On Hierarchical Construction of the State Space of an Automated Manufacturing System Modeled With Petri Nets

A coloured Petri net (CPN) is widely used to model discrete event systems due to its compact representation of the system by colour sets associated with places, transitions and I/O arcs. For real-world systems such as manufacturing systems, transportation systems, and communication protocols, a coloured timed Petri net (CTPN) is proposed to model timed behaviours. To control a discrete event system with a desired control specification, it is important to describe the control specification formally. For the CPN, a class of specification called coloured generalized mutual exclusion constraints (cGMEC) is utilized to specify the behaviours. However, cGMEC can only represent safety constraints and not temporal constraints. Therefore, in this paper, we propose a novel temporal logic based constraint called a coloured generalized mutual exclusion temporal constraint (cGMETC). The cGMETC is described by a signal temporal logic (STL) formula where each atomic predicate represents a cGMEC. We propose a method for optimal control of the CTPN under a given cGMETC. In particular, we formulate an optimal control problem and solve the problem by transforming it into an integer linear programming problem. Through a simulation of an optimal control problem of a manufacturing system, we demonstrate the effectiveness of the proposed approach.INDEX TERMS Petri nets, coloured timed Petri nets, temporal logic, generalized mutual exclusion constraints, integer linear programming. I. INTRODUCTIONA Petri net is an appropriate tool for modelling of discrete event systems [1], [2]. In particular, it has been applied to resource allocation problems including scheduling in manufacturing systems because it provides representation of systems with a large state space [3], [4], [5]. For real-world systems, however, the size of the systems increases, and the systems contain structures that are similar but not exactly the same. To model such systems, a coloured Petri net (CPN), which is an extension of Petri nets, has been studied [6], [7]. The CPN has colour sets that are associated with places, transitions and I/O arcs, and it provides a more compact representation for complex and large systems than ordinary Petri nets. There have been many studies utilizing the CPN,The associate editor coordinating the review of this manuscript and approving it for publication was Zhiwu Li .

Section: A Encoding the Trajectory Of Ctpnmentioning

confidence: 99%

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confidence: 99%

Optimal Control of Colored Timed Petri Nets Under Generalized Mutual Exclusion Temporal Constraints

Fujita

Ushio

2022

“…The validation of these steps [70]- [72] is also a required step to be combined also with formal modeling and verification of some critical behaviors [73]- [77]. Nowadays, different formalisms are proposed to model discrete-event systems such as Petri nets [78]- [81] and timed automata [82]. We cite also the computation tree logic [83] which is the most used for describing functional and extra-functional properties to be respected by discrete-event systems.…”

Section: Overview On Related Workmentioning

confidence: 99%

On Reconfiguration Theory of Discrete-Event Systems: From Initial Specification Until Final Deployment

Khalgui

Mosbahi

2019

Self Cite

This paper presents an overview on different research activities that we did in the recent decade for developing reconfigurable discrete-event systems (RDESs) from initial high-level specification according to user requirements until final low-level deployment in target hardware components. A reconfiguration is any run-time scenario that adapts the system's behavior to any evolution in the related environment by adding or removing services or also configuring their parameters, i.e., their frequency, execution time, or also their location in the considered hardware architecture. Since the development of distributed RDESs under functional and extra-functional constraints is required by experts, we propose a complete methodology that deals first with their initial design with a new general profile named R-UML extending unified modeling language (UML) or also with new specific technology-oriented profiles, the validation of the related models with a new language R-OCL extending object constraint language (OCL), before their transformation to formal formalisms, such as Petri nets, timed automata, or B method for simulation or also formal verification of different properties. The checked models are transformed into OS reconfigurable tasks in the operational level, before applying a co-design methodology under functional, real-time, memory, and energy constraints for minimizing redundancies in tasks and for optimizing the composition of software and hardware parts together. We describe technology-oriented solutions for the scheduling of distributed RDESs by parameterizing tasks and their exchanged messages between multi-speed networked processors. We finish with the real low-level deployment on target hardware devices before applying useful software and hardware tests for checking the delivered system quality. These contributions, published in different journal and conference papers, are applied to different applications in medicine, wireless sensor networks, transportation systems, manufacturing industry, smart grids and microgrids, embedded technologies, and so on. We find significant gains in terms of the system reactivity and flexibility under related constraints. INDEX TERMS Discrete-event system, modeling and verification, design and validation, implementation and scheduling, real-time and energy aware scheduling, test and simulation, co-design and deployment, application. I. INTRODUCTION Automatic flexibility becomes a required criterion for dynamic system adaptability to any possible evolution in related environment. A reconfigurable system is considered in this paper as a discrete-event system (RDES) that adapts its behavior to recover faults or also improve required performance at run-time. It is a set of wired/wireless networked devices that run independent/dependent control software tasks exchanging messages on the network [1], [2]. These tasks and consequently the related messages should be executed under functional, memory, real-time, and energy constraints described in user requirements [3]-[5]. A reconfi...

“…This technique is called the reduction technique [43]. In order to deal with the problem of state space explosion, researchers propose a method to reduce the initial marking of a given PN to a smaller one [44]. At the same time, in order to improve the ability of system modeling, researchers put forward many special subnets with good properties, such as state machines [45], marked graphs [46], and free choice nets [47].…”

Section: Introductionmentioning

confidence: 99%

A State-Equation-Based Method to Non-Reachability Analysis of Ordinary Petri Nets With Token-Free Circuit-Based Subnets

2022

Petri nets (PNs) can model various event-driven systems well and detect a fault via reachability analysis. Some state-equation-based approaches are designed for only subclasses of PNs with specific structures. A key issue for PNs' reachability analysis approach based on state equation is that a non-negative integer solution (NIS) to a state equation is necessary but not sufficient for a marking's reachability. In this paper, we propose a circuit-based subnet. For ordinary Petri nets with token-free circuit-based subnets, we present an algorithm to determine that the state equation has NISs but the marking is non-reachable. We adopt a divide-and-conquer strategy to consider each circuit-based subnet. The proposed method is tested on a PN-based flexible manufacturing system with unreliable resources. When unreliable resources are lost, the non-reachable markings can be determined effectively. Besides, simulations are done, and the results verify the efficiency of the proposed algorithm compared with the reachability-tree-based method.