This paper investigates the distributed adaptive event-triggered least-distance formation control problem for nonlinear multiagent systems (MASs) over switching digraphs via noncooperative game theory. First, distributed event-triggered estimators incorporating a switching-activated communication strategy are proposed to estimate the moving target and all agents’ decisions while reducing inter-agent communication. Based on the designed distributed estimators, a distributed time-varying Nash equilibrium (NE) seeking algorithm is established such that all agents’ decisions asymptotically reach the NE solution. Since high-order derivatives of the proposed distributed estimator states do not exist due to digraphs switching and event-triggering, the backstepping control design cannot be implemented. To overcome this difficulty, three-stage cascade filters are designed to provide sufficiently smooth signals. Then, based on the developed three-stage cascade filters, an adaptive event-triggered least-distance formation controller is proposed by the backstepping control technique. It is proved that the constructed formation control method can ensure that all agents achieve the least-distance formation, i.e., all agents’ outputs asymptotically reach a desired shape while minimizing the overall distance to the moving target. Finally, a simulation example on nonholonomic mobile robots is provided to illustrate the validity of the developed theoretical results.

The recent deployment of Automatic Identification System (AIS) enables real-time monitoring of vessel movements, generating massive volumes of navigational data. To extract meaningful behavioral patterns, trajectory clustering has become a key technique for knowledge discovery and decision-making in maritime scenarios, supporting tasks like route optimization, anomaly detection, and situational awareness. However, existing trajectory representation learning methods in maritime scenarios struggle to jointly capture spatial structural and motion dynamics. The non-uniform sampling and varying trajectory lengths also reduce the efficiency of traditional distance-based similarity calculations. Additionally, clustering methods based on pairwise similarity focus on local relationships and struggle to capture global structural relationships among trajectories. To address the aforementioned challenges, this study introduces a generalizable trajectory clustering framework. First, the raw vessel trajectory data are remapped onto two-dimensional grid to construct multi-channel trajectory images, effectively preserving their intrinsic spatiotemporal features. Second, we develop a feature enhance convolutional autoencoder (FE-CAE) that collaboratively models multiple attention modules to integrate spatial structural information and motion semantics in trajectory images, thereby learning discriminative trajectory representations and transforming trajectory similarity in the feature space, enabling fast, efficient and scalable similarity estimation. Finally, we construct trajectory network based on pairwise similarity, in which trajectories with similar navigation behaviors are tightly connected, and apply community detection to identify distinct navigational behavior patterns, thereby establishing a unified paradigm that bridges representation learning and network modeling. Extensive experiments conducted on large-scale AIS datasets from multiple real-world maritime water areas, and demonstrate that the proposed method outperforms widely adopted methods in both clustering efficiency and robustness. Therefore, underscoring the practical significance and wide applicability of the proposed trajectory clustering framework in advancing intelligent vessel traffic service.

Energy conservation and emission reduction in vessel operations are critical for sustainable shipping. Accurate prediction of vessel fuel consumption (VFC) is pivotal to this goal. To overcome the difficulty of fusing features from high-dimensional, heterogeneous sensor data in hybrid models, we propose a multi-branch learning method for VFC prediction that leverages multi-scale feature fusion. The core of our method is a two-stage attention fusion network (TSAFNet) with relevance-driven feature refinement, enhancing feature abstraction while enabling adaptive cross-branch integration. Experiments on a monthly dataset collected from fishing vessels indicate that TSAFNet outperforms ten baseline models. Even compared with the most competitive baseline, TSAFNet reduces mean absolute error by 42.0 % and root mean squared error by 25.7 %. Ablation studies and cross-vessel evaluations further demonstrate its robustness and generalizability. By enabling accurate VFC prediction, this study supports the optimization of vessel energy efficiency in green shipping, thereby contributing to maritime decarbonization.

This paper studies the data-driven distributed reinforcement learning (RL) optimal cooperative output regulation control problem for T-S fuzzy multi-agent systems (MASs) with unknown system dynamics and under DoS attacks. Since the communication topology of MASs is subject to DoS attacks, a distributed fuzzy resilient observer is developed to estimate the leader’s states. Based on the designed distributed fuzzy resilient observer, a fuzzy optimal control policy is presented by employing zero-sum differential game theory. Since the analytical solution of the optimal control design is reduced to solving the game algebraic Riccati equations (GAREs), a data-driven value iteration (VI) learning algorithm is presented to obtain the approximation solution of GAREs. It is proved that the proposed fuzzy distributed RL optimal control scheme not only achieves cooperative output regulation but also guarantees that regulated output asymptotically converges to zero. Moreover, the developed data-driven VI learning algorithm is proved to converge to the analytical solutions of GAREs and achieves the Nash equilibrium. Finally, we apply the developed fuzzy distributed RL optimal control method to multiple unmanned surface vehicle (USV) systems, the computer simulation results verify the effectiveness of the developed fuzzy distributed optimal control approach.

