Global and Large Scale System Models: Proceedings of the Center for Advanced Studies (CAS) International Summer Seminar Dubrovnik, Yugoslavia, August 21–26, 1978

232 Pages·1979·2.388 MB·English

by  A. V. Balakrishnan (auth.), Dr. Branislav Lazarević (eds.)

SEMINAR ON GLOBAL AND LARGE SCALE SYSTEM MODELS
SUMMARY AND CONCLUSIONS
A.V. Balakrishnan
University of California, School of Engineering
and Applied Science, Los Angeles CA 90024
Summary
We began with a review of relevant aspects of the Methodology
of System Modelling and System Theory. We had detailed presentation{
of the following specific models:
Mesarovic-Pestel Models
Bariloche Models
UNIDO (ARAB) Models
-
Following this there were reviews and critiques of these and
other models, and an overall evaluation of the current status of Global
Modelling, including a consideration of the possible future of this
activity.
We also discussed other large-scale systems: National Socio-
Economic Models and Corporate Models, including their interaction with
the global models.
The objectives set out for the conference were more than
adequately met. Thus, there was a decided emphasis on the Third World
in respect to world models. We brought together methodologists and
modellers perhaps for the first time. Particularly significant was the
participation of R.E. Kalman, the initiator of System Science, whose
observations on the methodological aspects were incisive.
Conclusions: Current Status of Global Modellin@
Global Modelling is an important and viable activity and
should receive more attention. It can play a vital role as a tool in
global policy decisions affecting the future of Mankind.
The models developed so far suffer from many drawbacks and
considerable improvement is required before serious use can be
recommended.
All models are implicitly normative and conditioned by the
Social-psychological milieu. Explicit acknowledgement of this by
modellers is essential to avoid misunderstanding.
Models do not take into account the variance in Socio-
economic structure between the developed and developing countries.
Models are not made available to potential users as freely
as they should be. This will help to remove fears and to expose
limitations. Sensationalism in announcing results must be avoided.
Enormous uncertainties are involved in many of the fundamen-
tal quantities the models deal with, including methodological diffi-
culties. The problem of fitting observed data, for instance, is itself
of great difficulty.
Global Models are still too primitive to provide other than
forecasts of qualitative value) and certainly inadequate to consider
Control. Greater communication between methodologists and modellers
and users (including social scientists) would be beneficial in this
regard.
A SYSTEM-THEORETIC CRITIQUE OF DYNAMIC ECONOMIC MODELS
R.E. Kalman
Swiss Federal Institute of Technology, Z~rich, Switzerland
University of Florida, Gainesville, Florida, USA
Abstract
This paper treats the theoretical aspects of modeling and
simulation of dynamical systems, especially those arising in economics.
Our aim is primarily methodological critique; while the
ultimate arguments rest on advanced mathematical concepts, the conclu-
sions are stated in quite elementary and intuitive terms.
There are important implications for the entire area of
"modeling".
i. The setting
If we view today's scientific scene along the broadest
possible horizon - to include economics, computers, artificial
intelligence, etc. - it is a striking fact that the classical disci-
plines have been breaking down and new fields are continually emerging.
Why is this happening? What is causing it?
It is the pre-thesis of this paper that this reorganization
of science is forced by the growing importance of the "system aspect"
of things. The classical recipe of "experiment-theory-confirmation",
which worked so well for simple, isolated, natural phenomena, does not
apply to many (most?) important current problems characterized by
complexity, interactions, and man-made structures. New modes of
thought are required.
Rather than attempt any sort of formal definition of the
"system aspect", we shall give just a few examples where this is
important and where it is not:
Important Negligible
Biology Physics
Engineering Astronomy
Computer Science Materials
Economics Literature
Thus the "system aspect" is of minor importance in the "natural
sciences" (but biology is a very prominent exception) and vital in the
so-called "artificial sciences" which deal primarily with entities
created by Man. We shall take most of our examples from economics,
because of the general theme of this meeting and also because economics
as a science has interesting questions in common with both biology and
engineering.
