In this article, the distributed surrounding control problem is addressed for the linear multi-agent systems, in which a hierarchical strategy framework is constructed consisting of optimal target assignment and game-driven surrounding control. Aiming at fulfilling the multiple targets surrounding task with high efficiency and balanced mission load, an optimal target assignment mechanism is developed with the assistance of the cross entropy method (CEM) and twin delayed deep deterministic policy gradient algorithm (TD3), where an evaluation function related to the arrival time from each agent to capture the target is proposed. Considering the high degree of autonomy of the targets, a surrounding control protocol driven by the dynamic graph game is proposed afterward. To find the equilibrium solution of the pursuit-escape game, the coupled Hamilton–Jacobi–Bellman (HJB) equation is solved by a delicately designed model based value iteration algorithm, whose stability is demonstrated by the rigorous theoretical analysis. Finally, we undertake numerical experiments to ascertain the efficacy of the introduced game-driven surrounding control strategy.

Effective policy optimization in multiagent reinforcement learning (MARL) necessitates extensive exploration of high-dimensional state-action spaces. However, such exploration may not only trigger unsafe states but also compromise system stability, posing significant challenges for deployment in safety-critical systems. To address this challenge, this article proposes a safety-stability layer that integrates robust control barrier functions (RCBFs) and input-to-state stable control Lyapunov functions (ISS-CLFs) for multiagent systems operating in unknown environments with uncertain dynamics. Furthermore, by integrating safety-stability constraints with a MARL framework, during the training phase, we exclusively focus on goal-reaching objectives to expand the policy network's exploration space, while in the deployment phase, policy outputs are filtered through a real-time safety-stability layer. In addition, an event-triggered mechanism for action compensation calculation is designed based on safety condition assessments to conserve computational resources. Finally, the effectiveness of the proposed method is validated through simulation experiments in dynamic multiunicycle environments. The results demonstrate that our approach not only ensures strict adherence to safety constraints but also significantly enhances the task execution efficiency of multiagent systems.

In this article, we investigate the adaptive safety-constrained control problem for quadrotor unmanned aerial vehicle (QUAV) clusters in dense forest environments to achieve adaptive navigation and obstacle avoidance. Compared to traditional methods, obstacle avoidance constraints are introduced for the first time, and the limitations of fixed formations and the need for prior data are eliminated. First, a cluster constraint mechanism is developed to constrain the distance between QUAVs within the cluster and the distance between the QUAV and the desired trajectory. Then, considering the lack of targeted obstacle avoidance constraint mechanisms in previous methods and the extensive prior data required by learning-based approaches, an obstacle constraint model is established to ensure that the QUAV maintains a safe distance from obstacles to avoid collisions. Finally, an adaptive safety control strategy for QUAV clusters is proposed by combining constraint conditions and stability criteria. Under the proposed control strategy, the QUAV clusters can achieve stable, safe, and efficient navigation and obstacle avoidance, and all constraints will always be satisfied. Furthermore, a numerical simulation experiment on a QUAV cluster navigation demonstrates the effectiveness and flexibility of this strategy.

This article presents a bearing-based formation control method for autonomous aerial vehicle (AAV) swarms, allowing users to specify both convergence time and precision in advance. Unlike traditional distance-based methods, which rely on intricate distance measurements, our approach simplifies constraints using bearing information, reducing hardware and sensing requirements. It also eliminates the need to update control commands for each AAV, as formation reconfiguration can be achieved solely by adjusting the motion trajectory of formation leaders. Moreover, the strategy demonstrates enhanced robustness in addressing real-world input constraints. A continuous hyperbolic tangent saturation function and an input saturation compensation system are incorporated, ensuring system convergence and precision while addressing singularity issues. In addition, unlike conventional bearing-based strategies focusing primarily on convergence time, the proposed algorithm enables preset control over both convergence time and precision. Finally, the effectiveness of the proposed approach is validated through several illustrative examples, including a 6-degree-of-freedom (6DoF) quadrotor AAV swarm, highlighting its practical applicability and performance.

