From: adams@bistro.berkeley.edu (Adam L. Schwartz)
Subject: Re: Early post
Organization: U.C. Berkeley -- ERL
Date: Tue, 12 Jan 1993 22:13:35 GMT

In article <1993Jan12.195520.8845@athena.mit.edu> memetral@athena.mit.edu (Max E. Metral) writes:
>What are some good papers to read to get an intro to fuzzy logic?  I'm very
>interested, but don't know where to start.

Most of the articles appearing in control journals about fuzzy logic
present fuzzy control in a very positive light.  Not everyone in the
control community feels so strongly in favor of fuzzy control.  I
wrote a technical reply to a fuzzy logic control article which
appeared in Control Systems magazine.  If you're interested in seeing
opposing viewpoints on the subject my reply and the author's reply to
my reply are in the Feb. 1992 issue of Control Systems Magazine.  The
original article appeared in that journal in the June, 1991 issue.

There was also an article about fuzzy control in a recent edition of
Spectrum magazine.  That article is an interesting case of exaggerated
claims by fuzzy logicians.  The article focuses on the miraculous
stabilization of an inverted pendulum with a mouse running around in a
small cage at the top of the pendulum.  The article states that the
stabilizing an inverted pendulum is a classic control problem.
However, the classic inverted pendulum problem requires that the
position of the cart (upon which the pendulum balances) be controlled
while keeping the pendulum upright.  The controller in the article
only balances the pendulum and does not control the position of the
cart.  This is an important difference because the first problem is a
"hard" non-minimum phase, unstable problem while the second is not
non-minimum phase.  In fact, looking at the equations for the inverted
pendulum, if the cart position is neglected, the dynamics are no
harder to control than a double integrator.  As for the mouse at the
end of the pendulum, its just a disturbance acting through a low-pass
filter (the pendulum).

I've also seen an article about the fuzzy control of a triple inverted
pendulum.  In that article, the author states that the problem is 
impossible to solve using conventional control.  This is, of course,
absurd.  Watch out for these types of claims.

Here are some other observations about the use of fuzzy logic for control:
1) Because fuzzy logic does not use a mathematical model of the system to be
controlled, it is impossible to use state variable observers.  As a result,
many articles about fuzzy control casually include the use of derivatives
of the output variables.  This is obviously causes implementation difficulties
and noise amplification problems.

2) Without a mathematical model of the system, it is impossible to conclude
stability about the closed-loop.  Worse yet, robustness analysis is out
of the question (although some authors have stated that fuzzy control is 
robust!).

3) The design methodology for fuzzy control is basically trial and error.


With all of this said, let me point out that I do see useful applications for
fuzzy control.  Particularly control problems which are basically static in
nature (and thus more akin to decision making problems.)

-Adam Schwartz