Re: Fuzzy control-illusion or future

Seppo Kemppainen (
22 Dec 1994 14:59:41 GMT

I jump in to defend fuzzy control from Johan Pensar's critic.
Johan wrote:
> >It is also something that has got more than it's share of public attention,
> >but as expert systems and neural networks who both have had a similar
> >development cycle, fuzzy control will fade to a more modest size.
> >In ten years from now, it may be a technique teached as an alternative
> >to nonlinear PID control, but it will not be something that revolutionized
> >the process control theory.

> You see, I don't say it's worthless, but as a rather approximative method it
> may sooner or later be recognized as a good alternative to e.g. PID controllers.
> It will, however, not solve all the (control) problems in the world.

I agree that fuzzy control is a rather approximative method. However, I
don't agree that it is only a good alternative to e.g. PID controllers.
The basic idea of fuzzy controllers is that sometimes control of the
process is much better known than the actual process itself. The human
operators can explain rather well what they do in certain situations.
So, in this sense fuzzy control is (or should be) more similar to expert
systems than just another kind of function approximation.

Nowadays the basic fuzzy reasoning method in fuzzy control is Mamdani's
max-min composition. It is good for building models for input-output
relations (i.e. function approximation), but it is not suitable for
'expert system' -like reasoning. I think that the main reasons for
the success of the Mamdani's method are:
- it is simple to implement and calculate -> there are good tools for
application developer
- even when the models are simple function approximations, they are
very useful in many applications...some of the reasons for usefulness
- fuzzy terms, e.g. 'very big', are very natural for human operators
- use of fuzzy terms leads to rulebases with quite few rules
- output values the reasoning method calculates are continues values leading
to 'smooth control' (did I make you vomit? :-) This may feel very clear
if you think fuzzy control as some kind of function approximation. But if
you think fuzzy control as some kind of expert system, it is not so clear
that the outputs it produces get reasonable continues values.

The way I see the future of fuzzy logic is that the revolutionary idea
behind all the fuzz is fuzzy sets. It is an extremly simple but powerful
idea for representing natural phenomens. At best it can lead to simple
and efficient calculating algorithms. So far Mamdani's method for fuzzy
control has been the most used method in practical applications, but I have
no doubt that some other methods will also gain much popularity in near
future. I don't claim that fuzzy logic will solve all (control) problems
in the world, but it can solve many (also control) problems better than
recent methods.

> If You work with control, it would be reasonable to assume that one first
> would look at what has been done and is being done in the field before
> jumping into conclusions. One of the "hot topics" today is robust control
> that looks at, exactly - inexact models of reality. If You would have
> bothered to look at e.g. H-infinity and \mu synthesis, You would know
> that You can compute optimal controllers for _uncertain_ processes.
> Without doubt, similar approaches will be developed also for the
> nonlinear case.
> That is, the control theory is _not_ based on some deterministic view of
> reality, but instead on a _uncertain_ and _stochastic_ view of nature!

> I would also like to mention some observations of peculiarities in
> the fuzzy control field,

> - People working with fuzzy control seems to have "floaten over" from
> mathematics and computer science, and have a rather limited view of
> the field. Statements like "the nature is fuzzy and can not be
> described by ordinary control theory" are all to common. I would like
> to rephraze it to "nature is uncertain, infinitely complex and contains
> stochastic noise". The control methods will simply have to be robust
> enough to cope with it.
> Fuzzy logic may look like heaven if You only have worked with 1's
> and 0's, but reality is analog and control science have been analog
> from the start. Even Bode&Co looked at the uncertainty issues of
> control, have You ever heard of gain and phase margins?, so nothing
> is new under the sun (though they looked mainly at SISO systems during
> that time).

Yeah, I am one of those floaters (background from computer science and
electronics). Fuzzy control has been one of my main interests recently
because there the real-world application of fuzzy logic has been most
active. I know practically nothing about great secrets of *optimal control
system theory*...sigh...But, I have figured that the methods of
fuzzy control can't be THAT bad. Because even with my neglible knowledge
of process control I have been able to build some useful control applications.

> - One funny thing in fuzzy control is that the cost (as far as I have seen)
> almost never is specified in any strict sense, say as the H2 norm or similar.
> Instead, in fuzzy papers one can see statements like "The control became
> smoother". Without a definition on performance, it would be impossible to
> make _any_ comparison on the control quality. All that would be possible to
> say is that "the process seems to be stable", as no rigorous proof of
> robust performance or stability has been presented as far as I know.

I admit that statements like "The control became smoother" are so
common in fuzzy papers that they also make me smile. But, as you said, and
I admitted, many people in fuzzy control area come from elsewhere, and
have a limited field of the control theory field. Therefore the evaluation
of built fuzzy controllers has not been very analytical.

But I have also had very serious doubts on the statement "The robustness and
stability of fuzzy controller can not be guaranteed." It is in some sense
true, because usually in fuzzy controllers only the expertise of the
human operator is modelled. Nothing is assumed from the process. Can the
robustness and stability of traditional control be guaranteed if nothing
is assumed of process' dynamic behaviour? I doubt it. On the other hand,
when fuzzy control is a certain kind of nonlinear controller, why are
they so special that normal nonlinear dynamic systems theory (and the
methods used there) does not work with fuzzy controllers?

Fortunately not all people working in fuzzy field are as ignorant of
conventional control theory as I and many others are. In book "D. Driankov,
H. Hellendoorn, M. Reinfrank: An Introduction to Fuzzy Control; Springer-
Verlag 1993." there is quite a lot stuff e.g. about stability and
robustness of FKBCs (Fuzzy Knowledge Based Controllers).
One easy sitation (I understood it well even without control engineer
background) from Driankov:
"So far major effort in fuzzy knowledge based control has been devoted to
development of particular FKBC for specific applications rather than to
general analysis and design methodologies for coping with the dynamic
behaviour of control loops."
I have found Driankov's book very useful, even when the book is mainly
oriented toward control engineers and theorists, not to us fuzzy
AI-people :-).

> To conclude, from a statistical point of view, fuzzy logic is a nice way
> to classify things that are in some sense not uniform, and I would use
> it too if I sometime would have to look at e.g. quality classifications
> or something similar.
> When taken out from it's statistical environment and implemented in
> control, fuzzy logic looses much of it's benefits and tends to be
> only another function approximation. The main reason for this is that
> the human thought may be fuzzy, but the nature is complex, dynamic and
> uncertain.

I agree that most current fuzzy controllers are just another function
approximation. But also as such they have turned out be very useful.
They don't only represent the input-output relationship, but they also
work as a model of it. Therefore they are, at least in principle,
quite easy to build and modify.
I think that there are also other uses than function approximation for
fuzzy logic in control systems. For example, strategic decisions and
other high-level control decisions seem to me like a field where fuzzy
logic can be very useful when suitable algorithms have been found.

Merry Christmas,

Seppo Kemppainen
VTT Electronics, Oulu, Finland
Embedded Knowledge-Based Systems