This article presents a prescribed performance scaling framework for uncertain nonlinear multiagent systems with unmeasurable states, addressing the secure formation fault-tolerant control problem considering collision avoidance and connectivity maintenance. A novel fuzzy preset-time observer is proposed, which achieves the earliest preset-time convergence of observation errors with the aid of a scalar function while it solves the problem of state unmeasurability and unknown nonlinear dynamics. A finite-time prescribed performance function based on norm inequality scaling is introduced to transform and constrain the graph theory-based formation errors into collision avoidance and connectivity maintenance guaranteed indicators and observation-based sliding-mode variables. Then, an adaptive estimation technique is employed to estimate the fault parameters to achieve fault-tolerant control. Finally, a series of simulation experiments are conducted to certify the feasibility and superiority of the proposed control scheme.

This study focuses on achieving hierarchical optimal synchronization in a fractional-order nonlinear multi-agent system (FONMAS) composed of a single leader and multiple followers, analyzed within the framework of Stackelberg–Nash game theory. The leader makes decisions by anticipating the optimal responses of all followers, whereas each follower concurrently reacts optimally to the leader's strategy by engaging in a Nash game. To obtain the optimal control policy of the FONMAS, a regularized fuzzy reinforcement learning approach is proposed. First, a fractional-order (FO) Hamilton–Jacobi–Bellman (HJB) equation in coupled form is formulated, which serves as the basis for deriving the optimal control policies of both the leader and the followers. It is further proven that these strategies constitute a Stackelberg–Nash equilibrium (SNE). Next, due to the asymmetry among agents, solving the FO coupled HJB equations becomes challenging. To address this, a hierarchical learning framework grounded in FO value iteration is proposed, which depends solely on partial knowledge of the system dynamics. We demonstrate that, given mild coupling assumptions, this method converges asymptotically to equilibrium policies. Furthermore, a regularized actor–critic (A-C) framework with fuzzy logic is employed to estimate the cost function and optimal control policy, and the FO weight update rules are developed by formulating a Lyapunov function for the optimal fuzzy weight deviation, ensuring convergence to optimal weight values. Ultimately, both theoretical analysis and simulation results support the efficiency of the proposed method.

This article investigates for the first time the predefined-time relative position tracking and attitude synchronization control problem with asymptotic tracking errors for spacecraft. Compared to previous studies, this article considers convergence speed and control accuracy simultaneously, ensuring the predefined-time stability and asymptotic convergence of the spacecraft relative tracking errors. The fuzzy logic systems are introduced to estimate the unknown nonlinear terms in the relative dynamic model. By combining the adaptive backstepping control method and the command filter technique, a relative position tracking and attitude synchronization control method is proposed. The improved filter compensation signals are designed to eliminate the impact of filtering errors on the control performance. With the proposed control method, the closed-loop spacecraft position and attitude control system can achieve predefined-time stability, and the spacecraft relative tracking errors can reach zero as time approaches infinity. Finally, simulation results are provided, fully demonstrating the effectiveness of the proposed method.

This article presents an optimal evolution strategy for continuous strategy games on complex networks via reinforcement learning (RL). In the past, evolutionary game theory usually assumed that agents use the same selection intensity when interacting, ignoring the differences in their learning abilities and learning willingness. Individuals are reluctant to change their strategies too much. Therefore, we design an adaptive strategy updating framework with various selection intensities for continuous strategy games on complex networks based on imitation dynamics, allowing agents to achieve the optimal state and a higher cooperation level with the minimal strategy changes. The optimal updating strategy is acquired using a coupled Hamilton-Jacobi-Bellman (HJB) equation by minimizing the performance function. This function aims to maximize individual payoffs while minimizing strategy changes. Furthermore, a value iteration (VI) RL algorithm is proposed to approximate the HJB solutions and learn the optimal strategy updating rules. The RL algorithm employs actor and critic neural networks to approximate strategy changes and performance functions, along with the gradient descent weight update approach. Meanwhile, the stability and convergence of the proposed methods have been proved by the designed Lyapunov function. Simulations validate the convergence and effectiveness of the proposed methods in different games and complex networks.

