Accurate decoding of motor imagery (MI) EEG signals is critical for brain-computer interface (BCI) applications, yet remains challenging due to the high dimensionality and complex dependencies of amplitude and phase information. We propose a Three-Dimensional Complex Covariance Tensor Network (3D-CCTN) that fuses amplitude and phase into high-dimensional complex covariance features, capturing spatial, spectral, and multivariate characteristics of EEG signals. A fully complex-valued 3D convolutional neural network is then used for robust feature learning and MI classification. Experiments on two public datasets demonstrate that our method outperforms state-of-the-art approaches, achieving at least 2.49% and 1.85% higher mean accuracies. These results highlight the effectiveness of amplitude-phase fusion in the complex domain for MI-based EEG decoding.

Many deadlock control methods rely on reachability graphs of Petri nets (PN), thus suffering from state-space explosion issues. This paper proposes a novel approach to designing liveness-enforcing supervisors for PN by constructing its maximally good step graphs (MGSG), a class of partial order techniques in mitigating the aforementioned issues. Specifically, we first categorize the MGSG markings into allowed and unallowed ones. Then, we define good and risky transitions at allowed markings. Through the execution of risky transitions, the initial marking cannot be reachable from the allowed ones. Next, we design a maximal number of risky transitions (MNRT) problem to compute control places. In MNRT, all allowed markings and the firing of all good transitions are permitted, while risky transitions are forbidden. The objective is to maximize the prevention of risky transitions by using a single control place, which can be achieved by solving an integer linear programming problem. MNRT problems are recursively solved for unforbidden risky transitions until their resulting markings are prohibited. Finally, a controlled PN is generated and has been demonstrated to retain liveness. The experimental results show that our approach effectively reduces the number of control places and mitigates state-space explosion issues over its state-of-the-art peers. Note to Practitioners—Raw materials are handled in manufacturing systems through a series of well-coordinated processes. However, multiple processes competing for the same resources (like machines or robots) may result in an undesirable deadlock situation, where production slows down or entirely halts. A liveness-enforcing supervisor is designed to counter such a situation. As a mathematical tool, PN can be applied to model manufacturing systems. The supervisor design involves adding control places and directed arcs into PN to ensure its liveness, which implies that the systems can execute their tasks and never enter into deadlocks. In this work, we develop a deadlock control approach, which can generate a live and controlled PN without exploring a complete state space of PN. Experimental results show the effectiveness of our approach in reducing the number of control places and its practicability applied to large-scale systems, thus surpassing state-of-the-art methods.

The automatic detection of defects in industrial photovoltaic film is crucial for ensuring the reliability of photovoltaic modules. Key challenges include limited defect samples, interclass feature similarities, and interference from complex backgrounds. Existing deep learning-based methods require large-scale datasets and focus solely on visual data, which limits their effectiveness in few-shot defect detection (FSDD). To address these challenges, we propose Contextual Ensemble Language-Image multimodal Network (CELIN), which enhances FSDD in photovoltaic films by incorporating textual information through prompt tuning. Unlike traditional language-image models that rely on single fixed text prompts, CELIN employs a position-aware context ensemble strategy to integrate position-specific prompt vectors, enabling the model to capture global contextual information and reduce background interference. In addition, a cross class mask method is introduced to differentiate between similar defect categories by blocking interclass interactions during attention computation, thereby minimizing misclassification. Extensive experiments on our own few-shot photovoltaic film defect dataset and various public benchmarks demonstrates that CELIN significantly outperforms existing methods.

Heterogeneous computing systems are extensively utilized to execute a wide range of time-critical services, which encompass numerous interdependent tasks organized in the form of workflows. In practice, the dynamic arrival of workflows often interleaves with their execution, leading to resource contention among multiple workflows and potentially causing QoS (Quality of Service) degradation. However, compared to the extensive research on single workflow scheduling, interleaved workflow scheduling has received relatively less attention. Moreover, the challenge of effectively scheduling limited computing resources to promptly complete consecutively arriving workflows remains underexplored, despite its practical importance. To fill this gap, this work proposes a method called Urgency-based List Scheduling (ULS) for dynamically scheduling deadline-constrained interleaved workflows. In ULS, a novel task property called urgency is introduced to prioritize tasks from multiple workflows by capturing real-time execution information, and each newly arrived workflow is scheduled with the outstanding tasks of prior workflows based on a list-based strategy to make more informed decisions. Extensive evaluation experiments are performed and the findings illustrate that ULS can achieve a reduction of at least 68% in deadline miss rates and 77% in overall tardiness compared to existing methods.

