Bernhard on fuzzy control

Apologies to those on the cybsys list who have already seen this.




***** 11497 0
Received: from BBN.COM by CCB.BBN.COM ; 22 Jul 92 11:57:17 EDT
Received: from pucc.Princeton.EDU by BBN.COM id aa29000; 22 Jul 92 11:56 EDT
Received: from PUCC.PRINCETON.EDU by pucc.Princeton.EDU (IBM VM SMTP V2R2)
   with BSMTP id 0603; Wed, 22 Jul 92 11:55:13 EDT
Received: from PUCC.BITNET by PUCC.PRINCETON.EDU (Mailer R2.08 ptf034) with
BSMTP id 3304; Wed, 22 Jul 92 11:50:09 EDT
Date: Wed, 22 Jul 1992 11:42:37 EDT
Reply-To: Cybernetics and Systems
Sender: Cybernetics and Systems
From: Cliff Joslyn <>
X-To: Cybernetics + Systems list <>
To: Multiple recipients of list CYBSYS-L

Really-Really-From: the Editors
Really-From: eletter@ivy.Princeton.EDU

[ The following is a cross-post from the E-LETTER on Systems, Control,
and Signal Processing ISSUE No. 52, PART 1, 15 July 1992. You are encouraged
to subscribe by sending mail to Bradley W. Dickinson at or bradley@pucc.bitnet - Moderator ]

    Pierre Bernhard, INRIA Sophia Antipolis, France, May 1992

--editor's note: This is reprinted, with permission and slightly updated, from
  the European Control Newsletter. We thought it would be of great interest
  to our readership.
  Short replies can be sent to the Eletter editors and will be posted in
  the next issue.


This is a slightly updated version of an older memo in French, which was never
intended to be published in a French journal, let aside in a European one. The
idea was rather to settle my mind, and have an answer ready to the very many
requests I recieved about fuzzy control, mainly due to the abundant
advertisement it enjoyed in the non technical press. A few things I wrote
about where fuzzy control is being applied are not compltely true anymore. But
I believe that globally the idea remains correct.

The original version bared a foreword acknowledging the help of Jean-Marie
Nicolas and Michel Grabisch, both of Thomson-Sintra, France.


The general theory of "fuzzy" logic currently enjoys a rapid developpement
with many applications, specially in Japan. What I write here is narrowly
confined to fuzzy control . This is only one of the many applications,
although often advertised as the most prominent one. It is in no way the only
one. I know, and say, nothing about applications to such things as knowledge
representation (which was the original motive behind fuzzy set theory), expert
systems and the like.


The basis of fuzzy control is to express a control law in terms of expert
rules. The rules define the control value, or its rate of change, for some
(range of) values of the measured variables or their rate of change. The
specific techniques of fuzzy set theory can be seen as a systematic way of
interpolating the data points.

The language used is one of sequential decisions, and as such is always
applied to control problems which are fundamentally conditional sequencing
problems, and where the continuous control part is completely elementary. It
is symptomatic that the yardstick used to juge the efficiency of this control
is always the PID. Take the often quoted example of a bathtub hot/cold water
mixer. It takes into account the fact that the water that first flows when one
opens the hot tap is cold, and therefore reaches the desired temperature
faster than a fixed gain PID. A "success" of fuzzy control.

In its original form at least, fuzzy control shares the ideology of expert
systems to automatise what an expert knows how to do, not to do things no
human expert can do. The motive of research in fuzzy control is therefore not
to push back the limits of what automatic control can perform, even less to
prove things about the performance of a control mechanism, such as stability,
optimality, sensitivity. As in expret systems, experimentation is the means of

The single stick balancing problem is also often quoted as test case. I
consider it unfair to fuzzy control. As a matter of fact, it is a simple
problem, with no sequencing involved. As a consequence, for a single boom,
adjusting the coefficients of a PID that would do the job is much faster than
using fuzzy control, and for the double boom with no measurement of the upper
boom's angle with the lower one, an human expert cannot do it, nor fuzzy
control either.

I think fuzzy control is a good tool where it applies, and I shall come back
to that point in the next section. However it has been oversold on unjustified
grounds, which obliges us to review some of the claims made.

  -1) Gentleness. "Because it is fuzzy, fuzzy control is more gentle to the
user than classical control which, for lack of fuzziness is by its essence
bang bang". Do not laugh, this has often been said. It impresses the ignorants
and the newsmen. The people who said that may have been themselves more
ignorant of what control is than outright dishonest.