In the rather crude contemporary methodology of the nascent
superscience of "systems", the notion of a model plays a central role.
By a model we may mean a simple abstract mental construct such as a
Keynesian economy or a gigantic computer program designed to simulate
a small part of such an economy, or anything in between.
Thus the theme of the paper is the theory of models. Is
there such a thing? Can it do something useful? Can models be studied
abstractly?
The answer to all these questions is YES. Going much beyond
that, it is the thesis of this paper that no serious modeling research
can be conducted today without reference to facts from system theory.
A good intuitive, concrete, and (physically) real example of
a system is a digital computer. It is easiest to digest system-
theoretic problem statements by first asking what they would mean in
terms of a compu£er. Questions are rejected as having no system-
theoretic content if they are nonsensical for a computer. (Think of
determining the mass of an electron.)
For a classical scientist (think of a physicist) it is un-
thinkable that the properties of a model purporting to relate to real
questions should or even could be studied irrespective of the physical
setting. By contrast, system theory makes the claim that it is pre-
cisely these abstract properties of models which require deeper study.
Not many specialists will welcome our thesis. Yet it is
based on facts. At the very least it deserves attention because it
promises to provide a unifying frame for all of science, opposing the
centrifugal tendencies of the last three hundred years.
So much by way of a philosophical manifesto.
For most of the paper, we shall be concerned with basic and
specific questions of modeling, as they may appear, for example, to an
economist who is part of a world-model-building team. The paper does
not aim beyond providing an outline for further discussion, so that
many points will necessarily have to remain vague.
2. The genesis of models
The usual procedure of making a model of a system is obvious.
A catalog of known facts and data is compiled and the equations (or
equivalent) are written down by taking into account all available
quantitative information. (Think of a computer: it is modeled by its
own circuit or block diagram.)
An absolutely essential assumption for this process to work
is that the "laws" governing physical phenomena are independent of the
system context. If a Japanese resistor is put into any part of an
American computer which is then connected to a French power supply,
there is no doubt whatever of the validity of Ohm's law, over a range
of some 1020. Nor does it matter where in the computer the resistor
is wired in or even whether the computer works on a time scale of giga
or picoseconds. Oversimplifying a bit, no matter what system is built,
who builds it, how it is built, and why it is built, Ohm's law is
immutable.
The essential feature of economics is that this is simply
not so. It is not enough to talk vaguely about "law of supply and
demand"; it is necessary to specify the market . I) What seems to have
happened historically is that the word "law", which expresses some of
the loftiest triumphs of nineteenth-century physics, was simply
appropriated into economics for its prestige value 2). Or perhaps
because of uninformed wishful thinking.
There are no "laws" in economics as this term is understood
in physics, because economics is a system-determined science.
I do not wish to debate this evident point here with myself
but will simply remark that the great insight of Keynes - that demand
may be autonomously determined - arose in a specific system context
(Western Europe in the 1930"s and perhaps the US, too)~ this observa-
tion alone is enough to bury any dreams of elevating the "law" of
supply and demand to coequality with the majesty of Ohm's law.
The nonuniversality or system-determinedness of economic
insights is very upsetting for the normal practice of modeling. The
quality and amount of (scientific) information incorporated in a model
is very much dependent on prior research results. In other words,
system theory can begin only after the basic science has been
straightened out )3
So it is legitimate to ask: what is the factual input of
economic theory to the process of building accurate models for pre-
diction or policy analysis and optimization? What is the scientific
value of accepted economic doctrine as applied to such questions?
I am afraid it is very little. Economics occupies an
unusual position in the sciences, in that system-theoretic questions
are coming inevitably to the fore before the basic facts have been
nailed down. It may be that this, too, is due to the system-
determinedness aspect of economics. The symptom is a great deal of
complaint that model building cannot progress because of controversies
surrounding fundamental assumptions. See, for example, BALL (1978).
