Explorando parâmetros na modelagem, síntese e implementação de controladores para sistemas a eventos discretos

Abstract

The Supervisory Control Theory (SCT) formally structures the design of controllers for Discrete Event Systems (DESs) based on the Theory of Finite Deterministic Automata (FDA) and Languages. Among the aspects that limit the application of this theory are problems of modeling, synthesis and implementation, since FDAs are usually limited in expressing advanced features of DESs, such as recognition and change of contexts. In recent years, several approaches have been proposed in the literature as a way to deal with these problems. Among them, the use of FDA with parameters, that is, formal structures that depart from an original, initial model, and incorporate to it details that allow identifying and altering contexts. Having a model that recognizes and manages context can add advantages to several stages of the design of controllers for DESs, depending on the mechanism used for parameterization. In general, parameters may be associated to states or transitions of an FDA, but each approach is structured under a specific formalism, so that the comparison and integration among them is not straightforward. Thus, each approach can lead to different control solutions, modeled, computed and implemented using different strategies. This makes it impossible for potential advantages of each to be combined at different stages of controller design. This work shows how to combine the advantages of using parameters in the modeling, synthesis and implementation of controllers for DESs. It is assumed that modeling tasks are more naturally conducted using parameterized states because in this approach, formulas and variables facilitate the implementation of the mechanism for identifying and managing the contexts of a DES. However, the parameterization of states by variables does not adequately explore aspects of modularization, since the domain of a variable is atomic and, when combined with other domains, of other variables, can lead to the explosion of state space, therefore preventing modeling advantages from spreading to the synthesis and implementation steps. In this sense, a conversion method is presented that allows migrating from the domain of parameterized states to the domain of parameterized events, preserving essentially the same behavior. The result is a set of modular FDA that dismember the atomic notion of a variable in the model of a DES. Then, the benefits of using models with parameterized events in efficient synthesis strategies and decentralized structure are discussed.