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ARTIFICIAL NEURAL

NETWORKS

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6.1 Introduction

Neural networks, fuzzy logic and genetic algorithms are exciting technologies

in the field of artificial intelligence. Artificial neural networks (ANN) have

revolutionized the way researchers solve many complex and real-world problems

in engineering, science, economics, and finance. The motivation for the

development of the neural network technology stemmed from the desire to develop

an artificial system that could perform "intelligent" tasks similar to those

performed by the human brain [20,22].

6.1.1 Structure of One Neuron

The science of the artificial neural networks is based on a collection of

simple processing units (neuron) that are massively interconnected in order to

produce meaningful behavior. In order to understand the structure of artificial

networks, the basic elements of the neuron should be understood.

Neurons are the fundamental elements in the central nervous system. The diagram

below Figure 6.1 shows the components of a neuron.

Figure 6.1: The diagram shows the basic elements of a neuron

A neuron is made up of three main parts - dendrites, cell body and axon. The

dendrites receive the signals coming from the neighboring neurons.

They send these signals to the body of the cell. The cell body contains the nucleus

of the neuron. If the sum of the received signals is greater than the threshold value,

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the neuron fires by sending an electrical pulse along the axon to the next neuron.

The point of contact between an axon of one cell and dendrites of another cell is

called a synapse.

The following model (Figure 6.2) is based on the components of the biological

neuron. The inputs X0-X3 represent the dendrites. Each input is multiplied by

weights W0-W3. The weight W corresponds to the strength of synapse. The cell

body is represented by the summation and the transfer function, and the output of

the neuron model, Y is a function, F of the summation of the input signals, and the

neuro output represents the signal on the axon [22].

Figure 6.2: Diagram of neuron model

6.1.2 Neural networks in Process Modeling and Control

Control of non-linear systems is a major application area for neural network

that have been applied very successfully in the identification and control of

dynamic systems. This control method derives the advantage from the fact that it is

not using any mathematical model of the system. Instead they use input output

relations. There are typically two steps involved when using neural networks forcontrol: -

1- system identification. 2- control design.

F

0w

1w

2w

0X

1X

2X

Y

FX

Y=F( WX )W

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In the system identification stage, a neural network model of the plant must be

developed. In the control design stage, the developed model is used to design (or

train) the controller[22].

6.2 Advantages of ANNs

1- The main advantage of neural networks is that it is possibe to be trained to

perform a particular function by adjusting the values of connections (weights)

between elements. For example, if it is required to train a neural model to

approximate a specific function, the weights that multiply each input signal would

be updated until the output from the neuron is similar to the function.

2- Neural networks are composed of elements operating in parallel. Parallel

processing allows increased speed of calculation compared to slower sequential

processing.

Figure 6.3: Diagram shows the parallelism of neural networks

3- Artificial neural networks have high memory. It corresponds to the weights in

the neurons. Neural networks can be trained offline and then transferred into a

process where adaptive online learning takes place.

In our case, a neural network controller can be trained to control non-linear

plant offline in the simulink environment. After that, the network weights are set.

Direction of signals

OutputInput

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The ANN is placed in a feedback loop with the actual process. The network will

adapt the weights to improve performance while it controls the plant.

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6.3 Training Neural NetworksNetworks of these artificial neurons do not have a fraction of the power of the

human brain, but they can be trained to perform useful functions. As in nature, the

network function is determined largely by the connections between elements.

Neural network can be trained to perform a particular function by adjusting the

values of the connections (weights) between elements.

Commonly neuralnetworks are adjusted, or trained, so that a particular input

leads to a specific target output. Such a situation is shown below. The network is

adjusted, based on a comparison of the output and the target, until the network

output matches the target [22,23].

Figure 6.4: Training neural network

6.3.1 Training Styles

In this section, two different styles of training are described.

In batch trainingthe weights and biases are only updated after all of the inputs are

presented.

In incremental trainingthe weights and biases of the network are updated each

time input is presented to the network. Incremental training is sometimes referred

to as online or adaptive training.

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6.3.2 Learning Rules

Learning rules can be defined as a procedure for modifying the weights and

biases of a network. (This procedure may also be referred to as a trainingalgorithm). The learning rules are applied to train the network to perform some

particular task.

There are general ly four steps in the train ing process: -

1 - Assemble the training data.

2 - Create the network object.

3 - Train the network.

4 - Simulate the network response to new inputs.

There are many types of neural network learning rules. They fall into three

broad categories: supervised learning, reinforced learning and unsupervised

learning.

In Supervised Learning, the learning rule is provided with a set of examples (the

training set) of proper network behavior:

{p1 , t1 } , { p2 , t2 } , { p3 , t3} , { pq , tq },

where pq is an input to the network and tq is the corresponding correct (target)

output. As the inputs are applied to the network, the network outputs are compared

to the targets. The learning rule is then used to adjust the weights and biases of the

network in order to move the network outputs closer to the targets.

