On the Enforcement of a Class of Nonlinear Constraints on Petri Nets

International audienceThis paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunc-tive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach

Algoritam za sprječavanje zastoja temeljen na uzastopnoj kontroli sifona Petrijeve mreže

This paper presents a formal calculation method of a deadlock prevention supervisor by the use of Petri nets. The proposed algorithm uses reachability tree to detect deadlock state and iterative siphon control method to synthesize the deadlock prevention supervisor. Such supervisor is maximally permissive and consists of minimal number of control places. The algorithm is intended for reversible or partially reversible P-T Petri net, but it can also be applied to Ordinary Petri nets. The calculation of the supervisor is illustrated by two examples. The first example shows the synthesis of deadlock prevention supervisor in a manufacturing system consisting of three conveyors and three robots, where the deadlock can occur due to concurrent requests of the conveyors for the robot engagements and unpredictable duration of those engagements. The second example shows the synthesis of deadlock prevention supervisor in a marine traffic system, where dangerous vessel deadlock situations may occur in case of vessels\u27 irregular motion through the system. To avoid this, the vessel traffic is supervised and controlled by traffic lights using the deadlock prevention supervisor, which is responsible for vessels\u27 stopping only in the case of dangerous situation and until this situation elapses.Članak opisuje formalnu metodu proračuna nadzornika za sprječavanje zastoja korištenjem Petrijevih mreža. Predloženi algoritam koristi stablo dostupnih stanja za detekciju stanja zastoja i metodu uzastopne kontrole sifona za sintezu nadzornika za sprječavanje zastoja. Nadzornik je najviše dopuštajući i sadrži najmanji broj kontrolnih mjesta. Algoritam je namijenjen za reverzibilne ili djelomično reverzibilne P-T Petrijeve mreže, ali se može koristiti i za obične Petrijeve mreže. Proračun nadzornika pokazan je na dva primjera. Prvi primjer prikazuje sintezu nadzornika za sprječavanje zastoja u fleksibilnom proizvodnom sustavu s tri robota i tri proizvodne trake, gdje se zastoj može dogoditi zbog međusobnog natjecanja transportnih traka za angažiranjem robota te zbog nepredvidljivosti trajanja tih angažmana. Drugi primjer prikazuje sintezu nadzornika u pomorskom prometnom sustavu, gdje se opasne situacije zastoja plovila mogu dogoditi poradi neodgovarajućeg pomicanja plovila kroz sustav. Da bi se to izbjeglo, promet plovila se nadzire i upravlja pomoću svjetlosne signalizacije korištenjem nadzornika za sprječavanje zastoja, koji je odgovoran za zaustavljanje plovila samo u slučaju opasnog stanja te dok to stanje ne nestane

Algoritam za sprječavanje zastoja temeljen na uzastopnoj kontroli sifona Petrijeve mreže

This paper presents a formal calculation method of a deadlock prevention supervisor by the use of Petri nets. The proposed algorithm uses reachability tree to detect deadlock state and iterative siphon control method to synthesize the deadlock prevention supervisor. Such supervisor is maximally permissive and consists of minimal number of control places. The algorithm is intended for reversible or partially reversible P-T Petri net, but it can also be applied to Ordinary Petri nets. The calculation of the supervisor is illustrated by two examples. The first example shows the synthesis of deadlock prevention supervisor in a manufacturing system consisting of three conveyors and three robots, where the deadlock can occur due to concurrent requests of the conveyors for the robot engagements and unpredictable duration of those engagements. The second example shows the synthesis of deadlock prevention supervisor in a marine traffic system, where dangerous vessel deadlock situations may occur in case of vessels\u27 irregular motion through the system. To avoid this, the vessel traffic is supervised and controlled by traffic lights using the deadlock prevention supervisor, which is responsible for vessels\u27 stopping only in the case of dangerous situation and until this situation elapses.Članak opisuje formalnu metodu proračuna nadzornika za sprječavanje zastoja korištenjem Petrijevih mreža. Predloženi algoritam koristi stablo dostupnih stanja za detekciju stanja zastoja i metodu uzastopne kontrole sifona za sintezu nadzornika za sprječavanje zastoja. Nadzornik je najviše dopuštajući i sadrži najmanji broj kontrolnih mjesta. Algoritam je namijenjen za reverzibilne ili djelomično reverzibilne P-T Petrijeve mreže, ali se može koristiti i za obične Petrijeve mreže. Proračun nadzornika pokazan je na dva primjera. Prvi primjer prikazuje sintezu nadzornika za sprječavanje zastoja u fleksibilnom proizvodnom sustavu s tri robota i tri proizvodne trake, gdje se zastoj može dogoditi zbog međusobnog natjecanja transportnih traka za angažiranjem robota te zbog nepredvidljivosti trajanja tih angažmana. Drugi primjer prikazuje sintezu nadzornika u pomorskom prometnom sustavu, gdje se opasne situacije zastoja plovila mogu dogoditi poradi neodgovarajućeg pomicanja plovila kroz sustav. Da bi se to izbjeglo, promet plovila se nadzire i upravlja pomoću svjetlosne signalizacije korištenjem nadzornika za sprječavanje zastoja, koji je odgovoran za zaustavljanje plovila samo u slučaju opasnog stanja te dok to stanje ne nestane

