Re: BISC Seminar Announcement April 15, 1999, 4-5pm , 310 Soda (fwd)

Frank Hoffmann (
Tue, 27 Apr 1999 23:10:22 +0200 (MET DST)

Berkeley Initiative in Soft Computing (BISC)
Dear BISC members,

sorry for the delay of posting recent BISC messages,
I was out of town last week. This is a reply from
Paul Werbos on last weeks BISC seminar announcement.


Frank Hoffmann

(BISC Administrator)

----- Forwarded message from Paul Werbos -----
>From Mon Apr 19 14:13 PDT 1999

HI, Folks!

This seminar announcement reminds us about chaos computing, which, at least
in the Iizuka meetings
has been treated as a major part of soft computing, co-equal to fuzzy logic
or neural networks.

I have some comments on this.

Black and white, gray or colorful universe - the role of dynamical systems
and chaos in fuzzy logic and soft computing

Speaker :
Robert Kozma
Division of Neurobiology
University of California at Berkeley

>Major components of soft computing are fuzzy logic, neural networks
>probabilistic reasoning, genetic programming and others. During the past
>decade, chaos computing has emerged as a new constituent of the soft
>computing paradigm. In this talk the following questions will be addressed:
>What chaos computing can offer to the soft computing family? How can it
>benefit from the powerful results achieved in soft computing to date? How
>can it exploit imprecision and partial truth in the data to achieve
>robustness and tractability of real-life problems?
>Examples of chaos computing and emergence of stable structures in
>mathematical, physical, and biological systems are given. This is a work
>jointly with Walter J. Freeman.

Just as neurocontrol (or learning control) and fuzzy control have received
major interest around the world,
leaders of the chaos community like Jim Yorke have argued that chaos
control also provides a major
possible paradigm shift with new benefits relative to classical control.

How can we evaluate that, and what is the relation to the OTHER new control

So far as I can tell, Yorke's key idea is that HIGH-PERFORMANCE, LOW-ENERGY
control can be achieved by deliberately DESIGNING an engineering plant to
responsive (high gain) and ACCEPTING a control strategy which tries to keep
the plant in
an acceptable region RATHER THAN keeping it locked on a specific setpoint.
In other words,
the design and the control admit a kind of chaotic trajectory within the
allowed region of state space.

This is not so novel as it seems. I have heard that the SR-71 is that kind
of plant... very high gain, with a natural
tendency to go into chaos if it is not actively controlled.

The practical questions here are as follows: (1) what is the DESIGN
methodology which lets us translate this
abstract concept into working controllers, for known plants?: (2) how do we
get stability results when using
such control strategies?

For the first question, I would propose that model-based adaptive critics
designs (as described in the Handbook of Intelligent Control or in
on the web) provide such a design methodology. The user may provide a
utility function which is the sum of two terms (1) one term which is "zero"
(zero COST) in the acceptable region, and rises
gently (perhaps ala e**kd, where d is distance from the region, or d*d)
outside that region; (2) a kind of energy-of-control cost term. Furthermore,
the "weights" in the controller may be chosen to be the weights in a
recurrent controller network (capable of generating chaotic behavior) PLUS
the actual design parameters of the physical system. In such a case, the
advanced adaptive critic control schemes should be able to TRAIN the
weights to FIND the minimum-energy stabilizing controller; this would be a
chaos controller, IF in fact the minimum-energy controller is
a chaos controller.

Notice that this would make a nice research project or PhD thesis project:
to go ahead and demonstrate this on the kind of problem where a chaos
controller might be of value. (And yes, such a project would be eligible
for consideration as a proposal to the program I help run at NSF...
see, and serach on the CNCI program.)

Also notice that the usual lookup-table sorts of reinforcement learning
would not be appropriate here, since they are not well-tuned to
deal with continuous-variable control problems.

So: that's the chaos-neural link. As for the fuzzy link... well... if I
were trying to bring in fuzzy here, I might consider using an Elastic Fuzzy
Logic (ELF) network
instead of an MLP in the approach above, without changing the approach
itself. I have no idea which would work better, when.

Best of luck,

Paul W.

P.S. mainly discusses stability in the case
where the model-based adaptive critics are applied to
ordinary setpoint or model reference control problems. However, the use of
a different utility function does not change
the methods as such.

----- End of forwarded message from Paul Werbos -----

Frank Hoffmann                               UC Berkeley
Computer Science Division                    Department of EECS
Email:              phone: 1-510-642-8282
URL:   fax:  1-510-642-5775
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