In this study, we employed the batch gradient method to investigate the monotonicity and convergence of the Elman neural network (ENN) based on the entropy error function (EEF) and regularization methods. This enhances network stability and sparsity while also boosting its ability to generalize. Traditional mean square error (mse) functions in complex networks often result in slower convergence during training, prone-to-local minima, and even incorrect saturation issues. To address this drawback, we propose a novel EEF for training ENN, effectively avoiding the problem of learning speed degradation. Furthermore, by leveraging smoothing group $L_{1/2}$ regularization $(\text {SGL}_{1/2})$ methods in studying ENN based on EEF, we effectively overcome the drawbacks of traditional group $L_{1/2}$ regularization $(\text {GL}_{1/2})$ leading to error function oscillations. In addition, we optimize the network architecture effectively in two key ways: reducing redundant nodes to near 0 and driving redundant weights toward 0 for remaining nodes, further boosting network sparsity. This article rigorously proves the monotonicity of the error function, alongside presenting strong and weak convergence outcomes for the novel method. The effectiveness and correctness of our approach are clearly illustrated through experimental results. The simulation results align with the theoretical findings.

To address the challenges posed by flight envelope limitation, external disturbances, model uncertainties and actuator failures in quadrotor unmanned aerial vehicles (UAVs), we propose an adaptive neural attitude control method that incorporates a Nussbaum function and nonlinear disturbance observer (NDO). By designing the Nussbaum function, we effectively address potential actuator failures while leveraging the NDO enables us to employ feedforward compensation strategy to mitigate perturbation effects. To handle the flight envelope limitation and model uncertainties, we introduce a nonlinear state-dependent function (NSDF) and neural networks (NNs), respectively. The NSDF is utilized to directly constrain the attitude, while the NNs are constructed to estimate the unknown components. Simulation results demonstrate that this approach successfully addresses the flight envelope limitation and maintains robust tracking performance even in the presence of external disturbances, model uncertainties and actuator failures in the controlled system.

This article considers Nash equilibrium (NE) seeking of networked mean field games (NMFGs) with event-triggered strategies in a fully distributed manner. To simplify the formulation of distributed online decision-making problems over a network, we introduce the NMFG over a spatiotemporal domain for large-scale equilibrium computation. By merging ideas from estimation theory and consensus theory, three parallel auxiliary variables are designed to dynamically estimate the aggregative behavior of the collection, called the mean field term. The leaderless consensus of players’ estimates and the optimization of local objective function need to be achieved simultaneously. In addition, the dynamic event-triggered mechanism and adaptive learning gain are introduced, which provide a natural and scalable framework for distributed communication and computation in large-scale complex networks. We further prove that convergence to NE can be guaranteed using the designed strategies. Finally, a numerical experiment is provided to validate the proposed algorithm.

This article addresses the nonsingular practical fixed-time adaptive fuzzy control problem of nonstrict-feedback multiagent systems (MASs) with actuator faults. By utilizing fuzzy-logic systems (FLSs), the identification of unknown nonlinearities in MASs is achieved while avoiding the algebraic loop problem. The singularities in fixed-time control are prevented by incorporating an adding power integration technique into the control scheme. Furthermore, we design an adaptive update law to mitigate the effects of unknown actuator faults and external disturbances. An adaptive fuzzy practical fixed-time MASs consistency control algorithm is proposed by combining these techniques with backstepping control. Based on stability analysis, the designed control scheme ensures that all MAS signals remain bounded within a fixed time and that the convergence time to achieve consistency does not depend on the initial states of the MASs. Finally, the validity of the proposed nonsingular practical fixed-time consensus control scheme is verified through simulation examples.

This article explores the tracking issue for dc-dc buck power converter with stochastic disturbance, specifically focusing on how output voltage tracks to a desired voltage in a finite-time when the load changes. Meanwhile, considering unmodeled dynamics and nonaffine inputs, we propose an innovative finite-time fuzzy prescribed performance switching tracking algorithm to achieve tracking goal. For realizing the requirements of performance, the algorithm converts the tracking error to a new state by means of a coordinate transformation via the tangent function. In addition, the universal approximation capacity of the fuzzy-logic system is utilized to estimate the unknown nonlinear term effectively. On this basis, the designed adaptive dynamic event-triggered controller can not only ensure that all the signals for the closed-loop system remain bounded in probability but also guarantee that the tracking error will converge to a predetermined small neighborhood. Meanwhile, different piecewise functions are added into the controller to characterize prescribed performance and avoid singularity problems, respectively. Finally, the effectiveness of the tracking control algorithm is fully demonstrated by the simulations of the dc-dc buck power converter.

