Networks
#0F Neural Networks
#7B Narrow view,nonlinear functions with
adjustment mechanism
#7B Broad view,new computing structures
#0F Adaptation
#7B Narrow view,special algorithms STR,
MRAS
#7B Broad view,mechanisms for adjust-
ment and learning
#0F We have only scratched the surface
#0F Building complex systems from simple
MISO components
Two Views on Arti#0Ccial Intelligence
Mind or matter
Representations of Neurons
Expert Control - Introduction
#0F Ordinary regulators contain a signi#0Ccant
amount of logic
#0F Adaptive controllers contain a large
amount of logic in the safety jacket
#0F A good way to structure logic and algo-
rithm
#0F New features
#0F Autonomous Control
#7B Control
#7B Tuning,gain scheduling and adapta-
tion
#7B Diagnostics
#7B Loop assessment
#7B Performance assessment
Expert Control - What is is?
#0F A feedback controller with a rule and
script based expert system built in
#0F Acquires knowledge automatically through
on-line experiments and interaction with
the process operator
#0F Orchestrates numerical algorithms for
control,identi#0Ccation and supervision
#0F Increases and re#0Cnes plant knowledge
successively
#0F May be viewed as a generalized adaptive
controller
c#0D K,J,#C5str#F6m and B,Wittenmark 8
Example of Functionality
#0F Are #0Ductuations normal?
#0F What algorithm is used in loop 17? Why?
#0F Why is derivative action not used?
#0F List all loops with substandard behavior
#0F Monitorloop15for stabilitymargins
#0F Plot static input-output relation forloop6
#0FList all loops where dead-time compensa-
tion is used
System Structure
Identi-
fication
Super-
vision
Excitation
ProcessControl S
Knowledge-
based system
Operator
Hybrid Systems
Expert control leads to complicated systems
that contain:
#0F Dynamical systems
#0F Finite state machines
#0F Logic
#0F Knowledge-based systems
They are not easy to analyse and design.
Much research is needed.
Conclusions
#0F Signal processing
#0F Towards higher automation levels
#0F Adaptation is an important ingredient
#0F Several other approaches
#0F Neural
#0F Conventional AI
#0F Expert systems
c#0D K,J,#C5str#F6m and B,Wittenmark 9
Adaptive Control
Theme,How does adaptive control relate to
adaptive signal processing and other systems
with "intelligent features".
1,Introduction
2,Adaptive Signal Processing
3,Intelligent Systems
4,Neural Networks
5,Expert Control - Hybrid Systems
6,Conclusions
Control and SignalProcessing
#0F Signal processing and control
#7B Similarities
#03 Same methodology
#03 Similarproblems
#7B Di#0Berences
#03 Time delays
#03 Sampling rates
#7B Di#0Berent market places
#7B Silly to have separate communities
#0F Relations to recursive estimation
#0F Output error estimation
#0F Adaptive noise cancellation
#0F Adaptive pulse code modulation
Adaptive SignalProcessing
Filter
e
- 1 S
y
x
y
x#28t#29=s#28t#29+n#28t#29 and y#28t#29=s#28t+#1C#29
Introduce
#0F s signal
#0F n disturbance
#0F x = s + n measurement
Let the desired output be y#28t#29=s#28t+#1C#29,Three
problems
#0F smoothing #1C#3C0
#0F#0Cltering #1C =0
#0Fprediction #1C#3E0
Adaptive versions,adaptive smoothing etc!
A recursive estimator is an adaptive predictor!!
Adaptive FilteringFIR
Process model
y#28t#29=b
1
u#28t,1#29+b
2
u#28t,2#29+#01#01#01+b
n
u#28t,n#29
Standard form
y#28t#29='
T
#28t,1#29#12
#12
T
=#28b
1
::,b
n
#29
'
T
#28t,1#29 = #28u#28t,1#29,:,u#28t,n#29#29
The adaptive #0Clter
^y#28t#29=
^
b
1
#28t,1#29u#28t,1#29+#01#01#01+
^
b
n
#28t,1#29u#28t,n#29
Estimate given by the standard RLS
Block diagram
e
FIR filter
Adjustment
mechanism
q
y
u
S
y
- 1
y
c#0D K,J,#C5str#F6m and B,Wittenmark 1
Adaptive FilteringARMA
Equation error models
y#28t#29+a
1
y#28t,1#29 +#01#01#01+a
n
y#28t,n#29
=b
1
u#28t+m,n,1#29 +#01#01#01+b
m
u#28t,n#29
Hence
#12
T
=#28a
1
::,a
n
b
1
::,b
m
#29
'
T
#28t,1#29 =
#10
,y#28t,1#29:::,y#28t,n#29
u#28t+m,n,1#29:::u#28t,n#29
#11
#12#28t+1#29=#12#28t#29+P#28t#29'#28t#29#0F#28t+1#29
#0F#28t+1#29=y#28t+1#29,#12
T
#28t#29'#28t#29
Output Error Estimation
Model
^y#28t#29+a
1
^y#28t,1#29 +#01#01#01+a
n
^y#28t,n#29
=b
1
u#28t+m,n,1#29 +#01#01#01+b
m
u#28t,n#29
Estimator
'
T
#28t,1#29 =
#10
,^y#28t,1#29^y#28t,2#29:::,^y#28t,n#29
u#28t+m,n,1#29:::u#28t,n#29
#11
"#28t#29=y#28t#29,'
T
#28t,1#29
^
#12#28t,1#29
Filter
Adjustment
mechanism
e
q
- 1 S
y
(a)
x
S
y
x
-
q
(b)
e
y
y
Block Diagrams
Equation error estimation
Output error estimation
Adaptive Noise Cancellation
#0F The Fenton Silencer #28A,C,Clarke,1957#29
#0F B,Widrow
#0F Lots of applications
#0F Hands free car phone
-
q
Microphone for
ambient noise
Driver's microphone
S
Filtered voice
signal
Traditional estimation based on RMS #28a
gradient algorithm#29
#12#28t +1#29=#12#28t#29+#0D
'#28t,1#29
#0B + '
T
#28t,1#29'#28t,1#29
#0F#28t +1#29
c#0D K,J,#C5str#F6m and B,Wittenmark 2
Adaptive Di#0Berential Pulse Code
Modulation#28ADPCM#29
Transmission of telephone signals.
