BISC Seminar, 19 September 1996, 4-5:00pm, 310 Soda Hall

Michael Lee (
Wed, 18 Sep 1996 19:06:04 +0200

NATURAL LOGIC CONTROL: A new design of regulators based on fuzzy logic
compensated connectives.

BISC Seminar


Laboratoire d'Automatique et d'Analyse des Systems

7 Av Colonel Roche

31077 Touluse Cedex, France

33 61 33 64 74 tel

33 61 55 35 77 fax

19 September 1996
310 Soda Hall


In the real world, any real regulation problems depends on the energy
disponibility, introducing natural saturations in the possibilities of the
control actions. The "Natural" apūproach consists in the normalization of
the control action signal in the unit interval so that the saturation
constraints are allways respected. By doing so the control signal becomes a
mapping between the vector output signal and the unit interval. If for each
component of the output signal a "marginal" control can be defined, the
controller must perform a combination of marginal control signals, all of
them being defined in the unit interval. NLC (Natural Logic Control
approach) takes advantage of that situation to imbed regulation design into
fuzzy logic compound implication.

SIMO (single input, multi-output) systems are difficult to be handled by
simple fuzzy controllers, because of the dimensionnality of the non-linear
hypersurface developped by such regulators The NLC overcomes this difficulty
by considering the connexion of as many outputs as necessary as a fuzzy
logical combination using t-norms and t-conorms.

The two extreme attitudes being the conjunction (AND) that leads to the
sharper result and the disjunction(OR) that leads to the milder one, it
appears convenient to compensate both attitudes by means of a linear
interpolation depending on a sinle parameter l in the unit interval.

In previous works it has been proved that if a De Morgan pair of fuzzy
connectives is choses, the properties of the result is completely ordered
with respect to l. This enables in practice a simple adaptivie procedure
that adjustes this parameter according to the desired performances of the
closed-loop system.

Simulation results in Matlab can be shown and commented.

Michael A. Lee
Post Doctoral Researcher
Berkeley Initiative in Soft Computing
387 Soda Hall                                      Tel: +1-510-642-9827
Computer Science Division                          Fax: +1-510-642-5775
University of California                    Email:
Berkeley, CA 94720-1776 USA       WWW: