In robotic job shops (RJS), a significant challenge lies in optimizing task allocation and robot routing simultaneously, especially since these tasks must be accomplished in real-time to efficiently manage unexpected situations, such as the urgent need for AGV recharging or sudden order additions. Deep reinforcement learning (DRL) shows promise for these complex scheduling tasks due to its ability to address problems characterized by substantial computational complexity. However, the rapid expansion of RJS state space and the difficulty of avoiding cyclic loops for AGVs pose significant challenges for DRL in realistic settings. To address these, we present a novel approach combining an artificial-potential-field (APF) with a deep Q-network (DQN) in a Petri net framework. The APF is designed for Petri nets to guide token movement toward goal place nodes. Throughout the learning process, the APF-guided mixed policy employs a cosine-annealing probability for APF policy and a piecewise linear probability for random policy. Initially, action selections predominantly rely on APF policy to efficiently gather high-reward experience. As training progresses, they shifts to more rely on the learned neural-network policy, with random exploration supplementing diversity, ensuring a robust transition from reward-driven exploration to precise decision-making. The APF-DQN method is tested in real-world RJS scenarios, showing superior exploration success and training efficiency over baseline DQN. It significantly outperforms both conventional dispatching rules and baseline DQN, reducing average makespan by over 55% compared to dispatching rules and by 14.9% relative to baseline DQN. This method significantly enhances traditional DQN by improving exploration success, learning efficiency, policy convergence, and adaptability to dynamic environments.

A state transfer graph and its generation algorithm are introduced to represent the state space of the place-timed Petri net model for a specific discrete event system. For a bounded place-timed Petri net possessing infinite states, it is proven that the state transfer graph comprises a set of finite nodes and an optimal schedule leading the net from an initial state to a target state in the minimal time. However, the size of a state transfer graph grows quite quickly with the net size and the total amount of tokens in the initial marking, which complicates the efficient calculation of an optimal schedule, particularly for real-world systems. To address this issue, two advanced rules are proposed to judge whether a state node is old and cut off when generating a state transfer graph. As a result, two variants of a state transfer graph are obtained, and it is proven that they all contain optimal schedules and are smaller than the state transfer graph, allowing more efficient solutions to scheduling issues. The state transfer graph provides a theoretic foundation for graph search algorithms, such as the Dijkstra, greedy-first, and A* algorithms, for scheduling problems of Petri nets. The proposed approach is demonstrated and verified through a flexible manufacturing benchmark system. The experimental results indicate that the state transfer graphs contain optimal schedules. Additionally, the old-state node judgment rules are effective in significantly reducing the computational burden of graph search algorithms for Petri nets.

The concept of k -level opacity is used to determine the level of opacity in a system. If the tolerance level k is higher, then the degree of opacity for any secret information will also be higher. However, if more non-secret information are not distinguished from secret ones, then the cost of achieving a control strategy will also be higher. In this paper, an optimization model that minimizes the discount total choosing cost while maintaining k -level opacity and releasing all the secret string is presented. If the secret language is k -level opaque w.r.t. its closure, the closure or the infimal controllable super-language of the closure is the optimal solution. If the secret language is not k -level opaque w.r.t. its closure, then a Multi-Stage Optimization Problem with Multi-Selection at each Stage (MSOP-MSS) is proposed. By analyzing the MSOP-MSS, an algorithm for handling the situation was proposed and used to obtain control strategy for the optimization model. The control strategy has been proven to be optimal. Finally, a complete algorithm, computational complexity analysis, and application examples are described.

In order to bridge the gap between the virtual and real worlds, this paper presents a novel model known as the parallel Petri net, specifically designed for the digital twin modeling and real-time coordination of cyber physical systems, where each operation is assumed to require a constant processing time. Unlike traditional Petri nets, the parallel Petri net incorporates new elements, such as actor and promoter functions in association with traditional places. In this framework, actors may function as either discrete-event or continuous-state controllers. The transition firing rules are defined to create an execution algorithm to drive the cyber physical system being modeled and co-run the corresponding parallel Petri net in parallel as a cyber model of the physical system, thereby applying its semantic control specifications, including manufacturing process sequences and recipes, to real-world actions. Due to its extensive modeling capabilities, the parallel Petri net offers a wide range of transition firing options in most states of practical operations. This enables simultaneous addressing of scheduling and control challenges to enhance the efficiency of physical systems. To this end, a reinforcement learning approach is developed based on the simulations of parallel Petri nets. It is demonstrated that the state-action value function can reliably predict the minimum time required to reach a goal state following a transition. Additionally, a deep Q-learning algorithm is presented, where the parallel Petri net serves as the operational environment, to train a neural network model for real-time scheduling. As a result, the parallel Petri net is capable of making intelligent decisions for cyber-physical systems through the neural network. Finally, the implementation framework for parallel Petri nets has been detailed, and experiments conducted in a manufacturing plant have verified the validity of the proposed techniques.

In this article, the fuzzy model predictive control (FMPC) problem is investigated for a class of non-linear systems in an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy form subject to hard constraints. To save transmission energy and reduce the calculation burden, a self-triggering scheme is incorporated into the FMPC strategy, which gives rise to the so-called self-triggered FMPC strategy. Based on the characteristics of the self-triggered FMPC strategy, the self-triggering instants rather than sampling instants are employed to construct the corresponding quadratic function and time-varying terminal constraint-like (TC-like) set. Then, to maximize triggering intervals and minimize the cost function, the fuzzy property and the self-triggering instants are fully considered to formulate a "min-max" problem over the infinite-time horizon, through which the feedback gain and next triggering instant are co-designed. Furthermore, the difference between the proposed quadratic functions of adjacent self-triggering instants is established, which contributes greatly to finding a certain upper bound of the objective function over the infinite-time horizon. Moreover, certain auxiliary optimization problems are developed for solvability and sufficient conditions are provided to ensure the asymptotic stability of the underlying IT2 T-S fuzzy system. Finally, two simulation examples are utilized to illustrate the validity of the proposed self-triggered IT2 T-S FMPC strategy.

This research investigates the control difficulties related to heterogeneous traffic flow in container terminals, featuring both connected and automated vehicles (CAVs) and human-driven vehicles (HDVs). The lack of signal control at intersections and the unpredictable routes taken by HDVs make the efficient transport of containers within a terminal quite challenging. To tackle this issue, we present an integrated traffic control policy aimed at enhancing transportation efficiency. For each unsignalized intersection, a virtual token ring system is introduced to manage the passage of vehicles, using a back pressure-based algorithm and specific token delivery rules to determine phase sequence and duration. Furthermore, we introduce an improved back pressure-based dynamic routing method for CAVs, which allows for the selection of roads with shorter travel time while adhering to a travel distance constraint when crossing an intersection. This approach aims to minimize disruptions from HDVs, reduce travel time, and prevent excessively long travel distances. Multiple experiments are conducted to verify the proposed method’s effectiveness.

This paper addresses the problem of fuzzy model predictive control (FMPC) for a class of nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models, subject to both hard constraints on control inputs and states, as well as communication network limitations. To mitigate data collisions and improve the reliability of data transmission, a random multiaccess protocol (RMP) is integrated into the FMPC framework, resulting in the proposed RMP-based FMPC approach. Specifically, a unified representation is developed to model the interplay between T-S fuzzy nonlinearities and the RMP for nonlinear systems with hard constraints. Utilizing a scheduling signal-dependent fuzzy quadratic function approach, a "min-max" problem is formulated by resorting to the objective function over the infinite horizon. The primary objective is to design a series of controllers using the FMPC approach, ensuring that the T-S fuzzy system remains mean-square stable under the prescribed constraints. By incorporating both the nonlinearities of the T-S fuzzy system and the dynamics of the RMP, sufficient stability conditions are derived via an auxiliary online optimization problem. Finally, the efficacy and applicability of the proposed approach are validated through two simulation examples, which demonstrate the robustness and effectiveness of the RMP-based FMPC strategy in handling both the network constraints and the system's nonlinear characteristics.

In order to address the problem of the real-time scheduling and control of batch chemical systems, this work proposes a model predictive control method based on Petri nets. First, a method is presented to construct a batch chemical system’s timed Petri net model. Second, a control structure is designed to augment the Petri net model to control the valves. This results in timed Petri nets that formally represent the process specifications of a batch chemical system. Third, a model predictive control method is developed to schedule and control timed Petri nets, where a proposed heuristic function is utilized to perform the optimization computation. The model parameters are dynamically adjusted using online data, and both scheduling and valve control instructions are calculated in real time. Finally, a series of experiments is carried out in a beer canning plant to verify the proposed method. According to the experimental results, the scheduling and control problem can be solved in real time, where the online computations can be performed in milliseconds, and the resulting scheduling strategies are optimal or near-optimal.

