An Advanced Environment for Hybrid Modeling of Biological Systems Based on Modelica

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

In this chapter, modeling of GRNs using Petri net theory is considered. It aims at providing a conceptual understanding of Petri nets to enable the reader to explore GRNs applying Petri net modeling and analysis techniques. Starting with an overview on modeling biochemical networks using Petri nets, the state-of-the-art with focus on GRNs is described. Other modeling techniques, for example, hybrid Petri nets are discussed. Basic concepts of Petri net theory are introduced involving special analysis techniques for modeling biochemical systems, for example, MCT-sets, T-clusters, and Mauritius maps. To illustrate these Petri net concepts, a more complex case study–the gene regulation in Duchenne Muscular Dystrophy–is explained in detail, considering the biological background and the interpretation of analysis results. Considering both, advantages and disadvantages, the chapter demonstrates the usefulness of Petri net modeling, in particular for GRNs.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

We propose a generalized concept of hybrid Petri nets as a modeling and design tool for the distributed dynamical systems involving asynchronous event-based communication. The proposed Petri net machine represents an extension of the standard discrete-event Petri nets, but differs conceptually from the conventional hybrid Petri nets in that dynamical processes are stored in the continuous places, similarly as in hybrid automata. In particular, the firing semantics of the corresponding continuous arcs is defined to capture the information exchange between the network nodes. While being primarily a graphical modeling tool, the proposed formalism of hybrid Petri nets infers a hybrid dynamical setting of event-triggered control problems, an approach that has been missing in the literature. The usability of our approach is illustrated in the context of the distributed event-triggered LQR and consensus problems, in conjunction with a systematic methodology for designing optimal adaptive scheduling schemes, governing the communication resources.

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

Hemojuvelin–hepcidin axis modeled and analyzed using Petri nets

A Petri net with controller is used to model discrete events in flexible job shop scheduling, the objective of scheduling problems is to minimize make-span, the scheduling results is obtained based on genetic and Tabu Search (TS) algorithm. It is proved capable of providing optimized schedule to the job-shop where the machine tool and manpower resources are both constrained. After crossover and mutation operations, an optimal or suboptimal scheduling plan can be found. The result of the test shows that this method is feasible and efficient. Job shop scheduling is the primary content and critical technology of the production management of CIMS, in the past during 30 years, a lot of researchers and results focus on it, but most of them deal with single objective and resource scheduling problems which are fixed processing route and constrained by machine, and production period is its optimal objective. Nevertheless, the production styles are variable and processing route is determined under the special condition. Moreover, job shop scheduling problem is the most difficult combined constraints optimal problem and typical NP hard problem which can't be solved in polynomial time by an effective algorithm. Up to date, there are some traditional algorithms to solve JSP problem (1-2). About paper (3), Petri net is used to construct JSP model and L1 which combines branch and bound algorithm with dynamic program is used to search its optimal solution. And paper (4), the job sequence is assigned by genetic code firstly, and then filtered beam search which based on breadth-first algorithm is adopted to search. In recent years, the Petri net as a discrete event dynamic system modeling and analysis tool(5), has been successfully applied to the flexible manufacturing system modeling, analysis and control. Some researchers put forward to be based on Petri network scheduling method, but only on the production line itself can not reflect the modeling, as in the production line of external control scheduling strategy influence. A hybrid algorithm is proposed to solve dual-resource scheduling problem in flexible production environment, and Petri net model with a controller, which can effectively model control. It combines the advantage of global search ability of GA with the self-adaptive merit of Tabu Search (TS) and improves its convergence. It is proved capable of global and part searching ability and efficient.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.

This paper presents an approach to perform Activity Based Costing (ABC) with Petri nets. ABC is a powerful methodology to calculate various of discrete event systems (e.g. production systems). Petri net models of discrete event systems are easy to create, comprehend, and to perform analysis, the mathematics behind Petri nets is also easy to grasp. This paper shows how ABC can be performed with Petri nets, so that various involved in a discrete event system can be easily measured with the help of the Petri net model. After a short introduction to ABC and Petri nets, this paper shows the approach which basically embeds various cost drivers as firing costs and firing times of transitions in a Petri net model. This work also presents a case study that is done with GPenSIM, a toolbox realized with this approach.

Material handling systems are usually modeled as discrete event systems. However, when the size of these systems grows, the overall system performances depend also on continuous time phenomena. We present a hybrid model based on a new Petri net formalism that merges the concepts of Hybrid Petri Nets and Colored Petri Nets to obtain compact models for these systems. An example is discussed in detail to motivate the introduction of a new formalism.

Performance regulation of event-driven dynamical systems using infinitesimal perturbation analysis

This paper presents a decentralized Petri net (PN) based wireless sensor node architecture (PN-WSNA) to construct a flexible and reconfigurable WSN for intelligent monitoring systems. PN is a graphic based discrete event dynamic system (DEDS) modeling approach, and it is advantageous for modeling the system with concurrent and asynchronous systems. Therefore, the PN is usually used to construct agent based intelligent monitoring systems. The PN-WSNA system consists of a PN-WSNA kernel program and a PN-WSNA management program. The PN-WSNA kernel program is developed as an agent that is installed in the sensor node, and it is responsible of receiving and decoding PN models, collecting sensor data from analog and digital channels, intercommunication between sensor nodes, PN model inference and decision. On the other hand, the PN-WSNA management program is executed on a remote host computer, and it is responsible of distance sensor node managements via routing tables. More specially, a user interface is provided for system managers to edit PN models in a graphic manner, and the PN models can be delivered to the corresponding sensor node online without physical visits. Therefore, the proposed PN-WSNA system not only performs a reconfigurable WSN architecture, but also provides an easy graphical PN edit environment for constructing intelligent agents. Such a system can be applied to the factory automation, intelligent diagnosis, climate monitoring, etc. Finally, a simple prototype system is constructed using the Zigbee BAT mote modules to verify the proposed PN-WSNA system.