Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

Heap Models, Composition and Control

International audienc

Object-oriented GUI design of a modeling environment for logical discrete event systems

Ce mémoire porte sur la conception et l'implémentation d'une partie de l'interface personne-machine orientée objet d'un environnement de modélisation de systèmes réactifs appelé MELODIES (Modeling Environment for LOgical Discrete Event Systems ). Cet environnement permet la conception, l'analyse, la simulation et le contrôle de systèmes à événements discrets. L'architecture de l'interface est basée sur certaines idées empruntées au schéma de conception Model-View-Controller (MVC) et au paradigme JSP Model 2 Architecture . Il en résulte une nette séparation entre l'interface personne-machine, les structures de données ainsi que les fonctions sous-jacentes. L'adoption d'une approche orientée objet, comme celle supportée par VisualAge for Java 4.0, au lieu d'une approche orientée fichier supportée par plusieurs environnements de développement (par exemple JBuilder for Java 3.0) permet une plus grande convivialité et une meilleure organisation des artéfacts de modélisation. Afin de déployer cette interface sur différentes plateformes et d'assurer une rapidité d'exécution, la boîte à outils Qt 3.0 et le langage C++, avec sa librairie STL, ont été utilisés dans l'étape de codification. De plus, XML a été retenu comme langage de représentation de données afin de permettre un déploiement éventuel de MELODIES sur le Web

Control and diagnosis of real-time systems under finite-precision measurement of time

A discrete event system (DES) is an event-driven system that evolves according to abrupt occurrences of discrete changes (events). The domain of such systems encompasses aspects of many man-made systems such as manufacturing systems, telephone networks, communication protocols, traffic systems, embedded software, asynchronous hardware, robotics, etc. Supervisory control theory for DESs studies the existence and synthesis of the supervisory controllers, namely, supervisors that restrict the system behaviors by dynamically disabling certain controllable events so that the controlled close-loop system could behave as desired. Extensive work on supervisory control of untimed DESs exists and the extension to the timed setting has been reported in the literature. In this dissertation, we study the supervisory control of dense-time DESs in which the digital-clocks of finite-precision are employed to observe the event occurrence times, thereby relaxing the assumption of the prior works that time can be measured precisely. In our setting, the passing of time is measured using the number of ticks generated by a digital-clock and we allow the plant events and digital-clock ticks to occur concurrently. We formalize the notion of a control policy that issues the control actions based on the observations of events and their occurrence times as measured using a digital-clock, and show that such a control policy can be equivalently represented as a digitalized -automaton, namely, an untimed-automaton that evolves over the events (of the plant) and ticks (of the digital-clock). We introduce the notion of observability with respect to the partial observations of time resulting from the use of a digital-clock, and show that this property together with controllability serves as a necessary and sufficient condition for the existence of a supervisor to enforce a real-time specification on a dense-time discrete event plant. The observability condition presented in the dissertation is very different from the one arising due to a partial observation of events since a partial observation of time is in general nondeterministic (the number of ticks generated in any time interval can vary from execution to execution of a digital-clock). We also present a method to verify the proposed observability and controllability conditions, and an algorithm to compute a supervisor when such conditions are satisfied. Furthermore we examine the lattice structure of a class of timing-mask observable languages, and show that the proposed observability is not preserved under intersection but preserved under union. Fault diagnosis for DESs is to detect the occurrence of a fault so as to enable any corrective actions. It is crucial in automatic control of large complex man-made systems and has attracted considerable attention in the literature of reliability engineering, control and computer science. For the event-driven systems with timing-requirements such as manufacturing systems, communication networks, real-time scheduling and traffic systems, fault diagnosis involves detecting the timing-faults, besides the sequence-faults. This requires monitoring timing and sequence of events, both of which may only be partially observed in practice. In this dissertation, we extend the prior works on fault diagnosis of timed DESs by allowing time to be partially observed using a digital-clock which measures the advancement of time with finite precision by the number of ticks. For the diagnosis purposes, the set of nonfaulty timed-traces is specified as another timed-automaton that is deterministic. We show that the set of timed-traces observed using a digital-clock with finite precision is regular, i.e., can be represented using a finite (untimed) automaton. We also show that the verification of diagnosability (the ability to detect the execution of a faulty timed-trace within a bounded time delay) as well as the off-line synthesis of a diagnoser are decidable by reducing these problems to the untimed setting. The reduction to the untimed setting also suggests an effective method for the off-line computation of a diagnoser as well as its on-line implementation for diagnosis. The aforementioned results are further extended to the nondeterministic setting, i.e., diagnosis of dense-time DESs using digital-clocks under nondeterministic event observation mask. We introduce the notion of lifting (associating each event with each of its nondeterministic observations), and show that diagnosis of dense-time DESs employing digital-clocks to observe event occurrence times under nondeterministic event observation mask can be reduced to that of the deterministic setting, i.e., diagnosis of the lifted dense-time DESs under the deterministic lifted event observation mask, and hence can be further reduced to diagnosis of the untimed setting

Time-optimal control of large-scale systems of systems using compositional optimization

Optimization of industrial processes such as manufacturing cells can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. In previous work we proposed Compositional Optimization as a method to solve these type of problems. This integrates optimization with techniques from compositional supervisory control, dividing the optimization into separate sub-problems. The main purpose is to mitigate the state explosion problem, but a bonus is that the individual sub-problems can be solved using parallel computation, making the method even more scalable. This paper further improves on compositional optimization with a novel synchronization method, called partial time-weighted synchronization (PTWS), that is specifically designed for time-optimal control of asynchronous systems. The benefit is its ability to combine the behaviour of asynchronous subsystems without introducing additional states or transitions. The method also reduces the search space further by integrating an optimization heuristic that removes many non-optimal or redundant solutions already during synchronization. Results in this paper show that compositional optimization efficiently generates global optimal solutions to large-scale realistic optimization problems, too big to solve when based on traditional monolithic models. It is also shown that the introduction of PTWS drastically decreases the total search space of the optimization compared to previous work

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

Modular Learning and Optimization for Planning of Discrete Event Systems

Optimization of industrial processes, such as manufacturing cells, can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. This is usually referred to as the state explosion problem and is a well-known problem within the control and optimization of automation systems. This thesis proposes two main contributions to improve and to simplify the optimization of these systems. The first is a new method of solving these optimization problems using a compositional optimization approach. This integrates optimization with techniques from compositional supervisory control using modular formal models, dividing the optimization of subsystems into separate subproblems. The second is a modular learning approach that alleviates the need for prior knowledge of the systems and system experts when applying compositional optimization. The key to both techniques is the division of the large system into smaller subsystems and the identification of local behavior in these subsystems, i.e. behavior that is independent of all other subsystems. It is proven in this thesis that this local behavior can be partially optimized individually without affecting the global optimal solution. This is used to reduce the state space in each subsystem, and to construct the global optimal solution compositionally.The thesis also shows that the proposed techniques can be integrated to compute global optimal solutions to large-scale optimization problems, too big to solve based on traditional monolithic models