Reinforced Learning is similar to supervised learning, except that, instead of

being provided with the correct output for each network input, the algorithm is

only given a grade. The grade (or score) is a measure of the network performance

over some sequence of inputs. This type of learning is currently much less

common than supervised learning.

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In Unsupervised Learning, the weights are modified in response to network

inputs only. There are no target outputs available [20,21].

6.4 Neural Network Structures

There are three main types of ANN structure, single-layer feedforward

network, multi-layer feedforward network and recurrent networks [20,22].

1- Single-layer Feedforward Network

The most common type of single layer feedforward network is the perceptron. The

details of the perceptron are shown Figure 6.5.

Figure 6.6: Diagram of the perceptron model

Inputs to perceptron are individually weighed and then summed. The perceptron

computes the output as a function F of the sum. The activation function, F is

needed to introduce non-linearities into the network. This makes multi-layer

networks powerful in representing non-linear functions. Once the weights are

adjusted, the feed-forward process is repeated. The weights are adapted until the

error between the target and actual output is low. The approximation of the

function improves as the error decreases.

2Multi-layer Feedforward Network

In multilayerfeedforward networks the direction of signals is from input to output.

There is no feedback in the layers. Feedforward neural networks (FNNs) are

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composed of layers of neurons, in which the input layer of neurons are connected

to the output layer of neurons. The diagram below (Figure 6.6) shows a three-

layered feedforward network.

Figure 6.6: Diagram of a feedforward neural network

Increasing the number of neurons in the hidden layer or adding more hidden layers

to the network allows it to deal with more complex functions. The weights in

multi-layer perceptrons MLPs are updated using backprobagation learning . The

weights are adjusted until the actual output of the MLP moves closer to the desired

output.

3- Recurrent Network

Recurrent networks (Figure 6.7) have at least one feedback loop. This means an

output of a layer feeds back to any proceeding layer.

Input

F

F

F

F

Hidden Layer Output Layer

Z

Z

Z

Output

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Figure 6.7: Diagram of a recurrent neural network

This procedure gives the network a partial memory due to the hidden layer receives

data at time t but also at time t-1. This makes recurrent networks powerful in

approximating functions depending on time.

6.5 Function Approximation

Backpropagation can train multi-layer feedforward networks with

differentiable transfer functions to perform function approximation. The two-layer

sigmoid/linear network can represent any functional relationship between inputs

and outputs if the sigmoid layer has enough

neurons. There are several different backpropagation training algorithms. They

have a variety of different computations [18,20,21].

Problem

It is desired to design a 2-layer feedforward NN to approximate the non-linear

function y=f(x), The hidden layer with 10 neurons has hyperbolic activation

function, and the output layer is linear and training the network so that mean

square error < = 0.005.

x -1: 0.1: 1

Y=

f(x)

-0.960 , -0.577 , -0.073 , 0.377 , 0.641 , 0.660 , 0.461 ,

, -0.201 , -0.434 , -0.500 , -0.393 , -0.165 , 0.099 ,

0.307 , 0.396 , 0.345 , 0.182 , -0.031 , -0.219, -0.320

The performance of the various algorithms can affect the accuracy required for the

approximation. This is demonstrated in the Figure 6.9, and the following table

summarizes the results of training the network using five different training

algorithms [Appendix B]. The fastest algorithm for this problem is the

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-1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

traingd

traingdx

traincgp

trainoss

trainlm

actual plant

Levenberg-Marquardt Backpropagation (LMBP) algorithm, and the approximation

must be very accurate [Appendix A]. This is the type of problem for which the LM

algorithm is best-suited function approximation problem. In many cases, trainlm

function is able to obtain lower mean square errors than any of the other algorithms

tested.

Figure 6.8: Backpropagation training algorithms

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Table 6.1: Summarizes the results of training algorithms

Algorithm Iteration MSE Goal

triangd

Batch Gradient Descent500 0.06159

Performance goal

was not met

traingdx

Variable Learning Rate

Backpropagation

95 0.00478Performance

goal met

traincgp

Conjugate Gradient with

Powell/Beale Restarts

12 0.00497Performance

goal met

trainoss

One-Step Secant16 0.00471

Performance

goal met

trainlm

Levenberg-Marquardt3 0.00159

Performance

goal met

6.6 Neural Network Based Control

Before the actual neuro-controller is developed in Matlab, the main types of

neuro-control are discussed. The four types of neural network control methods that

have been studied are supervised control, model reference control, direct inverse

control and internal model control [18,24].

1 - Supervised Control

It is possible to teach a neural network the correct actions by using an existing

controller. This type of control is called supervised learning. But why would we

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want to copy an existing controller that already does the job? Most traditional

controllers (feedback linearization) are based around an operating point. This

means that the controller can operate correctly if the plant operates around a certain

point. These controllers will fail if there is any sort of uncertainty or change in

unknown plant. The advantages of neuro-control are if an uncertainty in the plant

occurs, the ANN will be able to adapt its parameters and maintain controlling the

plant when other robust controllers would fail.