The evolution of artificial intelligence (AI) has accelerated the development of the maritime Internet of Things (IoT), enabling interconnected maritime ecosystems. Within the maritime IoT, spatio-temporal trajectory data from the automatic identification system (AIS) provide a basis for situational awareness, enabling vessels to perceive navigational risks. However, accurate vessel trajectory prediction is essential for reliable situational awareness. Although deep learning methods achieve stable performance in multi-vessel interaction scenarios, they often neglect semantic information underlying navigational behaviors, limiting generalization in complex environments. Therefore, we propose a social-navigation-scene multi-modal fusion framework (SNS-Aware) for vessel trajectory prediction, comprising four components. The Interaction Encoder captures hierarchical collaborative and conflict-driven interaction patterns. The Behavior Encoder based on temporal convolutional network (TCN) extracts spatio-temporal dynamics, while the Semantic Encoder employs Vision Transformer (ViT) to learn contextualized spatial features from navigation scenes. These multi-modal features are fused in Trajectory Generator, where a conditional variational autoencoder (CVAE) generates diverse realistic trajectories. In addition, binary navigable region masks impose spatial constraints to ensure physically feasible predictions, particularly in narrow waterways. Experimental results on multiple maritime datasets demonstrate that SNS-Aware outperforms baseline methods across various evaluation metrics. These reliable predictions enhance Maritime IoT situational awareness and support intelligent transportation systems.

Advances in maritime instrumentation and measurement (I&M), particularly through the widespread adoption of automatic identification system (AIS), have significantly accelerated the development of intelligent situational awareness systems (ISAS). As a critical component of ISAS, cooperative navigation demands greater accuracy and reliability in vessel trajectory prediction. Nevertheless, challenges arising from complex inter-vessel interactions and implicit intention inference expose limitations in modeling explicit and implicit relationships and ensuring the robustness of trajectory prediction. To address these challenges, we propose a cooperative intention enhance multi-modal graph convolutional network (CIE-MGCN) to learn and predict the future vessel trajectories. The CIE-MGCN is composed of three primary components: Interaction Extractor, Intention Constructor, and Trajectory Generator. In Interaction Extractor, we designed the social-community extractor (SCE) to construct diverse interaction graphs that capture both cooperative and adversarial relationships among vessel trajectories, and the multi-modal transformer (MMT) to fuse explicit interaction features across various modalities. In Intention Constructor, we introduce a conditional variational autoencoder (CVAE)-based approach to infer implicit relationships and capture potential future behavioral variations and multi-modal probability distributions of future trajectories are produced by Trajectory Generator. Extensive experiments on real-world navigation data show that CIE-MGCN outperforms state-of-the-art models in accuracy and robustness, owing to its strong reasoning and learning capabilities. These reliable predictions further support cooperative navigation within ISAS by enhancing coordination and decision-making among multi-vessel.

Intelligent shipping systems advance deep learning applications in ship trajectory prediction, enhancing maritime security risk identification. However, existing models struggle to capture multi-ship interactions in high-density areas due to the significant influence of neighboring vessels. To address this, we propose a trajectory prediction method integrating kullback-leibler divergence attention (KLDA) and a dual-stream parallel architecture. First, a transposition interactive convolutional network (TICNet) employs a dual-layer convolution structure to model dynamic interactions between target and adjacent ships. Second, KLDA mitigates amplitude interference by mapping feature vectors to probability distributions, decoupling similarity computation from input amplitude to suppress dominant local outliers in attention maps. Third, the time-feature dual-stream strategy separately models temporal dependencies via time-embedding sequences and encodes heterogeneous features as tokens using sample transposition, with self-attention explicitly capturing feature correlations. Finally, a cascaded transformer decoder (CTD) iteratively refines outputs through recursive optimization. Experimental results on three real-world scenarios demonstrate average displacement error reductions of 16.75%, 33.48%, and 45.63% compared to the best baseline, validating the method’s effectiveness in complex, high-density navigation environments.

