Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 726246, 15 pages
Research Article

Design of Logic Controllers Thanks to Symbolic Computation of Simultaneously Asserted Boolean Equations

LURPA, ENS Cachan, 61 avenue du Président Wilson, 94230 Cachan, France

Received 11 December 2013; Revised 6 February 2014; Accepted 7 February 2014; Published 28 May 2014

Academic Editor: Hamid R. Karimi

Copyright © 2014 Jean-Marc Roussel and Jean-Jacques Lesage. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Formal methods can strongly contribute to improve dependability of controllers during design, by providing means to avoid flaws due to designers' omissions or specifications misinterpretations. This paper presents a synthesis method dedicated to logic controllers. Its goal is to obtain the control laws from specifications given in natural language by symbolic computation. The formal framework that underlies this method is the Boolean algebra of -variable switching functions. In this algebra, thanks to relations and theorems presented in this paper, it is possible to formally express logical controllers specifications, to automatically detect inconsistencies in specifications, and to obtain automatically the set of solutions or to choose an optimal solution according to given optimization criteria. The application of this synthesis method to an example allows illustrating its main advantages.