In supervised control, a teacher provides the correct actions for the neural

network to learn (Figure 6.9). In offline training the targets are provided by an

existing controller, the neural network adjusts its weights until the output from the

ANN is similar to the controller. When the neural network is trained, it is placed in

the feedback loop. Because the ANN is trained using the existing controller targets,

it should be able to control the process.

OutputInput

Update

weights

Error

Process

ANN

Controller

+

+

-

-

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Figure 6.9: Supervised learning using an existing controller

At this stage, there is an ANN, which controls the process similar to theexisting controller. The real advantage of neuro-control is the ability to be adaptive

online (Figure 6.10). An error signal (desired signal real output signal) is

calculated and used to adjust the weights online. If a large disturbance uncertainty

occurs in the process - the large error signal is feedback into the ANN and this

adjusts the weights so the system remains stable.

Figure 6.10: Adaptive neural control

OutputInput Process

Error signal is used to

adjust the weights

Desired

responce

+

+

-

-

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2 - Model Reference Control

In the diagram above (Figure 6.10), the error signal is generated by subtracting

the output signal from the desired system response. In model reference control the

desired closed loop response is specified through a stable reference model (Figure

6.11). The control system attempts to make the process output similar to the

reference model output.

Figure 6.11: Model reference control

3 - Direct Inverse Control

The next type of control technique studied is direct inverse control. The

advantage of using inverse control over supervised control is that inverse control

does not require an existing controller in training. Inverse control utilizes the

inverse of the system model. The diagram below (Figure 6.12) is a simple example

of direct inverse control. A neural network is trained to model the inverse of the

process. When the inverse model (controller) is cascaded with the process the

output of the combined system will be equal to the setpoint. Notice that this ideal

control performance is achieved without feedback. The inverse non-linearities in

the controller cancel out the non-linearities in the process. For the non-linearities to

be effectively cancelled, the inverse model must be very accurate.

1elmodc )s(G)s(G

ANN Process

ReferenceModel

Output

+

-

+-

Input

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Figure 6.12: Direct inverse control

Inverse modeling is used to generate the inverse of the process. The system

output is used as an input to the network. The ANN output is compared with the

training signal (the system input) and this error signal is used to train the network

(Figure 6.13).

Figure 6.13: Inverse modeling of a process

4 - Internal Model Control (IMC)

Internal model control is based on direct inverse control. The problems associated

with direct inverse control such as process-model mismatch are reduced using

IMC. The diagram below shows the set-up of IMC (Figure 6.14).

)s(GP)s(GC

OutputSetpoint

Process

ANN

Input Output

+

-

ProcessNN -ControlFilter

NN-Model

YoutUin

d(s)

+

+

-

-

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Figure 6.14: Diagram of internal model control (IMC)

A neural network model is placed in parallel with the real system. The controller is

an inverse model of the process. The filter makes the system robust to process-

model mismatch. With the IMC scheme, the aim is to eliminate the unknown

disturbance affecting the system. The difference between the process and the

model d(s) is determined. If the ANN model is a good approximate of the process

then the d(s) is equal to the unknown disturbance. The signal d(s) is the

information that is missing from the NN-model and can be used to improve the

control.

Summary of Neuro-Controller MethodTo determine the type of neural controller to be used, the pros and cons of each of

the control methods was determined specifically relating to the non-linear system

(CPS).

To develop a supervised neural control lerfor the non-linear system, anexisting controller is required. A controller has already been developed using

feedback controller for the CPS [LQOSEIC or ESOSERIS]. This controller

could be used as a teacher. The model reference controlneeded stable reference

model. These methods will be implemented to design adaptive neuro controller

in this thesis.

I nverse model control and in ternal model control are both based ondeveloping an accurate inverse model of the non-linear plant. The problem with

these methods is that if the system open loop, it will be unstable. To develop an

inverse model, the plant must be stabilized using a controller. When a feedback

controller is used, the inverse model contains some of the dynamics of the

controller. The inverse model developed using a feedback controller would

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never be accurate enough to be used in direct inverse control. This type of

neural control is suited the control of stable open loop systems.

6.7Non-linear Identification Using Neural Networks

This section discusses the different methods of identifying the non-linear

system using neural networks. The most common method of neural network

identification is called forward modeling (Figure 6.15). During training both the

process and ANN receive the same input, the outputs from the ANN and process

are compared. This error signal is used to update the weights in the ANN. This is

an example of supervised learning. The teacher model (CPS) provides target values

for the learner (the neural network). There are two main types of neural networks(Feedforward and Elman) that will be used for identification.

Figure 6.15: Neural network forward modeling method

6.7.1 Feedforwad Neural Network Identification

In order to provide a set of targets for the network to learn, the simulink

model with feedback control is used (Figure 6.19). Initially single-input single-

output (SISO) neural networks were developed, the input being the control force

and the output pole angle or cart position. The first type of neural network to be

devolved are Feed-forward. Using Matlab it is possible to develop multi-layer

Nonlinear

system

CPS

OutputInput

update weights

+

-

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perceptrons (MLP). The Matlab code creates a feedforward network model in

Figure 6.16 presented in Appendix B.

Figure 6.16: Feedforward neural network model