I welcome you all to this
presentation
On:
Neural Network Applications
Systems Engineering Dept. KFUPM
Imran Nadeem & Naveed R. Butt
220504 & 230353
Part II: LMS & RBF
Part I: Introduction to Neural Networks
Part III: Control Applications
Part I: Introduction to Neural
Networks
Part I: Introduction to NN’s
There is
no restriction
on the unknown
function to be linear. Thus, neural
networks provide a logical extension to
create nonlinear adaptive control
schemes.
Universal Approximation Theorem: neural
networks can
reproduce
any nonlinear
function for a limited input set.
Neural networks are parameterized
nonlinear functions
whose parameters can
be adjusted to achieve different shaped
nonlinearities.
In essence, we try to adjust the neural
network to serve as an
approximator
for
an unknown function that we know only
through its inputs and outputs
Human Neuron
Part I: Introduction to Neural
Networks
Artificial Neuron
Part I: Introduction to Neural
Networks
Adaptation in NN’s
Part I: Introduction to Neural
Networks
Single Layer Feedforward NN’s
Part I: Introduction to Neural
Networks
Part I: Introduction to Neural
Networks
Multi

Layer Feedforward NN’s
Recurrent (feedback) NN’s
Part I: Introduction to Neural
Networks
A recurrent neural network distinguishes itself from
the feed

forward network in that it has at least one
feedback loop
. For example, a recurrent network may
consist of a single layer of neurons with each neuron
feeding its output signal back to the input of all input
neurons.
Recurrent (feedback) NN’s
Part I: Introduction to Neural
Networks
The presence of feedback loops has a profound impact
on the
learning capability
of the network and on its
performance.
Applications of NN’s
Part I: Introduction to Neural
Networks
Neural networks are applicable in virtually
every situation in which a
relationship
between
the predictor variables (independents, inputs)
and predicted variables (dependents, outputs)
exists, even when that relationship is very
complex
and not easy to articulate in the usual
terms of "correlations" or "differences between
groups”
Applications of NN’s
Part I: Introduction to Neural
Networks
Detection of medical phenomena
Stock market prediction
Credit assignment
Condition Monitoring
Signature analysis
Process control
Nonlinear Identification & Adaptive Control
End of Part I
Part II: LMS & RBF
Part II: LMS & RBF
LMS: The Adaptation Algorithm
RBF: Radial Bases Function NN
Part II: LMS & RBF
LMS: The Adaptation Algo.
Estimation Error
Actual Response
Estimated Response
Cost Function
Mean Square Error
Weight Updates
Adaptation Step Size
Part II: LMS & RBF
RBF

NN’s
Radial functions are a
special class
of
functions. Their characteristic feature is
that their response decreases (or increases)
monotonically
with distance from a central
point and they are
radially symmetric.
Part II: LMS & RBF
RBF

NN’s
Gaussian
RBF
Part II: LMS & RBF
RBF

NN’s
Neural Networks based on radial bases
functions are known as RBF Neural Networks
and are among the
most commonly used
Neural Networks
Part II: LMS & RBF
RBF

NN’s
Two

layer
feed

forward
networks.
Hidden nodes: radial basis functions.
Output nodes : linear summation.
Very
fast learning
Good for
interpolation, estimation
& Classification
Part III: Control Applications
Part III: Control Applications
Nonlinear System Identification
Adaptive Tracking of Nonlinear Plants
Nonlinear System Identification
Part III: Control Applications
Nonlinear System Identification
Part III: Control Applications
Continuously Stirred Tank Reactor
Nonlinear System Identification
Part III: Control Applications
Simulation Results
Using SIMULINK
Adaptive Nonlinear Tracking
Part III: Control Applications
Adaptive Nonlinear Tracking
Part III: Control Applications
Hammerstein Model
Adaptive Nonlinear Tracking
Part III: Control Applications
Simulation Results
Using SIMULINK
Adaptive Nonlinear Tracking
Part III: Control Applications
Simulation Results
Using SIMULINK
Thank you
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