Multirobot patrolling systems with various sensing and communications devices are deployed to guarantee maritime safety. Patrolling path planning for multiple robots can be modeled as a multiobjective optimization problem. The positions of patrolling nodes impact the length of patrolling paths and execution efficiency of robots. To compute them, a huge solution space is encountered. Besides, multiple patrolling nodes on the same line lead to the same patrolling scheme. Thus, how to promote solution (population) diversity becomes a new challenge. To tackle it, this work proposes a learning-inspired immune algorithm. It uses the historical information in the previous generations during iterations to realize a learning process. Unlike saving all the individuals themselves and training a model for them, the useful historical information is extracted by using upper confidence bound-based and actor–critic-inspired methods. Both time consumption and storage space can be dramatically saved. The experimental results indicate that the proposed algorithm can generate multiple patrolling schemes for the decision makers and outperforms the state-of-the-art.

This paper focuses on designing event feedback supervisors to enforce control specifications on Petri nets with uncontrollable and unobservable transitions. For each observation, the supervisor is able to select some controllable transitions to disable such that the system never reaches illegal markings. Two different methods are given to design such a supervisor. The first method computes the control policy by solving some integer linear programming problems, while the second one designs supervisors by taking advantage of the structural properties of a class of Petri nets. The computational efficiencies of these two methods increase successively at the expense of their application scopes. Two examples are given to illustrate the proposed methods, respectively. Note to Practitioners—The motivation of this paper consists in ensuring the behavior of a manufacturing system within a given legal behavior. The typical task for a designer is to design a supervisor to restrict that the system never reaches a forbidden state under limited control and observation ability. To this end, this paper proposes two different methods to design such a supervisor. The first one needs to solve integer linear programming problems, while the second one is based on the structural analysis of a special class of systems. It should be noted that although the application scope of the first method is wider, the second method has higher computational efficiency. Therefore, the suitable method can be chosen in accordance with the specific application scenario, which is significant and useful to manufacturing engineers.

Liveness is among the most significant properties when Petri net (PN) models of automated systems are analyzed, which ensures systems’ deadlock-freeness. Traditionally, the liveness analysis methods based on reachability graphs (RGs) of PNs often suffer from state-space explosion problems. In this article, we propose a novel liveness-analysis method for PN based on maximally good-step graphs (MGs), namely, the reduced form of RGs, which can effectively alleviate such problems in liveness analysis. First, we introduce the concept of sound steps and establish an algorithm for assessing the soundness of an enabled step at the current marking from a practice point of view. Second, we propose a definition of maximal sound steps and construct an algorithm for calculating a maximal-sound-step set at each marking whose computational complexity grows polynomial with the number of places and transitions. Then, we introduce a definition for good steps and an algorithm for generating maximally good step graphs of PN; and discuss its computational complexity with respect to the net size and initial marking. Next, we for the first time answer how to evaluate the liveness of PN by using MGs. Experiments in diverse large-scale automated manufacturing systems demonstrate that the proposed method significantly reduces state space and time consumption in the liveness analysis of network systems.

This work addresses multiobjective dynamic surgery scheduling problems with considering uncertain setup time and processing time. When dealing with them, researchers have to consider rescheduling due to the arrivals of urgent patients. The goals are to minimize the fuzzy total medical cost, fuzzy maximum completion time, and maximize average patient satisfaction. First, we develop a mathematical model for describing the addressed problems. The uncertain time is expressed by triangular fuzzy numbers. Then, four meta-heuristics are improved, and eight variants are developed, including artificial bee colony, genetic algorithm, teaching-learning-base optimization, and imperialist competitive algorithm. For improving initial solutions’ quality, two initialization strategies are developed. Six local search strategies are proposed for fine exploitation and a$Q$-learning algorithm is used to choose the suitable strategies among them in the iterative process of the meta-heuristics. The states and actions of$Q$-learning are defined according to the characteristic of the addressed problems. Finally, the proposed algorithms are tested for 57 instances with different scales. The analysis and discussions verify that the improved artificial bee colony with$Q$-learning is the most competitive one for scheduling the dynamic surgery problems among all compared algorithms.

The$\alpha $-separator problem ($\alpha $-SP) consists of finding the minimum set of vertices whose removal separates the network into multiple different connected components with fewer than a limited number of vertices in each component, which belongs to the family of critical node detection problems. The$\alpha $-SP problem is an important NP-hard problem with various real-world applications. In this paper, we propose a frequent itemset-driven search (FIS) algorithm to solve$\alpha $-SP, which integrates the concept of frequent itemset into the well-known memetic search framework. Starting from a high-quality population built by population construction and population repair, FIS then iteratively employs a frequent itemset recombination operator (to generate promising offspring solution), a tabu-based simulated annealing (to find local optima), a population repair procedure, and a population management strategy (to guarantee healthy/diverse population). Extensive evaluations on 50 benchmark instances show that FIS significantly outperforms the state-of-the-art algorithms. In particular, it discovers 29 new upper bounds and matches 18 previous best-known bounds. Finally, we experimentally analyze the importance of each key algorithmic component, and perform a case study on an air transportation network for understanding its network structure and identifying its influential airports.

