SYNTHESIS OF SUPERVISORS FOR PARAMETERIZED AND INFINITY NON-REGULAR DISCRETE EVENT SYSTEMS Claudio de Oliveira ∗ Jose Eduardo Ribeiro Cury ∗ Celso Antonio Alves Kaestner ∗∗ ∗ Federal University of Santa Catarina, Florian´ opolis, Brazil ∗∗ Federal Technological University of Paran´ a, Curitiba, Brazil Abstract: This article presents a model for discrete-event systems in which the plant consists of a finite State Transition System, or STS, equipped with a data collection. The data collection introduces variables whose values are updated by operations commanded by the discrete transitions in the STS. The specifications of desirable behaviors consist of predicates related to the occurrence of the events. The supervisor, based on the sequence of events occurred in the past, controls the system evolution through the disabling of events. The decision of disabling events originates from the evaluation of predicates computed from the specification of desirable behaviors. A method for the synthesis of supervisors attaining a specification with minimally restrictive control is presented. The main characteristics of our framework are the possibility of capturing non-regular behaviors and the construction of parameterized models which lead to generic solutions for a given class of problems. Copyright c  2007 IFAC. Keywords: Discrete Event Systems, Parametrization, Non Regular Behavior, Supervisors 1. INTRODUCTION The Discrete Event Systems (DES) model presented in this article results from the interaction between a supervisor and a plant. The plant is modeled as a State Transition System (STS) equipped with a data collection. Consequently the global state of the plant, named the configuration of the plant, is determined by the discrete state of the STS and by the values assigned to the variables in the data collection. The updating of the data collection is synchronized with the occurrence of events in the STS. The control strategy used by a supervisor consists of the enabling/disabling of events. Differently from the classical theory (Ramadge and Wonham 1987), in which the supervisor is implemented as a static table indexed by the discrete state of the closed-loop system, our supervisor deals both with the STS and the data collection, i.e., it operates on the variables that appear in the data collection. Consequently the control actions to be performed in each discrete state may be computed from the evaluation of predicates defined over these variables. This implies that the desirable behavior of the supervised system is described by predicates that limit occurrence of events. The use of variables and the restriction of events by symbolic predicates characterize our supervisor model as symbolic. Symbolic methods for the synthesis of supervisors were introduced in (Hoffmann and Wong- Toi 1992, Balemi et al. 1993). These methods explore intrinsic regularities and symmetries of the systems with the objective of reducing the size of the super- visors. Our main objective is not the reduction of the size of the supervisors, but the capture of non-regular behaviors and the construction of parameterized mod- els which lead to generic solutions for a given class of problems. 1st IFAC Workshop on Dependable Control of Discrete Systems (DCDS'07) ENS Cachan, France - June 13-15, 2007