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An Introduction to Cybernetics Robert Oates Room B50 rxo@cs.nott.ac.uk Overview What is “Cybernetics”? Control Theory and Cybernetics Ordinary Differential Equations (ODEs) for Simulation ODEs & Isoclines ODEs vs Agent Based Simulation Before we start… calculus! Integration

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an introduction to cybernetics

An Introduction to Cybernetics

Robert Oates

Room B50

rxo@cs.nott.ac.uk

overview
Overview
  • What is “Cybernetics”?
  • Control Theory and Cybernetics
  • Ordinary Differential Equations (ODEs) for Simulation
  • ODEs & Isoclines
  • ODEs vs Agent Based Simulation
before we start calculus
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
the original interdisciplinary research topic
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
what is cybernetics
What is Cybernetics?
  • The study of systems where the input affects the output
  • The study of control and communication in man and machine
  • The study of sailors
block diagram representation of a control system
Block Diagram Representation of a Control System

Control

System

System

Output

Input

+

-

block diagram representation of a control system10

Encoder

Block Diagram Representation of a Control System

Proportional

Integral

Differential

Controller

PID

Controller

Motor

Output (θA)

Input (θB)

+

-

pid controller
PID Controller

KP

Error

∫e.dt

KI

+

Input

To

System

+

+

de/dt

KD

cybernetics vs control theory
Cybernetics vs Control Theory
  • Control Theory
    • Control!
    • Manipulate inputs
    • Negative feedback is good
    • Positive feedback is bad
  • Cybernetics
    • Understand, characterise and unite
    • Feedback is feedback!
is positive feedback really that bad
Is Positive Feedback Really That Bad?

Negative

Feedback

Positive

Feedback

Combining

Feedback

a quick aside
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!
differential equations for system representation
Differential Equations for System Representation

+

x

y

-

+

-

}

But where do we start?

This technique can only

comment on systems

once we know the initial

conditions

isoclines
Isoclines
  • There are techniques that allow us to examine a system without knowing the initial conditions
  • Examine the isoclines!
isoclines20

dx/dt = 0

--

+-

dy/dt = 0

(5,3)

++

(2,1)

-+

--

Isoclines
  • Assessing stability and “flow”

y

x

sea angels cliones http www youtube com watch v vb5recdppai
Sea Angels (Cliones)http://www.youtube.com/watch?v=vB5recdpPaI

Muscle output

+

+

-

Ventral

Dorsal

+

-

External Stimulus

clione neuron interaction
Clione Neuron Interaction

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

Oxford University Press, 1999

isoclines in the clione nervous system

50

1

dv/dt=0

dR/dt=0

0

R

V(mv)

0.5

-50

X

Y

-100

0

0.5

0

10

-1

-0.5

0

5

Time (ms)

V(V)

Isoclines in the Clione Nervous System

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

simulation
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
daisyworld an investigation into ode s vs agent based simulations
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
rules
Rules

Occupied?

yes

no

P(Death) = γ

P(Growth of daisy type p)

=

apβ

references
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)