Transcript What is a Neural Network?

Lecture 5
Neural Control
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History
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Early stages
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1943 McCulloch-Pitts: neuron, origins
1948 Wiener: cybernatics
1949 Hebb: learning rule
1958 Rosenblatt: perceptron
1960 Widrow-Hoff: least mean square algorithm
Recession
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1969 Minsky-Papert: limitations perceptron model
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History
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Revival
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1982 Hopfield: recurrent network model
1982 Kohonen: self-organizing maps
1986 Rumelhart et. al.: backpropagation
very large-scale integrated circuitry (VLSI) and
parallel computers aided the developments in ANNs
1992 Hunt et al. applications of neural networks in
Control Engineering
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Neural Networks
What is a Neural Network?
•Biologically motivated approach to
machine learning
Similarity with biological network
Fundamental processing elements of a neural network
is a neuron
1.Receives inputs from other source
2.Combines them in someway
3.Performs a generally nonlinear operation on the result
4.Outputs the final result
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Similarity with Biological Network
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Fundamental processing element of a
neural network is a neuron
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A human brain has 100 billion neurons
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An ant brain has 250,000 neurons
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Synapses,
the basis of learning and memory
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BIOLOGICAL ACTIVATIONS AND SIGNALS
•Introduction to units ：
Dendrite: input
Axon: output
Synapse: transfer signal
Membrane: potential difference between
inside and outside of neuron
Fig3. Key functional units of a biological neuron
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ANN properties to control
 being non-linear by nature, they are
eminently suited to the control of non-linear
plants,
 they are directly applicable to multivariable control,
 they are inherently fault tolerant due to
their parallel structure,
 faced with new situations, they have the
ability to generalize and extrapolate.
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Artificial Neural Network- defination
An ANN is essentially a cluster of suitably
interconnected non-linear elements of very simple
form that possess the ability of learning and
adaptation. These networks are characterized by
their topology, the way in which they communicate
with their environment, the manner in which they
are trained and their ability to process information.
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Artificial Neural Network-- classifie
static when they do not contain any memory
elements and their input-output relationship is
some non-linear instantaneous func-tion,
dynamic when they involve memory
elements and whose behavior is the solution of
some differential equation
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5.1 The Elemental Artificial Neuron
elemental artificial neurons ------- vaguely approximate
physical neurons
ANNs ---- artificial neurons interconnected via branches
synaptic weights are the gains or multipliers
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5.1 The Elemental Artificial Neuron
A model of an artificial neuron --- node
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5.1 The Elemental Artificial Neuron
A static neuron has a summer or linear
combiner, whose output σ is the weighted
sum of its inputs, i.e.:
where w and x are the synaptic weight and
input vectors of the neuron
respectively, while b is the bias or offset.
A positive synaptic weight implies
activation, whereas a negative weight implies de-activation of the
input. The absolute value of the synaptic weight defines the strength of
the connection.
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5.1 The Elemental Artificial Neuron
The most common distorting (or compression) element f(.)
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5.1 The Elemental Artificial Neuron
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5.1 The Elemental Artificial Neuron
The input to the compression element σ may take on either of the following forms
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5.2 Topologies of Multi-layer Neural Networks
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5.2 Topologies of Multi-layer Neural Networks
the principal classes of ANNs
the manner in which the various neurons in the network
are connected, i.e., the network topology or network architecture,
• Hopfield recurrent network where the nodes of one layer interact
with nodes of the same, lower and higher layers,
• feed-forward networks in which information flows from the
lowest to the highest layers,
• feedback networks in which information from any node can return
to this node through some closed path, including that from the output
layer to the input layer and
• symmetric auto-associative networks
whose connections and
synaptic weights are symmetric.
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5.2 Topologies of Multi-layer Neural Networks
multi-layer feed-forward ANN
single-layered Hopfield network,
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5.3 Neural Control
the basic characteristics neural control
• is directly applicable to non-linear systems because of their
ability to map any arbitrary transfer function,
• has a parallel structure thereby permitting high computational
speeds. The parallel structure implies that neural controllers
have a much higher reliability and fault tolerance than conventional
controllers,
• can be trained from prior operational data and can generalize
when subjected to causes that they were not trained with, and
• have the inherent ability to process multiple inputs and generate
multiple outputs simultaneously, making them ideal for
multivariable intelligent control.
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5.4 Properties of Neural
Controllers
neural networks properties for control:
• possess a collective processing ability,
• are inherently adaptable,
• are easily implemented,
• achieve their behavior following training,
• can be used for plants that are non-linear and multivariable,
• can process large numbers of inputs and outputs making them
suitable for multi-variable control,
• are relatively immune to noise,
• are very fast in computing the desired control action due to
their parallel nature and do not require an explicit model of the
controlled process.
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5.5 Neural Controller Architectures
mid-1960s, Widrow and Smith demonstrated the first application of
a neural network in Control used a single ADALINE to control an
inverted pendulum
the late 1980s, ANNs for identification and control of systems
since the mid-1980s , Many architectures for the control of plants
with ANNs have been proposed
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5.5 Neural Controller Architectures
the case, a SISO discrete system identification
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Neural Controller Architectures
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Inverse model architecture
the objective is to
establish the inverse relationship P-1
between the output(s) and the input(s) of
the physical plant
Network training is based on some
measure of the open system error
between the
so that the overall relationship between the desired and the actual out-puts
e=d-y of the closed system.
input and the output of the closed
controlled system is unity,
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Specialized training architecture
training
is now based on some measure of the
closed system error ec=d-y
The result is
increased robustness coupled with the
advantages of conventional feedback
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Indirect learning architecture
two dynamic ANNs
one ANN is trained to model the physical plant following identification
the second ANN performs the controlling task using a feed-forward network.
Both ANNs are trained on-line from normal operating records.
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Indirect learning architecture
the identification phase
the overall error is used to train the controller ANN
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Indirect learning architecture
The advantage of this
architecture is that it presents easier training of the
controller ANN on-line since the error can be
propagated backwards through the simulator ANN at
every sampling instant.
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