#0F Standard sampling and AD conversion,8
kHz and 12 bit gives 96 kbit#2Fs
#0F Signal compression,8 kHz and 8 bit gives
64 kbit#2Fs
#0F Transmit only the innovation,8kHz and 4
bit gives 32 kbit#2Fs
Di#0Berential pulse code modulation #28DPCM#29
Filter
e
- 1 S
y
Transmis-
sion line
Filter
e
y
y
ADPCM standard
Filter
e
- 1
S
y
Transmis-
sion line
Filter
Adjustment
mechanism
q
q
Adjustment
mechanism
e
y
y
ADPCM Details
Filter
e
- 1
S
y
Transmis-
sion line
Filter
Adjustment
mechanism
q
q
Adjustment
mechanism
e
y
y
The need for standardization CCITT
Filter
H#28z#29=
b
0
z
5
+b
1
z
4
+:::+b
5
z
4
#28z
2
+a
1
z+a
2
Parameter estimator
^
b
i
#28t#29=#281,2
,8
#29
^
b
i
#28t,1#29 + 2
,7
signe#28t,i#29signe#28t#29
Fix point calculations
IntelligentSystems
#0F Semantics
#7B Adapt adjust to new conditions
#7B Learn to acquire knowledge or skill by
study,instruction or experience
#7B Intelligence capacityfor reasoning,
understandign and similarforms of
mental activity,Ability to adapt,
learn,recognize,abstract,bene#0Ct from
experience,cope with new situations
#0F Intelligent Control
#0F An Historical Perspective
#0F Mindsets
IntelligentSystems
#0F Technical & Biological Systems
#7B Understand
#7B Imitate
#0F Cybernetics
#7B Wiener 1948
#7B Ashby 1956
#0F Neural Systems
#7B Mc Culloch Pitts 1943
#7B Rosenblatt 1957
#0F Adaptive Systems
#7B Flight Control 1955
#0F Arti#0Ccial Intelligence
#7B Dartmouth Conference 1956
#7B Fuzzy Logic 1970
#0F Mind and Matter
c#0D K,J,#C5str#F6m and B,Wittenmark 3
Examples
#0F Adaptive systems
#0F Learning systems
#0F Arti#0Ccial intelligence
#0F Expert systems
#0F Neural networks
#0F Neuro-Fuzzy systems
Neural Networks
#0F The beginning
#7B McCulloch and Pitts 1943
#7B Wiener 1948
#7B Hebb 1949
#0F First successes
#7B Rosenblatt 1958
#7B Widrow-Ho#0B 1961
#0F Into the Doldrums
#7B Minsky and Papert 1969
#7B Survivors Andersson,Grossberg,
Kohonen
#0F A Revival
#7B Hop#0Celd 1982
#7B The Parallel Distributed Process Group
#7B The Snowbird Conference
#0F Cult Status
#7B Neuro Fuzzy
Neural Networks
#0F Real Neurons
#0F A simple arti#0Ccial neuron
y#28t#29=f
,
X
a
i
u
i
#28t#29
#01
#0F Arti#0Ccial neural systems
Mindsets
#0F Theory versus Experiments
#0F Analytic versus Heuristic
#0F The role of prior information
#7B White boxes
#7B Grey boxes
#7B Black boxes
c#0D K,J,#C5str#F6m and B,Wittenmark 4
Neural Paradigms
#0F A simple arti#0Ccial neuron
y#28t#29=g
,
X
a
i
u
i
#28t#29
#01
#0F Types of networks
#7B Feedforward nets
#03 Rosenblatts Perceptron
#03 Multilayer nets
#03 Radial basis functions
#7B Nets with feedback
#03 Boltzmann nets
#03 Kohonen nets
#7B Nets with feedback and dynamics
#03 Boltzmann
#03 NACHT Networks
#0F Silicon neurons
Applicationsof Neural Nets
#0F Nonlinear function with training mecha-
nism
#0F Pattern recognition
#0F Classi#0Ccation
#0F Optimization
#0F Content adressable memory
#0F Soft sensing
#0F Prediction
#0F Control
#0F Building complex systems from simple
components
#0F New computing architectures?
