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Lecture 5

Neural Control

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History Early stages

1943 McCulloch-Pitts: neuron, origins 1948 Wiener: cybernatics 1949 Hebb: learning rule 1958 Rosenblatt: perceptron 1960 Widrow-Hoff: least mean square algorithm

Recession 1969 Minsky-Papert: limitations perceptron model

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History Revival

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?

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

•Biologically motivated approach to machine learning

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Similarity with Biological Network

• Fundamental processing element of a neural network is a neuron

• A human brain has 100 billion neurons

• 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

Fig3. Key functional units of a biological neuron

•Introduction to units ：

Dendrite: input

Axon: output

Synapse: transfer signal

Membrane: potential difference between inside and outside of 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 multi-variable 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-- classifiestatic 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 Neuronelemental artificial neurons ------- vaguely approximate physical neurons

synaptic weights are the gains or multipliers

ANNs ---- artificial neurons interconnected via branches

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5.1 The Elemental Artificial NeuronA model of an artificial neuron --- node

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A static neuron has a summer or linearcombiner, 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 neuronrespectively, while b is the bias or offset.

A positive synaptic weight impliesactivation, whereas a negative weight implies de-activation of theinput. The absolute value of the synaptic weight defines the strength ofthe connection.

5.1 The Elemental Artificial Neuron

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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 manner in which the various neurons in the networkare connected, i.e., the network topology or network architecture,

• Hopfield recurrent network where the nodes of one layer interactwith nodes of the same, lower and higher layers,

• feed-forward networks in which information flows from thelowest to the highest layers,• feedback networks in which information from any node can returnto this node through some closed path, including that from the output layer to the input layer and• symmetric auto-associative networks whose connections andsynaptic weights are symmetric.

the principal classes of ANNs

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5.2 Topologies of Multi-layer Neural Networks

single-layered Hopfield network, multi-layer feed-forward ANN

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5.3 Neural Controlthe basic characteristics neural control

• is directly applicable to non-linear systems because of theirability to map any arbitrary transfer function,• has a parallel structure thereby permitting high computationalspeeds. The parallel structure implies that neural controllershave a much higher reliability and fault tolerance than conventionalcontrollers,

• can be trained from prior operational data and can generalizewhen subjected to causes that they were not trained with, and• have the inherent ability to process multiple inputs and generatemultiple outputs simultaneously, making them ideal formultivariable intelligent control.

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5.4 Properties of Neural Controllers• 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.

neural networks properties for control:

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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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the case, a SISO discrete system identification

5.5 Neural Controller Architectures

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Neural Controller Architectures

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Inverse model architecture

the objective is toestablish the inverse relationship P-1 between the output(s) and the input(s) of the physical plant

so that the overall relationship between the input and the output of the closedcontrolled system is unity,

Network training is based on some measure of the open system error between thedesired and the actual out-puts e=d-y of the closed system.

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Specialized training architecture

trainingis 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 architectureThe advantage of this

architecture is that it presents easier training of the controller ANN on-line since the error can bepropagated backwards through the simulator ANN at every sampling instant.