As for the optimal scheduling issue of closely coupled the path planning of automated guided vehicles (AGVs) and task allocation in flexible manufacturing systems (FMSs), a heuristic optimization method is proposed based on Petri nets and an artificial potential field (APF). First, a manufacturing system with AGVs is described as a task Petri net and a path one, and then its Petri net model is obtained by composing the two nets together. Second, the topology of the Petri net model is used to design the potential energy parameters for the network junctions, and, consequently, the APF is designed for the Petri net model. Third, a heuristic functions is proposed to estimate the minimal terminate times of the Petri net model by means of its APF. Further, a heuristic beam search algorithm is presented to calculate a near optimal schedule by the Petri net model and its APF. Finally, numerical experiments are carried out, and the results show that optimal or near-optimal schedules can be calculated in the reasonable times by our algorithm.

Numerous mobile robots are employed for mate-rial transporting in today's manufacturing industry. Therefore,it is crucial to consider the time consumption of both processoperations and transportation to minimize the makespan. Thispaper addresses the joint scheduling optimization problem ofautomated guided vehicle (AGV) routing and task allocationfor robotic job shops (RJSs). A novel artificial potential field(APF) design method is developed based on place-timed Petrinets (PNs) for heuristic scheduling in RJSs. First, a real-life scaleRJS is modeled with a place-timed PN, which contains a routesubnet and several task ones. The scheduling problem is thentransformed into a search one for the transition firing sequencewith the minimum makespan, which can be obtained by theA* algorithm. Second, a task-APF design method is proposedfor sorting processes. It defines potential energy parameters forplaces in task subnets by utilizing the topological structure ofPNs. The heuristic functionhMPDis obtained, and it is proved tobe admissible. Experimental results show that thehMPDheuristicenables the A* algorithm to generate an optimal schedule forRJSs, and its search efficiency surpasses that of the mostadvanced admissible heuristic functions available, particularlyin the scenario described in this paper. However, its searchefficiency decreases significantly when the number of jobs andAGVs increases. Third, a route-APF design method is proposedfor AGV routing, and a novel heuristic function, denoted byhTPD,is developed based on the task-APF and route-APF. Experimentalresults demonstrate thathTPDis more adaptable for schedulingRJSs with large-scale jobs and multiple AGVs thanhMPD, whichimproves the search efficiency by an average of one order ofmagnitude. It can find an optimal or near-optimal schedule withina reasonable amount of time, even when dealing with hundredsof jobs and multiple AGVs.

A novel inference approach is presented based on knowledge Petri nets and resolution rules. First, a knowledge base is modeled as a knowledge Petri net, where logical clauses are represented by monitor places, called semantic places. Second, a resolution pair is defined to identify a pair of semantic places, which, corresponding to two clauses that can be resolved, can be used to generate a new place in the knowledge Petri net. Such a new place represents an unknown clause implied by the knowledge base. Third, a method is proposed to decide whether a resolution inference is redundant based on the resolution pair. The size of a knowledge Petri net can be reduced, and the inference computation is saved in this way. Fourth, an inference algorithm is proposed employing the resolution pair and knowledge Petri net, proven to be sound and complete. Its computational complexity is polynomial with respect to the number of logical variables and clauses. In addition, another inference algorithm is developed for a given complete knowledge base and a set of newfound clauses. The algorithm is proven to be sound and complete, which offers significantly reduced computational complexity and specifically is linear concerning the number of new clauses. Finally, the wumpus world problem is taken as an example to illustrate and verify the proposed inference algorithms.

This work focuses on real-time and joint optimizing issues to handle the routing of automated guided vehicles and allocating processing tasks for automated manufacturing systems. A real-time scheduling approach is proposed based on Petri nets and deep reinforcement learning. First, the considered system is modeled with a placed-timed Petri net, which plays the role of the environment for deep reinforcement learning. Second, a novel graph convolutional network (GCN), called Petri-net-GCN, is designed by using the topological structures of a Petri net model such that it can adapt to changes in Petri-net structures caused by abrupt events such as new orders and failures of devices. Third, a deep Q-network method is presented to train Petri-net-GCN to predict the minimal time to lead a Petri net to its goal if an action (transition) is taken at a present state. Consequently, Petri-net-GCN can replace scheduling rules to schedule an automated manufacturing system in real time. Finally, numerical experiments are carried out where there exist failures of devices and new orders. The results show that Petri-net-GCN can adapt to the Petri-net changes caused by abrupt events and performs much better than the first-in-first-out and longest-processing-time-first rules, which are applicable for real-time scheduling issues in practice.

This paper presents an automatic planning method for pipe-line systems under complex logic control rules based on Petri nets. Petri nets are usually modeled manually, which can lead to incomplete models of complex logic control systems. To address this issue, we extend the planning domain definition language (PDDL), which can be automatically translated into Petri nets. For complex logic control pipe-line systems, given a set of tasks, it is difficult to quickly formulate the process execution sequence through manual calculation. This paper designs an automatic pipe-line system planning method based on Petri nets, which can accurately generate Petri nets model and process execution sequences. The beer filtration system is taken as an example to illustrate the method.