#0F New hardware - silicon neurons?
Feedforward Networks
#0F The perceptron
#0F Multilayer nets
#0F Representation power #28Kolmogorov#29
#0F f#28x
1;x
2;:::;x
n
#29=
P
n
i=1
b
i
g#28
P
m
j=1
a
ij
x
j
#29
#0F Locality
#0F Parameterization
#0F "Overtraining"
#0F Similarity to fuzzy
KohonensNetwork
#0F Lateral inhibition
#0F Learning with and without teacher
#0F Self-organizing map
#0F Applications
#7B Competitive learning
#7B Automatic classi#0Ccation
#7B The phonetic typewriter
c#0D K,J,#C5str#F6m and B,Wittenmark 5
The PhoneticTypewriter
Hop#0Celds Networks
#0F Arbitrary connections
#0F Dynamics in neurons
#03
dx
dt
=,x+ Ay; y
i
= f#28x
i
#29
#0F Steady state y
i
= f
,P
a
ij
x
j
#01
#0F Applications
#7B Optimization
#7B Associative memory
Neural Networks for Control
Replace
dx
dt
= Ax+ Bu; y = Cx
by
dx
dt
= f#28x;u#29; y = g#28x#29
where f and g are feedforward networks
a)
x
B
A
C
uy
Neural
network
u
yx
b)
Neural
network
1
s
1
s
Traininga Network
Process
Neural
network
Input
-
+
Desired response
e
Input
Desired response
Neural
network
-
+
M
e
Desired response
Neural
network
-
+
e
M
Process
model
Setpoint
a) Modeling/identification
b) Inverse modeling
c) Control design
Compare with MRAS
c#0D K,J,#C5str#F6m and B,Wittenmark 6
SiliconNeurons
#0F DeWeerth,Nielsen,Mead and #C5str#F6m:
A Simple Neuron Servo,IEEE Trans on
Neural Networks,1991:2.
#0F Pulsed operation
#0F Integration of sensing,actuating and
control
#0F Interesting possibilities
#0F Chip area
#0F Power consumption
#0F Reliability
Experiments
Network implemented in analog VLSI
Comparison with PI Control
Issues in Neural Networks
#0F Properties of individual neuron
#0F Network structure
#0F Parameterization
#0F "Learning" issues
#7B Algorithms
#7B With or without teacher
#7B Self-organization
#7B Overtraining
#0F Representation power
#0F The MISO paradigm
c#0D K,J,#C5str#F6m and B,Wittenmark 7
Summary of Neural Networks
#0F Neural Networks
#7B Narrow view,nonlinear functions with
adjustment mechanism
#7B Broad view,new computing structures
#0F Adaptation
#7B Narrow view,special algorithms STR,
MRAS
#7B Broad view,mechanisms for adjust-
ment and learning
#0F We have only scratched the surface
#0F Building complex systems from simple
MISO components
Two Views on Arti#0Ccial Intelligence
Mind or matter
Representations of Neurons
Expert Control - Introduction
#0F Ordinary regulators contain a signi#0Ccant
amount of logic
#0F Adaptive controllers contain a large
amount of logic in the safety jacket
#0F A good way to structure logic and algo-
rithm
#0F New features
#0F Autonomous Control
#7B Control
#7B Tuning,gain scheduling and adapta-
tion
#7B Diagnostics
#7B Loop assessment
#7B Performance assessment
Expert Control - What is is?
#0F A feedback controller with a rule and
script based expert system built in
#0F Acquires knowledge automatically through
on-line experiments and interaction with
the process operator
#0F Orchestrates numerical algorithms for
control,identi#0Ccation and supervision
#0F Increases and re#0Cnes plant knowledge
successively
#0F May be viewed as a generalized adaptive
controller
c#0D K,J,#C5str#F6m and B,Wittenmark 8
Example of Functionality
#0F Are #0Ductuations normal?
#0F What algorithm is used in loop 17? Why?
#0F Why is derivative action not used?
#0F List all loops with substandard behavior
#0F Monitorloop15for stabilitymargins
#0F Plot static input-output relation forloop6
#0FList all loops where dead-time compensa-
tion is used
System Structure
Identi-
fication
Super-
vision
Excitation
ProcessControl S
Knowledge-
based system
Operator
Hybrid Systems
Expert control leads to complicated systems
that contain:
#0F Dynamical systems
#0F Finite state machines
#0F Logic
#0F Knowledge-based systems
They are not easy to analyse and design.
Much research is needed.
Conclusions
#0F Signal processing
#0F Towards higher automation levels
#0F Adaptation is an important ingredient
#0F Several other approaches
#0F Neural
#0F Conventional AI
#0F Expert systems
c#0D K,J,#C5str#F6m and B,Wittenmark 9
