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TitleAdaptive Control of Ill-Defined Systems
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Page 1

ADAPTIVE
CONTROL OF
ILL-DEFINED SYSTEMS

Page 2

NATO CONFERENCE SERIES

I Ecology
II Systems Science
III Human Factors
IV Marine Sciences
V Air-Sea Interactions
VI Materials Science

II SYSTEMS SCIENCE

Recent volumes in this series

Volume 5

Volume 6

Volume 7

Volume 8

Volume 9

Volume' 10

Volume 11

Volume 12

Volume 13

Volume 14

Volume 15

Volume 16

Applied General Systems Research: Recent Developments
and Trends
Edited by George J. Klir

Evaluating New Telecommunications Services
Edited by Martin C. J. Elton, William A. Lucas, and
David W. Conrath

Manpower Planning and Organization Design
Edited by Donald T. Bryant and Richard J. Niehaus

Search Theory and Applications
Edited by K. Brian Haley and Lawrence D. Stone

Energy Policy Planning
Edited by B. A. Bayraktar, E. A. Cherniavsky, M. A. Laughton, and
L. E. Ruff

Applied Operations Research in Fishing
Edited by K. Brian Haley

Work, Organizations, and Techonological Change
Edited by Gerhard Mensch and Richard J. Niehaus

Systems Analysis in Urban Policy-Making and Planning
Edited by Michael Batty and Bruce Hutchinson

Homotopy Methods and Global Convergence
Edited by B. Curtis Eaves, Floyd J. Gould,
Heinz-Otto Peitgen, and Michael J. Todd

Efficiency of Manufacturing Systems
Edited by B. Wilson, C. C. Berg, and D. French

Reorienting Health Services: Application of a Systems Approach
Edited by Charles O. Pannenborg, Albert van der Werff,
Gary B. Hirsch, and Keith Barnard

Adaptive Control of III-Defined Systems
Edited by Oliver G. Selfridge, Edwina L. Rissland, and
Michael A. Arbib

Page 172

CONCEPTUAL MODELS OF Ill-DEFINED SYSTEMS

number

>---.~- =1t--~--t

display

Initialise: x · - y . - 0
OP · - n+"
SH X

Input number N: *SW : = N

Press oEeration f: if implied ":" ,
OP '- f
Y · - X
SW Y

Press "=": X '- OP(X,Y)
SW X

169

i.e. switch points to X

store N in register
SH points to

do actions for "="

set switch to Y

; set switch to X

Fig. 2. Register model for the Four-Function calculator.

of Human Factors advisors, we can predict that this area of the
calculator's use will cause trouble. People will mis-remember the
magic sequences, will feel uncomfortable with these kinds of
calculations, and will go to some lengths to avoid having to use
these facilities.

It should by now be becoming clear that as a proposal for the
form of conceptual models, surrogate models are in a number of
ways unsatisfactory. Firstly, the model of the FF c~lculator
shown in Figure 2 fails to exhibit certain psychologically
important properties of the calculator, such as the confusing
behaviors just discussed. It is true that the model is
"objectively" correct, so that running the model on these
sequences is as good as using the calculator itself to demonstrate
the existence of the problems. But simply examining the model
gives no hint of the difficulty. It is therefore not only
inadequate as a psychological model but also misleading as a basis

Page 173

170 R. M. YOUNG

for design. Secondly, surrogate models lend themselves best to
what is a rather atypical use of the machine, that of predicting
its response to a given sequence of keys. Normally, of course,
using a calculator involves being given a task and having to
devise the necessary input steps. And thirdly, another way the
surrogate model fails to reflect the psychology of the user is
that it has no way to capture the common observation that for
simple, routine calculations the user soon builds up a learned
repertoire of steps which saves having to re-derive them each time
from basic principles. Each of these shortcomings suggests that
it would be profitable to examine more directly the relationship
between the calculation being performed and the actions the user
has to take. This is done by the kind of model discussed next.

Task/action mapping models

The second kind of conceptual model, called a task/action
mapping model, derives from the observation that the performance
of a particular calculation, such as the addition of 2 and 3, can
be viewed from at least two different perspectives. In terms of
the task domain of arithmetic, the calculation can be described as
the numerical evaluation of an arithmetical expression consisting
of the binary operator "+" applied to the two operands 2 and 3.
In the action domain of keypresses and answers from the calcul-
ator, the same calculation can be described as the typing of the
key sequence "2 + 3 =" followed by the reading of the result from
the display. Clearly, these two descriptions are closely related.
The task/action mapping model is a way of characterising the
correspondence between them.

