Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1

Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested

On detectability of labeled Petri nets and finite automata

Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate detectability. This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong detectability. The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong detectability is strictly stronger than eventual strong detectability for labeled Petri nets and even for deterministic finite automata

On detectability of labeled Petri nets and finite automata

We study detectability properties for labeled Petri nets and finite automata. We first study weak approximate detectability (WAD) that implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We also consider two new concepts called instant strong detectability (ISD) and eventual strong detectability (ESD). The former property implies that for each possible infinite observed output sequence each prefix of the output sequence allows reconstructing the current state. The latter implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. Results: WAD: undecidable for labeled Petri nets, PSPACE-complete for finite automata ISD: decidable and EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata ESD: decidable under promptness assumption and EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata SD: belongs to P for finite automata, strengthens Shu and Lin's 2011 results based on two assumptions of deadlock-freeness and promptness ISD<SD<ESD<WD<WAD for both labeled Petri nets and finite automataComment: 44 pages, 21 figure

Structural Sequence Detectability in Free Choice Interpreted Petri Nets

This paper is concerned with the structural sequence detectability problem in Free Choice Interpreted Petri nets, i.e. with the possibility of recovering the firing transition sequence in Free Choice Interpreted Petri nets using the output information when the initial marking is unknown. Based on the Free Choice Interpreted Petri net structure, three relationships are proposed which are devoted to capture the confusion over the transitions. These relationships depend on interpreted Petri nets structures such as T-invariants, P-Invariants, attribution and distribution places. Thus, the approach herein presented exploits the interpreted Petri nets structural information in order to determine the structural sequence detectability of an interpreted Petri net.Consejo Nacional de Ciencia y Tecnologí

Partial Reconfiguration of Control Systems using Petri Nets Structural Redundancy

This paper deals with the partial reconfiguration of the discrete control systems due to resource failures using the structural redundancy of the global system model. The approach herein proposed introduces a new subclass of Interpreted Petri Nets (), named Interpreted Machines with Resources (), allowing representing both the behaviour of a system and the resource allocation. Based on this model, an efficient reconfiguration algorithm is proposed; it is based on finding the set of all redundant sequences using alternative resources. The advantages of this structural reconfiguration method are: (1) it provides minimal reconfiguration to the system control assuring the properties of the original control system, (2) since the model includes resource allocation, it can be applied to a variety of systems such as Business Processes, and FPGAs, among others, (3) it takes advantage of the implied features of Petri net models, such as structural analysis and graphical visualization of the system and control. The method is illustrated through a case study that deals with a manufacturing system controller, which includes both alternative resources and operation sequencesITESO, A.C.CINVESTA

TIME CONDITION SYSTEMS

The current thesis considers the issue of state estimation of condition systems, a form of petri net with signal inputs and outputs. In previous research the problem of unobservability due to progress confusion was identified, in the presence of which state estimation is not possible. Here we introduce the notion of Time Condition Systems , a class of condition systems that uses timing information from condition models to overcome state estimation problem caused by progress confusion. To make use of the timing information in the plant model, a procedure called Exploded Time Plant is synthesized. This procedure makes the plant model an observable model. It is proved that this procedure does not alter the structural and temporal behavior of the plant model and the plant maintains its integrity. The time plant(s) and the corresponding Exploded time plant(s) are subsequently used to develop observer(s) and controller(s) for Time condition models

Adaptive Process Management in Cyber-Physical Domains

The increasing application of process-oriented approaches in new challenging cyber-physical domains beyond business computing (e.g., personalized healthcare, emergency management, factories of the future, home automation, etc.) has led to reconsider the level of flexibility and support required to manage complex processes in such domains. A cyber-physical domain is characterized by the presence of a cyber-physical system coordinating heterogeneous ICT components (PCs, smartphones, sensors, actuators) and involving real world entities (humans, machines, agents, robots, etc.) that perform complex tasks in the “physical” real world to achieve a common goal. The physical world, however, is not entirely predictable, and processes enacted in cyber-physical domains must be robust to unexpected conditions and adaptable to unanticipated exceptions. This demands a more flexible approach in process design and enactment, recognizing that in real-world environments it is not adequate to assume that all possible recovery activities can be predefined for dealing with the exceptions that can ensue. In this chapter, we tackle the above issue and we propose a general approach, a concrete framework and a process management system implementation, called SmartPM, for automatically adapting processes enacted in cyber-physical domains in case of unanticipated exceptions and exogenous events. The adaptation mechanism provided by SmartPM is based on declarative task specifications, execution monitoring for detecting failures and context changes at run-time, and automated planning techniques to self-repair the running process, without requiring to predefine any specific adaptation policy or exception handler at design-time