Contributions to the deadlock problem in multithreaded software applications observed as Resource Allocation Systems

Desde el punto de vista de la competencia por recursos compartidos sucesivamente reutilizables, se dice que un sistema concurrente compuesto por procesos secuenciales está en situación de bloqueo si existe en él un conjunto de procesos que están indefinidamente esperando la liberación de ciertos recursos retenidos por miembros del mismo conjunto de procesos. En sistemas razonablemente complejos o distribuidos, establecer una política de asignación de recursos que sea libre de bloqueos puede ser un problema muy difícil de resolver de forma eficiente. En este sentido, los modelos formales, y particularmente las redes de Petri, se han ido afianzando como herramientas fructíferas que permiten abstraer el problema de asignación de recursos en este tipo de sistemas, con el fin de abordarlo analíticamente y proveer métodos eficientes para la correcta construcción o corrección de estos sistemas. En particular, la teoría estructural de redes de Petri se postula como un potente aliado para lidiar con el problema de la explosión de estados inherente a aquéllos. En este fértil contexto han florecido una serie de trabajos que defienden una propuesta metodológica de diseño orientada al estudio estructural y la correspondiente corrección física del problema de asignación de recursos en familias de sistemas muy significativas en determinados contextos de aplicación, como el de los Sistemas de Fabricación Flexible. Las clases de modelos de redes de Petri resultantes asumen ciertas restricciones, con significado físico en el contexto de aplicación para el que están destinadas, que alivian en buena medida la complejidad del problema. En la presente tesis, se intenta acercar ese tipo de aproximación metodológica al diseño de aplicaciones software multihilo libres de bloqueos. A tal efecto, se pone de manifiesto cómo aquellas restricciones procedentes del mundo de los Sistemas de Fabricación Flexible se muestran demasiado severas para aprehender la versatilidad inherente a los sistemas software en lo que respecta a la interacción de los procesos con los recursos compartidos. En particular, se han de resaltar dos necesidades de modelado fundamentales que obstaculizan la mera adopción de antiguas aproximaciones surgidas bajo el prisma de otros dominios: (1) la necesidad de soportar el anidamiento de bucles no desplegables en el interior de los procesos, y (2) la posible compartición de recursos no disponibles en el arranque del sistema pero que son creados o declarados por un proceso en ejecución. A resultas, se identifica una serie de requerimientos básicos para la definición de un tipo de modelos orientado al estudio de sistemas software multihilo y se presenta una clase de redes de Petri, llamada PC2R, que cumple dicha lista de requerimientos, manteniéndose a su vez respetuosa con la filosofía de diseño de anteriores subclases enfocadas a otros contextos de aplicación. Junto con la revisión e integración de anteriores resultados en el nuevo marco conceptual, se aborda el estudio de propiedades inherentes a los sistemas resultantes y su relación profunda con otros tipos de modelos, la confección de resultados y algoritmos eficientes para el análisis estructural de vivacidad en la nueva clase, así como la revisión y propuesta de métodos de resolución de los problemas de bloqueo adaptadas a las particularidades físicas del dominio de aplicación. Asimismo, se estudia la complejidad computacional de ciertas vertientes relacionadas con el problema de asignación de recursos en el nuevo contexto, así como la traslación de los resultados anteriormente mencionados sobre el dominio de la ingeniería de software multihilo, donde la nueva clase de redes permite afrontar problemas inabordables considerando el marco teórico y las herramientas suministradas para subclases anteriormente explotadas

Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR–AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach

Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

A Synthesis Method for Designing Shared-Resource Systems

In system synthesis, one needs to derive from a given set of processes a system design which reflects exactly the functionalities of the processes and is free from erroneous situations such as deadlock and capacity overflow. This is especially important for shared-resource systems, in which errors are easily induced because of the sharing of common resources among different competing processes. In this paper, a synthesis method is proposed for designing shared-resource systems. It begins with specifying the given processes as augmented marked graphs. These augmented marked graphs are then synthesized through the fusion of commonplaces which represents the shared resources. The net so obtained serves to represent the integrated system which reflects exactly the functionalities of the processes in the sense that the event sequences as well as the pre-conditions and post-conditions of each event occurrence are preserved. Based on the known properties of augmented marked graphs, the system properties such as liveness, boundedness and reversibility can be analysed effectively. The method is applied to manufacturing system design. Promising results are obtained