To ensure opacity, it is optimal to retain as many as possible occurring event sequences. Contrary to this problem, the other optimal goal is to preserve the minimal occurring event sequences. Based on the choosing cost, an optimal opacity-enforcing problem with minimal discount choosing cost is presented under two constraints in this paper. The first constraint is the opacity of the controlled system. The second is the retention of the secret to the maximum. To solve the model, two scenarios on opacity are considered. For the two scenarios, some algorithms are presented to achieve the optimal solution for the model by using the method of dynamic programming. Then, the solutions produced by the algorithms are proved to be correct by theoretical proof. Finally, some illustrations and an application example on location privacy protection for the algorithms are given.

This paper explores the application of the cell transmission model in assessing and mitigating incident-related traffic congestion within urban traffic networks. The authors introduce an extended traffic control approach that leverages the cell transmission model to emulate and analyze urban traffic gridlock scenarios triggered by accidents. They have created a versatile traffic simulation tool grounded in the cell transmission model, compatible across different platforms, to effectively replicate the spread and alleviation of traffic congestion resulting from accidents. The study delves into the use of the cell transmission model to formulate strategies for dissipating traffic jams caused by accidents and evaluates the efficacy of these strategies. In sum, this research showcases the potential of the cell transmission model as a valuable instrument for orchestrating traffic flow within urban environments.

本文提出了一种基于知识Petri网和归结规则的推理方法.通过知识Petri网描述命题逻辑知识库,将归结规则映射到知识Petri网上,根据库所和变迁的连接关系,定义了知识Petri网中的归结结构.利用归结结构,给出了基于知识Petri网的归结推理算法和扩展知识库的推理算法,并利用Wumpus实例验证了推理算法.该推理方法是可靠且完备的,能够利用知识Petri网的网络结构降低计算复杂性.

With the aim of promoting environmental sustainability and enhancing transport efficiency, battery-powered connected and automated vehicles (B-CAVs) are employed to replace diesel-powered ones in horizontal transport systems (HTSs) of container terminals. The operational efficiency of an HTS can be increased by the cooperation of B-CAVs. However, it is time-consuming to charge them. Therefore, their battery management becomes a critical issue of a transport schedule. To run container terminals more economically and efficiently, this work proposes an integrated scheduling approach to B-CAVs tasks' dispatch and route planning, where battery management is taken into account. An integer programming model is constructed with the goal of minimizing the total travel distance. Then, a sustainable charging policy is designed to ensure the consistent transport capacity of an HTS. Furthermore, a congestion-free path plan-based improved genetic algorithm is presented to obtain a near-optimal plan for dispatching B-CAVs to perform transporting and charging operations. A series of experiments are carried out to verify the effectiveness and efficiency of our approach.

针对开关电源开关器件频率升高带来的高频变压器原边出现电流尖峰问题,设计了C型、Z型、分段式3 种不同绕法的高频变压器模型.通过推导不同绕法高频变压器分布电容的差异,分析了电流尖峰产生的机理,提出采用分段式绕法能有效减小分布电容的大小,进而减小原边电流尖峰.在实验中通过磁路耦合的方法搭建了高频变压器有限元分析工作电路,在推挽电路模型中具体仿真分析了3 种不同绕法高频变压器对原边电流尖峰的影响.本文实际绕制了3 种不同绕法的高频变压器样机,利用谐振原理测量了分布电容大小,并在开关电源中针对高频变压器的实际工作电路,通过控制变量实际测量了3 种不同绕法的高频变压器原边电流波形.仿真及实验结果均验证了其有效性.

The knowledge reasoning is a core area of artificial intelligence, which aims to investigate how to reason from known（knowledge bases and inference rules） to unknown in order to assist an agent to make rational decisions.Since an environment where an agent lives may be unobservable and uncertain, its knowledge base usually contains both deterministic and uncertain rules, and the reasoning process requires their close collaboration. However, they cannot be represented in a unified way by the reported methods, and their corresponding reasoning processes are often separated from each other. Therefore, an inference method is proposed based on a knowledge Petri net to realize the certainty and uncertainty joint reasoning in a unified architecture. First, a new knowledge Petri net is defined, which can be used to describe not only deterministic rules but also prior probabilities. Second, according to structures of a knowledge Petri net, a probabilistic independent pruning algorithm is given, which can greatly reduce the computational complexity of uncertainty reasoning. Finally, a new inference algorithm is given to realize the joint inference by utilizing a knowledge Petri net and the probabilistic independent pruning algorithm, and the Wumpus world is taken as an example to illustrate and verify the theoretic results.