The alternative is not to base economics on a priori theory
but to proceed directly from data to model. This actually happens in
many cases in physical contexts where the situation is too complicated
to permit using a "clean" theory. (Example: oil exploration.) And it
can always be done, in principle~ in fact it is one of the central
themes of system-theoretic research. (Think of a computer: it is not
necessary to be given its circuit diagram, it can also be tested by
determining all possible input/output responses.) See HAZEWINKEL (1978)
for an example of recent system-theoretic work.
The process of doing economics via the data to model alter-
native is well under way already (e.g., at this conference). This may
have to be viewed as an dncipient breakdown of economics as it is con-
ventionally defined and practiced. Modeling obviously requires a
different cocktail of expertise than orthodox economics based on handed-
down knowledge. An added difficulty, and an argument for the data-to-
model methodology, is the intrinsically adaptive nature of economic
systems which means that ideological biases, expressed through policy
making, constantly shift the reality which we wish to capture 4).
3. Disclaimer
To the obvious question, "Does system theory deal with the
real world?" the answer is NO - that's quite simple. System theory
studies models and it does not accept responsibility for the accuracy
or relevancy of these models - that headache is reserved for the
practitioners.
Once a model is fixed and accepted as "real", system theory
tries to ask deep questions, via mathematics. This is not a matter of
laziness or conceit; it is absolutely necessary in view of the claimed
universality and application-insensitivity of system theory )5
The initial discoveries of properties of real systems will
obviously be made without any help from system theory. On the other
hand, as we shall see later, system theory can be very handy for des-
troying illusions often found in "practical" work on real systems.
So delimited, system theory uses the power of mathematics to
penetrate into abstract questions. Until there is something like a
well-developed experimental-biological system methodology, there is no
feasible alternative to mathematics.
System theory operates by seeking to form concepts on a
"higher" level, because only in this way can we get universality and
independence of particular fields of applications. And in system-
determined areas, like economics, progress depends very much on system
theory provoking the right questions.
When the fundamental scientific investigation has not come
up with adequate models on which to base the next (system theoretic)
level of study - and this may well be the case in numerous areas of
economics - then system theory itself can, in principle, provide the
missing models by brute-force data analysis independently of the
application constraints. This is discussed in Section .5
It is utterly impossible to give an accurate technical
account of the accomplishment and problem settings of system theory
without the requisite (often rather heavy) mathematical apparatus.
Here we shall aim only at providing conceptual guidelines. Although
much of the theory has not changed since the mid-1960 ,s" the reader
will find the present emphasis quite different from that in KALMAN
(1968).
4. Reachability and observability
From here on, we shall generally talk about systems rather
than models. By a system we always mean two things simultaneously:
)i( a concrete (physical) system which serves as motivation for our
questions and concepts; (ii) a mathematical system, a "model" of the
real system, which is the anchor point of all precise definitions and
theorems. We will, however, not give any mathematical details here
but refer the reader to the literature.
Two of the most primitive and yet, as it has turned out, most
useful questions we can ask about a system are:
What influence have the inputs on the system?
What do the outputs tell about the system?
To make these questions more specific, we recall the notion
of state. It is convenient to think of all information processing
taking place inside a system as expressed via transformations of
states. Thus the first question concerns the effect of input on state
and the second the effect of state on output. It is the study of
interactions of the internal state variables with the inputs and out-
puts which makes system-theory a nonclassical subject 6).
If every part of a system is accessible to inputs, that is,
if any state can be produced by a suitable input, the system is (com-
pletely) reachable. By dual reasoning, if the internal condition of
the system, that is, the instantaneous values of its state variables,
can always be determined from the information contained in the output,
the system is (completely) observable.
Reachability and observability are concepts which belong to
pure system theory. They do not depend on the particular physical
embodiment of any given system. (Of course, the system must be modeled,
that is, we must be able to represent its behavior by some set of
equations.) These notions may seem to be at first rather empty and
abstract, but in fact they have extremely far-reaching implications in
theory as well as in practice.
