# Re: Fuzzling Theoretical Problem

Peng YongHong (meyhpeng@cityu.edu.hk)
Thu, 18 Mar 1999 01:32:42 +0100 (MET)

I though your questions are same as what I have been thinking for a few years.

>
> My question is this:
> "Under what instances can we say that fuzzy logic is the most advantageous
> method for control or modelling of a system, and why is it advantageous. To
> be more precise is there any situation now where control or modelling using
> adaptive control, neural networks GA etc. could not be used but that fuzzy
> logic can?"

It is very different between the modelling of fuzzy logic, adaptive and neural
network and GAs:
General speaking,
1) Adaptive control (AC) thchnique is a control method based on on-line
identifying mathematic model of controlled process. Adaptive control can be well
used in time-varying process whose model is quite certain.
2) neural network provides a non-linear modeling method, which is more powerful
when the model cannot express in a mathematic equation. Moreover, NN is a general
modelling method which uses general learning algorithm.
3).Fuzzy logic control is a approach for dealing imprecise information anf
lingustic knowledge using fuzzy set theory. Fuzzy modelling is a method for
descripe non-linear system in a set of fuzzy rules.
4) Neuro-fuzzy provides a powerful way to combining NN and FL, which can not only
deal with fuzzy information but also self-learning.
5) GA is a new-developed optimization method, which can used in NN system, FL
system or NF system.

>
> That is my main question, but I also have sub-questions if anyone cares to
>
> (i) "What exactly is the present limit of classical control and modelling of
> non-linear systems? (it is often stated that classical control cannot be
> used for non-linear and time-varying systems)"

The limit of classical control theory need the mathematic model of system for
analysis and design the controller.
Fuzzy Logic control is more suitable when mathematic model is not available but
knowledge could be obtained.

>
> (ii) "Is there any mathematical analytical statement that can determine the
> robustness of a fuzzy system to noise as opposed to other models"

A lot of book concerning such subject, foer example: Adaptive Fuzzy System and
Control, Wang L X, Prentice Hall, 1994.
However, more research is necessary for concerning robustness of adaptive
neuro-fuzzy controller.

> I thank you for your time and patience,

```--
------------------------------------------------------
Dr. PENG, YongHong
MEEM Dept., City Univ. of HongKong
Email: meyhpeng@cityu.edu.hk
-------------------------*-----------------------------------

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