Resource allocation systems (RASs) exist in various fields of modern society. The deadlock control problem is a crucial issue in control theory of RAS. This work is concentrated on a special class of shared resource and process-oriented Petri nets whose initial marking can have only a token in every resource place. Using mixed-integer programming (MIP) and iterative siphon control, we present a two-stage deadlock prevention policy. In particular, a modified MIP technique is developed for the first stage to compute a specific type of emptiable siphons and a siphon control method introducing monitors with related arcs whose weights all equal to one is established in the second stage. This policy leads to a maximally permissive liveness-enforcing supervisor and such an obtained controlled net is ordinary. Moreover, it avoids the exhaustive enumeration of siphons and the reachability analysis. Examples are provided to explain the policy.

In cyber–physical systems (CPSs), it is of great importance to handle network attack issues. In this article, we consider the supervisory control layer of CPSs, focusing on closed-loop control systems vulnerable to sensor-reading modification attacks (SM-attacks), which may disguise the occurrence of an event as a different event by modifying appropriately sensor readings in sensor communication channels. In particular, we consider the plant modeled as a bounded Petri net and the control specification consisting in liveness enforcing. Based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a so-called basic supervisor, a method that synthesizes a liveness-enforcing supervisor tolerant to an SM-attack is proposed.

This work focuses on a class of Petri nets (PNs) called Weighted Systems of Simple Sequential Processes with Resources (WS3PR). We study how to enforce liveness to WS3PR by appropriately allocating resources. A sufficient condition that guarantees liveness of a net system in this class is first derived. Then, based on such a condition, we propose an algorithm that computes an initial marking of resource places that guarantees the liveness of a WS3PR system where the initial marking of the idle places is given. Note that, we do not guarantee that the resulting solution is optimal, in the sense that a smaller initial marking of resource places that still leads to liveness could exist. However, several numerical examples show that the solution resulting from the proposed approach is optimal.

The main contribution of this correspondence paper consists in a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. In more detail, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to compute an approximation of the admissible marking set in terms of a disjunction of transformed linear constraints. The optimality of the solution is guaranteed provided that certain conditions are satisfied during the intermediate steps of the iterative approach. In all the other cases, the set of markings described by the transformed constraints could be surely contained in the admissible marking set.

The efficient siphon computation is the key to the development of siphon-based deadlock control strategies with good performance. This work studies the computation of minimal siphons in a class of Petri nets called S4PR. Firstly, we propose a function with polynomial complexity to determine whether a resource subset can generate a minimal siphon. Next, using the technique of problem partitioning, a new approach is developed to compute all minimal siphons in S4PR. Finally, an example is given to illustrate the proposed approach.

Deadlock prevention policies for flexible manufacturing systems (FMS) usually suffer from redundant monitors since some monitors may be added to the siphons that are originally controlled. To eliminate these redundant monitors, the controllability condition of siphons is studied in this work. For a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR), new concepts of simple and complex strict minimal siphons (SMS) are introduced. More importantly, a necessary and sufficient condition of controllability of complex SMS is proposed for the first time. Based on this condition, an algorithm is given to control all SMS via M-controlling part of them and a structurally simple optimal liveness-enforcing supervisor can thus be synthesized for some classes of S3PR. Two examples are provided to illustrate the application of the proposed algorithm and show its superiority to prior work.

Reachability is an important dynamic property of Petri nets. Its determination given an unbounded net and initial marking has remained an open problem since 1960s. Due to its extreme difficulty, a great deal of research has been focused on some subclasses of unbounded nets. For arbitrary ones, this work intends to propose a new reachability tree (NRT), which consists of only but all reachable markings from its initial marking. Furthermore, an NRT-based method to decide deadlocks of unbounded nets is presented. An example is provided to show the new results.

Deadlocks are a rather undesirable phenomenon in flexible manufacturing systems (FMSs). This work, by adding monitors, develops a deadlock prevention policy for FMSs that can be modeled by a class of Petri nets called α-S3PR with i-resources. First, an algorithm is presented to reduce an S3PR via a i-resource. Based on the algorithm, i-resources in α-S3PRs are classified into two types: 1) A-ξ-resources and 2) B-ξ-resources. Next, for an α-S3PR with only B-ξ-resources, it is proved that a maximally permissive liveness-enforcing supervisor can be designed by controlling all emptied strict minimal siphons. For an α-S3PR containing A-ξ-resources, a liveness-enforcing supervisor can be designed by iteratively reducing the net via A-ξ-resources and adding the corresponding monitors. Finally, a deadlock prevention algorithm for α-S3PRs is presented. Two FMS examples are used to illustrate its application. Its comparison results with other state-of-the-art deadlock prevention policies validate its overall advantages in terms of computational complexity, structural complexity, and behavior permissiveness.