This paper studies the fuzzy cooperative formation control problem of nonlinear multiagent systems (NMASs) subject to communication delays and jointly connected switching networks. Due to time delays in agent communication and network disconnections under the jointly connected condition, some followers fail to receive the leader's matrices and states or receive them with delays. To estimate the leader's matrices and states, we propose novel adaptive distributed observers that first estimate the leader's matrices and then use these estimates to generate an estimate of the leader's states. Subsequently, based on the adaptive distributed observers, a fuzzy cooperative formation controller is formulated by the backstepping control technique and fuzzy logic systems (FLSs). It is proven that the estimation errors of adaptive distributed observers converge to zero exponentially. Moreover, the proposed formation cooperative control method can guarantee that controlled NMAS is stable, and formation errors converge to a small neighbourhood around the origin. Finally, we apply the developed formation cooperative control method to marine surface vehicles (MSVs), the simulation and comparison results verify its effectiveness.

This article proposes the adaptive neural network finite-time inverse optimized formation fault-tolerant control (FTC) strategy for multiple unmanned surface vehicle (multi-USV) systems with intermittent actuator faults. In the process of controller design, the neural networks (NNs) are adopted to approximate unknown functions in multi-USV systems and an auxiliary system is constructed. By integrating the prescribed performance functions and fault-tolerant compensation technology into the backstepping control design, an adaptive NN finite-time inverse optimized formation fault-tolerant controller is designed based on the inverse optimized control theory. It is proved that the designed adaptive NN finite-time inverse optimized formation FTC scheme can realize the formation control objectives in the presence of intermittent actuator faults and minimize the cost function in a finite-time interval. Meanwhile, the formation tracking errors are able to converge within the prescribed performance bounds. The computer simulations verify the effectiveness of developed finite-time inverse optimized formation FTC scheme.

Large Language Models (LLMs), as generative artificial intelligence systems built on the transformer architecture, are widely applied to complex tasks such as language understanding, question answering, mathematical reasoning, and code generation, with their core functionality relying on the attention mechanism. Nevertheless, the conventional attention mechanism is constrained by static, predefined similarity functions, which introduce fixed inductive biases. These biases hinder its adaptability to dynamic or non-stationary environments, leading to suboptimal weight allocation and even attention collapse or vanishing in stable contexts, thereby undermining its capability to model context-dependent semantic relationships. To address these limitations, this paper proposes Q-Attention, a novel value-driven, feedback-oriented framework that formulates attention weights as states and discrete perturbations as actions (i.e., decrease, increase, and remain), enabling reward-driven weight optimization via Q-learning. The method employs task loss as a differentiable reward signal and integrates prioritized experience replay to steer policy updates toward high-impact adjustments. Furthermore, the continual predictive learning module enhances training stability in stochastic environments by reconstructing attention state transitions from historical experiences. Evaluation on benchmark tasks demonstrates that Q-Attention consistently outperforms standard attention mechanisms: it achieves an average accuracy gain of 1.14% on CIFAR-10 and Fashion-MNIST, and on the Traffic and Japanese Vowels datasets, it reduces the mean absolute error by 7.11% while improving accuracy by 2.06%, validating its effectiveness in dynamic attention weight optimization.

In recent years, the rapid development of unmanned surface vessel (USV) navigation technology has driven a surge of interest in path planning algorithms. As a core technique in this field, traditional evolutionary algorithms have been widely applied to solve USV path planning problems under multiple constraints. However, these algorithms commonly encounter limitations such as low search efficiency and slow convergence. Based on the latest advances in path optimization, this paper proposes a novel stochastic schemata exploiter (SSE) algorithm. SSE adopts the framework of genetic algorithms and uses integer encoding to map feasible paths to chromosomes. It breaks through the traditional selection–crossover model of subpopulation generation by extracting common schemata through semi-ordered permutation and combination strategies to guide offspring evolution. Specifically, SSE integrates schema theory into the iterative process, prioritizing the retention of high-fitness individuals and extracting advantageous schemata. A bounded mutation operation is further employed to enhance search capability, enabling both strong global exploration and rapid convergence. Simulation experiments under multiple constraints—including path length, navigation safety, and path smoothness—demonstrate the effectiveness and superiority of the SSE algorithm. Comparative experiments with genetic algorithm (GA), ant colony optimization (ACO), and the Q-learning algorithm show that SSE achieves significantly better overall performance in path planning tasks.