The explicit mathematical condition for the reachability of
linear systems has been known since the late 1950"s. This condition
is ~eneric. It is difficult to construct a system or a model which is
not reachable; in fact, this can be done only by artificially confining
the inputs to certain "layers" of the system. (This is not so in
physics: when the law of conservation of momentum holds, there is no
complete reachability. At this point the classical (physical) and the
modern (system-theoretic) points of view are orthogonal to each other).
If a system is not reachable as presented, it can be reduced
to a reachable one by throwing away all its unreachable states.
Reachability (sometimes called controllability) is a
necessary condition for the solution of optimal control problems.
Moreover, it is also a sufficient condition in the sense that the
solution of control problems, with well defined model, reduces to an
applied mathematical task which is well understood. Thus since
(almost) any system is reachable (without any regard as to where the
model was obtained from), it follows that (almost) any system can be
optimally controlled. Knowing these facts, system theorists are not
impressed by patronizing praise from economists that "optimal control
theory is a useful tool ... for medium term policy analysis". (See
BALL (1978, Section 267). It is not a question of a tool; the tool
is more general than the problem. The question is getting the right
equations, and that has been always regarded as the responsibility of
the economists.
Just as reachability is the fundamental system-theoretic
concept underlying all questions of control, so observability is the
fundamental concept for all questions of estimation of unmeasurable
variables. It is not correct to argue (think of a physicist) that
"what can be measured can be controlled", if this is to mean also that
"what cannot be measured cannot be controlled". Unmeasurable variables
manifest themselves by their effect on the measurable ones. This
means - if the system is observable - that unmeasurable variables can
be determined from the measured variables by computation. Just like
reachability, observability is also a generic property. Hence the
unmeasurable variables can be (almost) always determined from the
outputs.
The great popularity and impact of the so-called "Kalman
filter" depends precisely on the fact that this system-theoretic
result provides the correct solution for the reconstruction of vari-
ables from noisy data in the generic situation - which is just
stochastic counterpart of observability. See KALMAN (1978).
There are major implications on time series analysis, as
discussed in KALMAN (1979).
An unobservable system can be reduced to an observable one
by simply throwing away unobservable states.
Combining the two kinds of reductions mentioned, any system
may be simplified to one which is both reachable and observable. Such
systems are called canonical. This is one of the basic new ideas of
system theory, as we shall now explain.
5. Realization theory
System theory begins with mature models. To claim
10
universality system theory must therefore first resolve the question:
Can system-theoretic results be made independent of the biases of the
investigators who have provided the model to be studied? Can two
different methodologies applied to the same system yield different
models? Can there be any "absolutes" in modeling which must not be
violated in spite of honest differences of opinion or background?
(The reader may notice that my use of the "absolute" is an
allusion to a substitute for a "physical law".)
What justifies the intrusion of system theory into so many
areas of local expertise is precisely its ability to give a true,
clear, and immutable answer to these questions. Knowing this, the
intrusion will be perhaps less resented.
Technically, the discipline which deals with these issues is
called realization theory. A realization is a model representing the
behavior of a (concrete) system, subject to the condition that it is
compatible with all available information concerning the behavior of
the system. By behavior we normally mean data of the input/output,
stimulus/response type, but the conceptual framework is extremely
general and does not depend on such special formalizations. In a
sense, a realization is a computationally specific way of simulating
the behavior of a real system.
It is almost a tautology to show that realizations always
exist. The theoretical problem is nontrivial only because, in general,
the process
data ) model
is many-to-one. The question is whether there is a way (a canonical
way) of defining models so that they depend only on the data and not
on any external biases introduced, for example, by the special proce-
dures or algorithms used for constructing a realization. In the vast
majority of models which have been developed historically such biases
are present and cannot be justified upon closer scrutiny. The problem
is subtle. It requires a mathematical point of view which cannot be
rendered into ordinary language with unerring precision.
I shall express the essential result in the following way:
THEOREM. Consider a ~iven, fixed amount of input/output
data on a dynamical system. Then
)i( Any two canonical realizations based on the same data
are isomorphic.