Deadlock detection for concurrent systems via static analysis is in general difficult because of state-space explosion; indeed it is PSPACE compete. This paper presents a new method to detect the deadlocks. A concurrent system consisting of several processes that communicate using a resource sharing mechanism is represented by a set of ordinary differential equations of a restricted type. The equations describe the system state changes, and their solutions, also called state measures, indicate the extent to which the state can be reached in execution. Based on the solutions, the resource deadlock can be detected. By taking into account the computation errors of numerical solution for the differential equations, the detection can be performed via a MATLAB solver, as shown in the experiments. The complexity of the proposed method is polynomial.

In this article, an algorithm is proposed to design liveness-enforcing supervisors for systems of simple sequential processes with resources (S 3 PR) based on complementary places. Firstly, a mixed integer programming (MIP) based deadlock detection method is used to find unmarked strict minimal siphons from an infinite-capacity net. Next, the finite-capacity net, in which liveness can be enforced, is obtained by adding capacity function to the infinite-capacity net. Finally, complementary-place transformation is used to transform the finite-capacity net into an infinite-capacity net. This article focuses on adding a complementary place to each operation place that is related to unmarked siphons, deals with the deadlock problem from a new view point, and hence advances the deadlock control theory. Compared with the existing methods, the new policy is easier to implement for real industrial systems. More importantly, design of a complementary-place supervisor is very easy. Finally, in some cases, the new policy can obtain a structurally simpler supervisor with more permissive behavior than the existing methods do. A flexible manufacturing systems (FMS) example is used to compare the proposed policy with some other methods.

For a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict-free nets, this paper proposes an algorithm to transform a given generalized mutual exclusion constraint (GMEC) into an optimal admissible one. Based on the proposed constraint transformation, a method is given to synthesize an optimal monitor-based supervisors. The proposed method utilizes an optimal monitor-based supervisor to enforce a GMEC containing infinite elements, which has not been seen in any prior research. Moreover, it has higher computational efficiency at the expense of application scope than some existing methods. An example is used to illustrate the application of the proposed method.

This paper proposes a new modified reachability tree (NMRT) approach for a class of unbounded generalized Petri nets called ω-independent nets. The NMRT of an ω-independent net consists of all and only reachable markings from its initial marking. Moreover, the applications of the NMRT to deadlock analysis for ω-independent nets are developed. The proposed method has a larger application scope than all the existing methods. Several examples are provided to show its superiority over them.

Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S3PR. When they are applied to some classes of S3PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.

Strict minimal siphons (SMS) play an important role in the development of deadlock control policies for flexible manufacturing systems (FMS). For a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR), the resource circuit-based method is an effective way to compute SMS. In this paper, a more effective one to compute SMS is proposed. First, the concepts of loop resource subsets and their characteristic resource subnets are proposed. Next, sufficient and necessary conditions for loop resource subsets to generate SMS are established. Finally, an algorithm is given to find all the SMS based on loop resource subsets. Since the number of loop resource subsets is much less than that of resource circuits and their combinations, the computational efficiency of the SMS enumeration task is significantly improved by the proposed method. An FMS example is used to illustrate the application of the proposed method, and computational time comparisons are provided on several S3PRs to show its superior efficiency.

For a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict free (FSBCF) nets, this work studies their structure and properties and proposes an algorithm to transform a given generalized mutual exclusion constraint (GMEC) into an optimal admissible one. Compared with the path-based constraint transformation approaches, the proposed method has much higher computational efficiency. An example is used to illustrate the application of the proposed method.

The mixed integer programming (MIP)-based deadlock detection method plays an important role in the development of deadlock prevention policies for flexible manufacturing systems (FMS). In this paper, an optimal deadlock prevention policy is proposed for a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR) without any ξ-resource. A ξ-resource is a one-unit resource place shared by two or more minimal siphons that do not mutually contain each other. Compared with the MIP-based deadlock prevention policies that suffer from the problem of limited behavior permissiveness and high structural complexity, the proposed one can obtain an optimal liveness-enforcing supervisor with lower structural complexity. An FMS example is used to illustrate the application of the proposed deadlock prevention policy.

A siphon-based algorithm for deadlock prevention of Petri nets called Algorithm H2 is proposed in the above paper. However, the illustrative examples for Algorithm H2 are incorrect because of the redundant weighted control (WC) places which control some marked siphons. This correspondence modifies the illustrative examples by removing the redundant control places and getting a maximally permissive control for the original net. As no WC place is presented in the modified examples, the examples cannot well illustrate Algorithm H2.