# An Introduction to Cybernetics

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30 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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1

An Introduction to Cybernetics

Robert Oates

Room B50

rxo@cs.nott.ac.uk

2

Overview

What is “Cybernetics”?

Control Theory and Cybernetics

Ordinary Differential Equations
(ODEs) for Simulation

ODEs & Isoclines

ODEs vs Agent Based Simulation

3

Before we start… calculus!

Integration

Calculates the area under a curve

Just adds up at each ‘sample’

Differentiation

Calculates the gradient of a curve

The difference between each ‘sample’

Differentiation is to integration what
division is to multiplication

4

Calculus

t

x

T

5

The Original Interdisciplinary Research
Topic!

Product of The Macy Conferences
(1946

1953)

Contributors include

Norbert Weiner

John Von Neumann

Claude Shannon

Warren McCulloch

Walter Pitts

6

What is Cybernetics?

a)
The study of systems where the
input affects the output

b)
The study of control and
communication in man and
machine

c)
The study of sailors

7

The Steersman (
Κυβερνήτης)

8

Block Diagram Representation of a
Control System

System

-

Control

System

Input

Output

+

9

Block Diagram Representation of a
Control System

Boat

-

Steersman

Input / Desire

Output

+

Transducer (Eyes)

Error

10

Block Diagram Representation of a
Control System

Motor

-

Proportional

Integral

Differential

Controller

Input (
θ
B
)

Output (
θ
A
)

+

Encoder

PID

Controller

11

PID Controller

Error

K
P

K
I

K
D

∫e.dt

de/dt

+

+

+

Input

To

System

12

Cybernetics vs Control Theory

Control Theory

Control
!

Manipulate inputs

Negative feedback is good

Cybernetics

Understand, characterise and unite

Feedback is feedback!

13

Is Positive Feedback Really That Bad?

Negative

Feedback

Positive

Feedback

Combining

Feedback

14

Ordinary Differential Equations (ODEs)
for System Representation

y
x
dt
dx
21
2
13
2

y

x

2
3
8
13
y
x
dt
dy

-

-

+

+

15

Numerical Simulation Based on
Differential Equations

Euler’s Method

n
n
t
n
n
y
x
x
x
21
2
13
2
1

y
x
dt
dx
21
2
13
2

)
(
x
f
dt
dx

)
(
1
n
t
n
n
x
f
x
x

16

Euler’s Method

t

x

)
(
x
f
dt
dx

x
0

x
1

x
2

x
3

x
4

17

A Quick Aside

Better numerical integration
techniques exist

The best one in general is Fourth
-
Order Runge
-
Kutta. The wikipedia
page is actually very good!

18

Differential Equations for System
Representation

y
x
dt
dx
21
2
13
2

y

x

2
3
8
13
y
x
dt
dy

-

-

+

+

}

But where do we start?

This technique can only

comment on systems

once we know the initial

conditions

19

Isoclines

There are techniques that allow us
to examine a system without
knowing the initial conditions

Examine the isoclines!

20

Isoclines

x

y

Assessing stability and “flow”

dx/dt = 0

dy/dt = 0

(5,3)

(2,1)

+
-

++

-
+

--

--

21

Sea Angels (Cliones)

Dorsal

Ventral

External Stimulus

+

-

-

Muscle output

+

+

22

Clione Neuron Interaction

Taken from Hugh R Wilson’s “Spikes, Decisions and Actions”,

Oxford University Press, 1999

23

Isoclines in the Clione Nervous System

Time (ms)

0

5

10

V(mv)

-
100

-
50

0

50

dv/dt=0

dR/dt=0

X

Y

-
1

-
0.5

0

0.5

V(V)

R

0

1

0.5

dR/dt and dV/dt models taken from Nagumo et al (1962)

24

Simulation

ODEs are not the only way to
perform simulation

Many other techniques exist

It would be interesting to compare
ODEs to agent
-
based simulation

25

Daisyworld

An Investigation into
ODE’s vs Agent
-
Based Simulations

The Parable of Daisyworld

James Lovelock and Andrew Watson

Designed to illustrate “Gaia Theory”

Grey planet

Two species of daisy

black and
white

A sun getting hotter

26

Daisy Fitness

β
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
Temperature
Fitness
27

Population Dynamics

)
(

x
a
dt
da
P
P
Fitness

Death

Rate

28

Agent
-
Based System

29

Rules

Occupied?

P(Death) =
γ

P(Growth of daisy type p)

=

a
p
β

yes

no

30

References

Watson, A. J. and J. E. Lovelock (1983).
Biological homeostasis of the global
environment: the parable of Daisyworld.
Tellus 35B, 284
-
289.

Isoclines example taken from Dr Richard
Mitchell’s lecture notes (1999)