Explorando o uso de aproximações na síntese e na implementação de controladores para sistemas a eventos discretos

Abstract

The Supervisory Control Theory (SCT) defines an automatic operation for the synthesis of controllers for Discrete-Event Systems (DESs). Despite its several extensions and improvements, the SCT still faces significant complexity issues that limit its practical application. In particular, these limitations permeate the stages of modeling, synthesis and implementation of controllers. Recently, an approach based on event-refinements has been proposed in the literature as a way of simplifying modeling tasks, thus extending the applicability of the SCT to a greater range of problems. However, this approach does not lead directly to computational gains in the synthesis procedure. Actually, it can be shown that the computational cost to calculate the controller is the same, with respect to the approach without refinements. Also, it can be shown that the cost in terms of hardware/memory to implement the control solution with or without refinements is the same. In order to extend the advantages of event refinements to the synthesis, the literature exploits the use of approximations. An approximation can be associated to the idea of model abstraction. In practice, its construction is materialized by the removal of part or all the mechanism that distinguishes refined events in the system model, thus making it simpler, but less precise. This level of imprecision may imply obtaining sub-optimal controllers, case in which the approach must be reconstructed until it leads to the optimal controller. This reconstruction is a manual process, which depends on the perception of the enginner and that, not rarely, is executed according to a trial-and-error strategy. In this dissertation, the construction of an approximation is automated and its benefits are extended to the stage of synthesis and implementation of controllers. Initially, a method for the construction of a special class of approximations that always leads to the optimal controller, without the need for any post-synthesis verification is proposed. Next, an architecture is proposed as a way to extend the benefits of refinements and approximations to the implementation phase. This approach allows the control system to be implemented in a decentralized manner, through a communicating system, which accomplishes the same role as a centralized implementation, but with gains in memory consumption to represent the control action in hardware. Finally, the last contribution of this dissertation extends the use of approximations to a modular case. This approach increases the applicability of the SCT to cover larger problems, since, by definition, the modular control is independent of the size of the system and can be derived incrementally.