The mapping analysis begins by trying to describe the structure
of the task and action domains in such a way that there is a simple
and direct mapping between their corresponding parts. The simpli-
city of this mapping serves as a measure of the acceptability of
the proposed model, and the possibility of constructing a satis-
factory model of this kind acts as a criterion for the quality of
an existing or proposed deSign. Normally it will not be possible
to achieve a direct mapping over the whole of the domains, so one
or more central core tasks and their corresponding core action
sequences are ch~ which can be put into close co~pondence.
For the FF calculator discussed above, the description of the
domains is shown in Figure 3. The core, prototypical task is
taken to be a "basic calculation" (i.e. a binary operation applied
to two numbers), and the other tasks are cast as variants of it.
For instance an iterative task such as adding up a column of num-
bers is described as a repeated series of basic calculations, the
result of each step being used as the first operand for the next.
In the action domain, the possible sequences are described by a
grammar which casts them as variants of the core sequence "Number
Operator Number =". each component of which corresponds directly

Page 343

348

Policy, 28,29,31,34,35
predicate calculus, 3
Preoperational stage, 281
Prepositional grammar, 118
Pretectum, 210
Prey-selection, 209
Primitives, 21, 23
Probing a system, 158
Problem solving, 15, 16, 19-20
Production system, ~

Classifier system
Production systems, 117
Programming languages, 125

Randomness, 14, 313-314
Random walk, 22
Reaching, 221
Realizability, 83
Reference, 151
Reference signal, 75
Reflection theorist, 121
Regulation, 75
Relaxation algorithm, 216
Representation, 327-330 ~ also

Schema
Representation of motor output,

178
Representational biases, 242
Representations, 254, 261,

263, 268
Retinotopy, 208
RT, see run and twiddle
Rule-based system, ~

Classifier system
Run and twiddle, 23, 25

Sampling, 319, 320-321, 322-325
Schema, 8, 217, 320, 321, 322,

325-326
Schema-assemblage(s), 217, 218
Scripts, 119
Second language learning, 237
Second law of thermodynamics, 101
Second-order physical

transitions, 108
Selective information, 105
Self-discovery, 281-283
Self-organization, 22
Self-organizing systems, 14
Senescence, 93

SUBJECT INDEX

Sensibility, 267
Sensorimotor knowledge

in adults, 294
of four-dimensional space, 29

Sensorimotor schemes, 290
as objects of assimilation, 292

Sensors, 75
Sensory prostheses, 298
Servomechanism, 25
Shock waves, 108
Sign language, 244
Signals, 75
Signal flow graph, 84
Silk moth, 24
Simulation, by computer, 23
Ski11(s), 187-204

learning, 187, 188, 197
Slide-box metaphor, 217
Social coordination of action,

293
Soft-coupled system, 90
"Soft" couplings, 110
Spatial algorithms, 302
Specialization, 268
Spectral analysis, 103
Speech planning, 231
Speed/accuracy trade-off, 195,

196, 199
Stabili ty, 45
Stability theory, 89
Stabilization, 268
Stare decisiS, 150
Start-up, 151
State, 79
State-determined systems, 12
State space, 79
Stereopsis, 212
Stimulus-matching problem, 213
Stochastic, 27
Stochastic system, 6
Strategies, 257, 261
Stress/nonstress, 230
Stress, speech, 243
Stress timing, 240
Structural stability, 85, 97, 107
Structure of systems, 18, 19
Structured stimuli, 208
Style of the brain, 208
Subject strategies, 192, 194,

195, 203

Page 344

SUBJECT INDEX 349

Supervisor, 78
Symbolic servo-mechanism, 116
Synergy, 220
System, 9'7

open system, 97
dissipative, 97
complex, 97

TEIRESIAS, 133, 136
Thalamus, 210
"The Advice Taker", 117
Ther apy, 264
Thermodynamic engine, 103, 104
Thermodynamic variables, 2
Time until adjacency, 212
Timing, 254, 255, 265-267
Toad, 208
Tok Pisin, 237
Tracking, 21, 75
Trailing, 21, 24, 242
Transmission zero, 85
Transport coefficients, 108
Tuning, 220
Tuning of motor schemas, 220
Twiddling, 22
Typing errors, 179
Typing skill, 178

Ultra-stable systems, 14, 115
Uncertainty, 28
Uncertainty principle, 14
Ungrammatical utterances, 228
Unobservable, 82
"Us" and "them", 5

"Virtual hand", 296
Visual tracking, 67

WM, see World model
World model (module in

learning systems),
128

Worms, 210

Zipfian distribution, 105

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