This article investigates the adaptive neural network (NN) cooperative optimal output-feedback control problem for nonlinear multiagent (NMA) systems under switching topology. Since the optimization point of global cost function is unknown, an optimal signal generator and high-order filter are established to estimate optimization point and high-order derivatives of optimal virtual signals. Meanwhile, a NN state observer is designed to estimate unmeasurable states. Based on the NN state observer and high-order filter, an adaptive NN cooperative optimal output-feedback control scheme is proposed by backstepping control design technology. It is shown that the proposed adaptive NN cooperative optimal output-feedback control method ensures that all signals of systems are bounded and the global cost function is minimized. In addition, we apply the proposed cooperative optimal control approach to marine surface vehicle systems (MSVSs)

Path planning is a key problem in autonomous navigation of unmanned surface vehicles (USVs). It is well known that particle swarm optimization (PSO) algorithm is a commonly used algorithm applied to path planning, while this paper proposes a novel path planning algorithm based on the velocity pausing particle swarm optimization (VPPSO) method. To evaluate its performance, we compare the VPPSO algorithm with four algorithms: particle swarm optimization (PSO), sparrow search algorithm (SSA), genetic algorithm (GA), gray wolf optimization (GWO) and differential evolution (DE) algorithm. The experimental results show that VPPSO outperforms the other algorithms in terms of path length, computational efficiency, and obstacle avoidance. Specifically, VPPSO converges faster and generates shorter and smoother paths while reducing computation time. The results suggest that the VPPSO algorithm is a promising approach for solving complex USV path planning problems under various constraints, such as energy consumption, navigation safety, and obstacle avoidance.

In recent years, topic of AI has gained increasing attention, and autonomous ship navigation is at the forefront. Ship trajectory prediction is fundamental to autonomous ship navigation. More efficient ship trajectory prediction has become a key focus in maritime management and navigation technology research. When faced with complex marine environments, the prediction accuracy and generalization ability of these methods are often unsatisfactory. Such models are not only time-consuming and labour-intensive but also struggle to fully capture the nonlinear relationships and spatiotemporal dynamics present in voyage data. This article, based on the aforementioned background, explores the method of using Automatic identification system (AIS) data and sequence-to-sequence (Seq2Seq) models for ship trajectory prediction. Subsequent experimental results indicate that, compared to traditional methods, the trajectory prediction based on Seq2Seq model shows significant improvements across multiple evaluation metrics, particularly in prediction accuracy and the capture of complex navigation behaviors. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

This paper studies the optimal output feedback event-triggered tracking control design problem for Takagi-Sugeno (T-S) fuzzy systems. To reduce the communication resources and controller update times, an event-triggered mechanism is designed via employing the tracking error and triggered control input signal. Based on the presented event-triggered mechanism and optimality theory, an optimal output feedback event-triggered tracking controller is developed. Since the analytical solution of the controller gains is reduced to the Agebraic Riccati Equations (AREs), which is difficult to solve directly, a Q-learning value iteration (VI) algorithm is formulated to obtain its approximation solution. It is proved that the designed optimal output feedback event-triggered tracking controller can ensure the fuzzy system to be stable and the developed Q-learning VI control algorithm is convergent. Finally, we apply the proposed optimal event-triggered output feedback control method to the truck-trailer system, the simulation and comparison results validate the effectiveness of the designed control method and its theory.

In this study, a fuzzy inverse Q-learning optimal control strategy is presented for dynamic positioning of unmanned surface vehicle (USV) systems. Firstly, the controlled USV systems are modeled by Takagi-Sugeno (T-S) fuzzy systems and then based on the controlled USV systems (learner USV systems), T-S fuzzy expert USV systems are constructed. Secondly, since the learner USV only knows the expert USV's optimal control policy and does not know the parameters of expert USV's cost function, an inverse Q-learning algorithm is presented that consists of an internal Q-learning iteration loop and an outer inverse optimal control iteration loop. The internal loop aims to find optimal control policy and the worst-case disturbance input via learner USV system's cost function by employing zero-sum differential game theory. And the outer one is to revise state-penalty weight via observing expert USV's optimal control policy. It is proved that the developed inverse Q-learning algorithm is convergent. Also, the proposed inverse Q-learning optimal control scheme can make the T-S fuzzy learner USV systems asymptotically stable and obtain Nash equilibrium point. Finally, computer simulation results verified the feasibility of the presented fuzzy inverse Q-learning optimal control strategy.