Recently, deep unfolding methods have achieved remarkable success in the realm of Snapshot Compressive Imaging (SCI) reconstruction. However, the existing methods all follow the iterative framework of a single image prior, which limits the efficiency of the unfolding methods and makes it a problem to use other priors simply and effectively. To break out of the box, we derive an effective Dual Prior Unfolding (DPU), which achieves the joint utilization of multiple deep priors and greatly improves iteration efficiency. Our unfolding method is implemented through two parts, i.e., Dual Prior Framework (DPF) and Focused Attention (FA). In brief, in addition to the normal image prior, DPF introduces a residual into the iteration formula and constructs a degraded prior for the residual by considering various degradations to establish the unfolding framework. To improve the effectiveness of the image prior based on self-attention, FA adopts a novel mechanism inspired by PCA denoising to scale and filter attention, which lets the attention focus more on effective features with little computation cost. Besides, an asymmetric backbone is proposed to further improve the efficiency of hierarchical self-attention. Remarkably, our 5-stage DPU achieves state-of-the-art (SOTA) performance with the least FLOPs and parameters compared to previous methods, while our 9-stage DPU significantly outperforms other unfolding methods with less computational requirement. https: / /gi thub. com/ZhangJC-2k/DPU

How to effectively utilize the spectral and spatial char-acteristics of Hyperspectral Image (HSI) is always a key problem in spectral snapshot reconstruction. Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multi-head division and propose a novel Spectral-Spatial Recti-fication (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral in-formation and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR

The rapid growth of electric vehicles (EVs) has led to significant challenges in providing efficient and sustainable charging solutions. This paper addresses the battery swapping station (BSS) recommendation problem by proposing a novel conflict-free genetic algorithm (CFGA) integrated with a Nash equilibrium seeking (NES) approach to identify optimal Nash equilibrium (ONE) solutions to such a non-cooperative optimization problem. The CFGA employs specialized crossover and mutation operators to generate offspring that satisfy the constraints of the problem, ensuring that each EV decides a unique battery swap strategy without conflict. Firstly, an order crossover operator is proposed to preserve the order of genes in the chromosomes. Secondly, a replacement and exchange mutation operator is proposed to enhance mutation diversity. The resulting optimal solution is then used as the initial strategy for the NES, which iteratively converges to the ONE. The proposed CFGA with NES algorithm is evaluated under both small-scale and large-scale cases, demonstrating its effectiveness in achieving a balance between costs for EVs and utilization for BSSs. The study's findings have practical implications for the smart grid and EV integration, offering a robust method for optimizing EV infrastructure and operations.

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It$\hat {\rm \textbf {o}}$differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method.Note to Practitioners—In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

This article presents a framework for exploring optimal evolutionary strategies in continuous-action social dilemma games with a hierarchical structure comprising a leader and multifollowers. Previous studies in game theory have frequently overlooked the hierarchical structure among individuals, assuming that decisions are made simultaneously. Here, we propose a hierarchical structure for continuous action games that involves a leader and followers to enhance cooperation. The optimal evolutionary strategy for the leader is to guide the followers’ actions to maximize overall benefits by exerting minimal control, while the followers aim to maximize their payoff by making minimal changes to their strategies. We establish the coupled Hamilton–Jacobi–Bellman (HJB) equations to find the optimal evolutionary strategy. To address the complexity of asymmetric roles arising from the leader-follower structure, we introduce an integral reinforcement learning (RL) algorithm known as two-level heuristic dynamic programming (HDP)-based value iteration (VI). The implementation of the algorithm utilizes neural networks (NNs) to approximate the value functions. Moreover, the convergence of the proposed algorithm is demonstrated. Additionally, three social dilemma models are presented to validate the efficacy of the proposed algorithm.

In this article, we propose a convergence analysis method for evolution dynamics in information loss networks, which overcomes the analytical difficulties caused by complex network relationships. Evolutionary game theory is a widely-used tool for analyzing player behavior in networks, where players typically adopt binary strategies, either cooperation or defection. However, player behavior in real-world scenarios is often multidimensional and complex, and thus a dynamic model of continuous action iterated dilemma (CAID) with continuous strategy is proposed to enrich the strategies of players, allowing them to choose intermediate states between cooperation and defection, providing a more accurate representation of the evolution of cooperation than traditional dynamic models. Meanwhile, the convergence of traditional models is often analyzed using Jacobian matrices, which requires a significant amount of derivation related to the complex network structure, leading to inefficiencies. As such, a new convergence analysis method based on the Lyapunov function has been designed to circumvent these complex calculations. Additionally, as there is often noise present during the transfer of information between players, we further analyze the convergence of dynamic models in information loss networks using the Lyapunov function. Two examples based on the prisoner’s dilemma and snowdrift dilemma on networks are proposed to show the effectiveness of the designed convergence analysis.

