  In this paper, we introduce the problem of synthesizing optimal controllers
for discrete event systems and we propose a procedure for solving this problem,
where the method and specifications are represented by finite state automata
and with increasing complexity. We will subscribe to the synthetic methodology
by the control theory initiated by supervision by Ramadge and Wonham. For an
illustration on a simple example, then a model with a complexity high. In this
spirit, languages, methods and tools development used to specify and
development must reach a level of quality to meet the requirements expressed.
Face this situation, we are helping in this work the systematic use of formal
methods in systems development cycles in the equipping and adapting the UML
(Unified Modeling Language) which is the most exploited in industrial projects.