  -2) Ease of implementation. This requires a more careful examination. The
proponents of fuzzy control acknowledge that there are very many parameters to
chose to setup such a control law. If the comparison item is PID, then the
later is clearly easier to implement. If the comparison item is a problem that
the PID would not solve (or a PID with, say, cubic terms added to it), then
one has to look at the boundary of the possibilities of fuzzy control. And the
simplicity is gone. (It requires something like 49 rules to balance a single
stick while maintaining control of its translation). As a matter of fact, the
very idea of what is simple depends very much on one's educational background.
What is true is that fuzzy control lets one solve control problems with no
mathematical education whatsoever. Where a more fundamental simplicity comes
in is when the overall problem contains both conditional sequencing and simple
continuous control. Again we shall come back to that.

  -3) Robustness. I have seen no publication that scientifically substantiates
the claim of greater robustness of fuzzy control as compared to modern control,
nor any that disproves it for that matter.

  -4) Lower computational requirements. This I consider as a false claim. The
method of iterpolation used is computer intensive (all rules are continuously
evaluated and their conclusions weighted according to their degree of truth in
a sophisticated way). What is true is that this is of no real importance,
because thanks to specialized chips, it is cheaply done.

A definite weakness of this approach is that the inherent complexity of the
interpolation process induced makes it essentially impossible to prove
anything about the control laws generated. Anyhow, this poof would not be in
the spirit of the method: the human controller does not "prove" his know-how

Let us quote the three reasons Dr Sugueno (scientific director of Laboratory
for International Fuzzy Engineering) gives for the success of fuzzy control in

  i) The carefull choice of the applications
ii) The quality and the efficiency of Japanese engineers
iii) The good fit with Japanese way of thinking

We leave it to the reader to interpret these explanations. The last one should
not be underestimated, coupled with an "invented here" syndrome, in a more
nationalistic society than ours.

One could deduce from the above that there is little more than a regression
from mathematical analysis to empirical imitation of the human operator, and
disregard the whole story. I believe that this would miss the point.


The chalenge is less scientific than industrial. It is threefold.

The first striking fact is the wide range of elementary applications that have
been widely quoted as success stories for fuzzy control. The good idea there
is not to have included a fuzzy digital controller, it is to have included a
digital controller. Japanese industry has been the first to understand that
digital devices are from now on cheap and reliable, and to draw the practical
consequences, that they can be put to use in cheap home appliances and other

The response of Europe here should be to encourage our industry to use digital
devices more extensively to improve consumer products.

A second remark is that qualifying simple control problems as "research"
(since fuzzy control was new) has given the Japanese university scientists an
opportunity to discover the pragmatic questions that standard industry had to
face. What they discovered were problems were the practical difficulty to use
commercially available tools was to make coexist simple continuous time
controls with complicated sequencing tasks. What fuzzy control brought them
was a single language to describe both, in terms of expert rules.

A european response might build upon the clear European lead in synchronous
programming. But then such tools as the new real time languages (ESTEREL,
SIGNAL, LUSTRE, to quote the three that cooperate in France) should be
carefully hidden to the user, deeply burried in a system providing an
elementary interface, devised to let the user solve elementary control
problems of that type, with little control knowledge.

The genial feature of the Japanese fuzzy control culture has been to bring a
tool well suited to their engineers (often with less control engineering
education than their European counterpart) to solve simple problems. (And fuzzy
control has been a good excuse, because it is unable to solve advanced,
multivariable, control problems).

There is a niche for fuzzy control, or any tool sharing the peculiarities we
described, (and better ones might be devised : fuzziness is not unavoidable in
that respect. The real important feature is rather rule based control ) that
we would be foolish to ignore, mainly since larger economic dividends may be
at stake with simple problems than with advanced ones.


The formidable advertisement that fuzzy control has enjoyed in the (mainly non
technical) literature is of course not devoid of commercial aims. This is not
the place to analyze them in details. Let us just recall that since consumer
products are concerned, the non technical press was indeed the place where this
commercial drive had to be carried out. Later will come the market for the
specialized chips.

Finally, my friends in industry drew my attention to a last point which is
probably not the least important one. This very article serves the purpose of
entrenching the idea that there is a completely new theory behind fuzzy
control, since it is being debated in scientific circles and universities, in
Japan first and now in the US and Europe. If this is a completely new theory,
nothing that is constructed referring to it can fall under old patents.
Therefore, Japanese industry (or, for that matter, any industry clever enough
to seize that opportunity) is instantly freed from all previous patents. It
is straightforward to program (approximately) a PID controller with saturation
using fuzzy control. Because it will be a fuzzy controller, it cannot be
challenged by an old patent. And of course this is true of many other devices.

This is a matter for industry to address, not academia.