Directed control of discrete event systems

For the control of discrete event systems, the notion of directed control refines that of supervisory control. A directed controller is one that selects at most one controllable event to be enabled at any state (without disabling any uncontrollable event), which is in fact how a discrete event control is implemented. In contrast, a supervisory controller computes a maximal allowable set of controllable events at each state, leaving undecided exactly which one is to be enabled. We model discrete event systems using the automaton formalism. Under directed control, our first goal is to achieve logical correctness of the controlled system behavior as specified by safety and nonblocking. Subsequently we address the best performance issue by providing an optimization based framework. The optimization task is to direct a system in such a way that regardless of the history of evolution, it accomplishes a pending task in a minimal cost. In a state-based setting, we formulate and study the existence and synthesis problems with the above objectives. We first show that the existence and the synthesis of a safe and nonblocking directed controller are both solvable in polynomial complexity. Then we present a novel approach with polynomial complexity for the synthesis (and the existence) of an optimal director, thus providing a complete solution to the problems in study

Model Properties for Efficient Synthesis of Nonblocking Modular Supervisors

Supervisory control theory provides means to synthesize supervisors for systems with discrete-event behavior from models of the uncontrolled plant and of the control requirements. The applicability of supervisory control theory often fails due to a lack of scalability of the algorithms. We propose a format for the requirements and a method to ensure that the crucial properties of controllability and nonblockingness directly hold, thus avoiding the most computationally expensive parts of synthesis. The method consists of creating a control problem dependency graph and verifying whether it is acyclic. Vertices of the graph are modular plant components, and edges are derived from the requirements. In case of a cyclic graph, potential blocking issues can be localized, so that the original control problem can be reduced to only synthesizing supervisors for smaller partial control problems. The strength of the method is illustrated on two case studies: a production line and a roadway tunnel.Comment: Submitted to Journal of Control Engineering Practice, revision

Non-blocking supervisory control for initialised rectangular automata

We consider the problem of supervisory control for a class of rectangular automata and more specifically for compact rectangular automata with uniform rectangular activity, i.e. initialised. The supervisory controller is state feedback and disables discrete-event transitions in order to solve the non-blocking forbidden state problem. The non-blocking problem is defined under both strong and weak conditions. For the latter maximally permissive solutions that are computable on a finite quotient space characterised by language equivalence are derived

Application of supervisory control theory to theme park vehicles

Due to increasing system complexity, time-to-market and development costs reduction, new engineering processes are required. Model-based engineering processes are suitable candidates because they support system development by enabling the use of various model-based analysis techniques and tools. As a result, they are able to cope with complexity and have the potential to reduce time-to-market and development costs. Moreover, supervisory control synthesis can be integrated in this setting, which can further contribute to the development of control systems. To evaluate the applicability of recently developed supervisor synthesis techniques and to show how they can be integrated in an engineering process, a theme park vehicle is chosen as a case study. The supervisor synthesized for the theme park vehicle has successfully been implemented and integrated in the existing resource-control platform

A Graph-Transformation Modelling Framework for Supervisory Control

Formal design methodologies have the potential to accelerate the development and increase the reliability of supervisory controllers designed within industry. One promising design framework which has been shown to do so is known as supervisory control synthesis (SCS). In SCS, instead of manually designing the supervisory controller itself, one designs models of the uncontrolled system and its control requirements. These models are then provided as input to a special synthesis algorithm which uses them to automatically generate a model of the supervisory controller. This outputted model is guaranteed to be correct as long as the models of the uncontrolled system and its control requirements are valid. This accelerates development by removing the need to verify and rectify the model of the supervisory controller. Instead, only the models of the uncontrolled system and its requirements must be validated. To address problems of scale, SCS can be applied in modular fashion, and implemented in hierarchical and decentralized architectures. Despite the large body of research con rming the bene ts of integrating SCS within the development process of supervisory controllers, it has still not yet found widespread application within industry. In the author's opinion, this is partly attributed to the non-user-friendly nature of the automaton-based modelling framework used create the models of the uncontrolled system (and control requirements in even-based SCS). It is believed that in order for SCS to become more accessible to a wider range of non experts, modelling within SCS must be made more intuitive and user-friendly. To improve the usability of SCS, this work illustrates how a graph transformation-based modelling approach can be employed to generate the automaton models required for supervisory control synthesis. Furthermore, it is demonstrated how models of the speci cation can be intuitively represented within our proposed modelling framework for both event- and state-based supervisory control synthesis. Lastly, this thesis assesses the relative advantages brought about by the proposed graph transformation-based modelling framework over the conventional automaton based modelling approach

Structuring Multilevel Discrete-Event Systems With Dependence Structure Matrices

Despite the correct-by-construction property, one of the major drawbacks of supervisory control synthesis is state-space explosion. Several approaches have been proposed to overcome this computational difficulty, such as modular, hierarchical, decentralized, and multilevel supervisory control synthesis. Unfortunately, the modeler needs to provide additional information about the system's structure or controller's structure as input for most of these nonmonolithic synthesis procedures. Multilevel synthesis assumes that the system is provided in a tree-structured format, which may resemble a system decomposition. In this paper, we present a systematic approach to transform a set of plant models and a set of requirement models provided as extended finite automata into a tree-structured multilevel discrete-event system to which multilevel supervisory control synthesis can be applied. By analyzing the dependencies between the plants and the requirements using dependence structure matrix techniques, a multilevel clustering can be calculated. With the modeling framework of extended finite automata, plant models and requirements depend on each other when they share events or variables. We report on experimental results of applying the algorithm's implementation on several models available in the literature to assess the applicability of the proposed method. The benefit of multilevel synthesis based on the calculated clustering is significant for most large-scale systems