## Neural network for control engineering

**Neural Network for Control Engineering**
**Dr.-Ing. Sudchai Boonto**
Department of Control System and Instrumentation Engineering
King Mongkuts Unniversity of Technology Thonburi
• A common application of neural networks is the solution of
classification problems (e.g. pattern recognition)
• In control applications, neural networks are mainly used to
• Nonlinear version of the linear FIR, ARX, ARMAX, OE, BJ
• Inverse model, model based control etc.

**Neural Network for Control Engineering**
**Neural Network for Control Engineering**
•

**dendrites **represent a highly branching tree of fibres that carry

electrical signals to the cell body. 103 to 104 dendrites per neuron.

•

**soma **or cell body realizes the logical functions of the neuron.

•

**axon **is a single long nerve fibre attached to the soma that serves

as the output channel of the neuron.

•

**synapse **is a point of contact between an axon of one cell and a

**Neural Network for Control Engineering**
• the neuron is modelled as a multi-input nonlinear device with

*r*
inputs

*φ*1

*, φ*2

*, . . . , φr*, one output

*v *and weighted interconnections
• an extra input with a value fixed to 1 is provided that can be used

**Neural Network for Control Engineering**
The sum

*h *of the

*r *weighted inputs and the bias is passed through a
static nonlinear function

*f *(

*h*) according to

*v *=

*f *(

*h*) =

*f*
*v *=

*f *(

*wT φ *+

*w*0)

**Neural Network for Control Engineering**
The nonlinear function

*f *is called the activation function of the neuron.

Three types of activation function are commonly used:

**Neural Network for Control Engineering**
The step function as activation function is defined by

*v*(

*h*) =

*σ*(

*h*) =

*v *=

*σ*(

*w*1

*φ *+

*w*0)

**Neural Network for Control Engineering**
**Neural Network for Control Engineering**
The output of a linear activation function is equal to its input

**Neural Network for Control Engineering**
*v*(

*h*) =

*f *(

*h*) = 1 +

*e−h*
**Neural Network for Control Engineering**
*v*(

*h*) =

*f *(

*h*) =

*eh *+

*e−h*
**Neural Network for Control Engineering**
We can turn to networks formed by connecting single neurons.

The network has

*r *inputs

*φ*1

*, . . . , φr*, a bias and

*s *outputs

*v*1

*, . . . , vs*.

**Neural Network for Control Engineering**
The output of the summing junction of the

*ith *neuron is
where

*wij *is the gain from input

*j *to the

*ith *neuron. Defining theweight vector

**Neural Network for Control Engineering**
The vector

*v *of network outputs is then

*v *= . =

*f*(

*W φ *+

*w*0)
A single-layer network of this form is called a perceptron network.

**Neural Network for Control Engineering**
Several perceptron layers can be connected in series to form a multilayer

**Neural Network for Control Engineering**
*v*1 =

*v*1 =

*f *1(

*W *1

*φ *+

*w*1
The network output – the output of the second layer is
=

*f *2(

*W *2

*v*1 +

*w*2

*y *=

*f *2(

*W *2

*f *1(

*W *1

*φ *+

*w*10) +

*w*20)

**Neural Network for Control Engineering**
**Neural Network for Control Engineering**
• a commonly used network structure is a two-layer perceptron
network with sigmoidal activation functions in the hidden layer, and
linear activation functions in the output layer.

• An important property of such networks is their universal
• Any given real continuous function

*g *: R

*r → *R can be
approximated to any desired accuracy by a two-layer sig-lin
• however on indication about the number of hidden units required

**Neural Network for Control Engineering**
1. Lecture note on

*Neural and Genetic Computing for Control*
2.

*System Identification: Theory for the user *Ljung, L.,1999, Prentice
3.

*Neural Networks for Modelling and Control of Dynamic Systems*
Norgaard, M. Ravn, O. Poulsen, N. K. and Hansen, L. K.

**Neural Network for Control Engineering**
Source: http://staff.kmutt.ac.th/~sudchai.boo/Teaching/inc691/lecture18.pdf

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