This article proposes a teacher-guided peer learning approach that employs a continuous action iterated dilemma (CAID) model based on an incremental network. Traditional peer learning approaches often assume static communication relationships between students, which is not consistent with actual society, and this affects the effectiveness of peer learning. Additionally, every student is a highly unique individual, and using a single mathematical model to mimic their behavior would result in research findings with limited applicability. Therefore, this article presents several innovations. First, we propose an incremental network generation algorithm that generates an effective communication network to improve classroom efficiency by enhancing the convergence of information between classmates. Second, considering the multiple unknown nonlinear environmental impacts, we design a student dynamic model based on CAID with multiple layers of nonlinearity to fit the different environmental impacts that different students receive. Finally, based on the incremental network and student dynamic model, we design the Lyapunov function to prove the convergence of the proposed model. This mathematical proof ensures that the proposed model is stable and unaffected by parameters, making it more applicable.

In this article, an expert system-based multiagent deep deterministic policy gradient (ESB-MADDPG) is proposed to realize the decision making for swarm robots. Multiagent deep deterministic policy gradient (MADDPG) is a multiagent reinforcement learning algorithm proposed to utilize a centralized critic within the actor-critic learning framework, which can reduce policy gradient variance. However, it is difficult to apply traditional MADDPG to swarm robots directly as it is time consuming during the path planning, rendering it necessary to propose a faster method to gather the trajectories. Besides, the trajectories obtained by the MADDPG are continuous by straight lines, which is not smooth and will be difficult for the swarm robots to track. This article aims to solve these problems by closing the above gaps. First, the ESB-MADDPG method is proposed to improve the training speed. The smooth processing of the trajectory is designed in the ESB-MADDPG. Furthermore, the expert system also provides us with many trained offline trajectories, which avoid the retraining each time we use the swarm robots. Considering the gathered trajectories, the model predictive control (MPC) algorithm is introduced to realize the optimal tracking of the offline trajectories. Simulation results show that combining ESB-MADDPG and MPC can realize swarm robot decision making efficiently.

A safe time-varying formation (TVF) control framework is proposed in this article for heterogeneous multiagent systems under the constraints of denial of service (DoS) attacks, noncooperative dynamic obstacles, and input saturation. The framework integrates both the cyber-layer and physical-layer components to address the challenges posed by these adverse conditions. In the cyber-layer, a distributed resilient observer is provided based on a control Lyapunov function (CLF)-quadratic program (QP). This observer estimates a reference exosystem, effectively decoupling heterogeneous dynamics from unsafe networks and optimizing the system resilience against DoS attacks. At the physical-layer, for the first time, a collision-free TVF controller is presented based on the CLF-exponential control barrier function-QP. The controller guarantees high-order heterogeneous agents' operation safety under noncooperative obstacles and input saturation. The effectiveness and advantages of the proposed algorithms are verified through the comparative simulations and experiments conducted on a physical system comprising unmanned aerial vehicles and unmanned ground vehicles.

This article studies the predefined time control design issue for uncertain nonlinear systems with full-state error constraints and unmeasurable states for the first time. Compared with existing works, this study enables the controlled system to stabilize within a predetermined time and ensures that the full-state tracking errors converge to a desired control accuracy range, even in the absence of measurable state information. Fuzzy logic systems (FLSs) are applied to handle unknown nonlinear dynamics, and FLSs-based nonlinear state observer is constructed to estimate unmeasurable states. With the universal barrier Lyapunov function and the dynamic surface control technique, an output-feedback-based full-state error constrained control strategy with predefined time stability is proposed, in which a nonsingular predefined time filter is constructed to avoid high computational complexity. Under this control strategy, the predefined time stability of the closed-loop system is achieved and the full-state error constraints are satisfied. Finally, a series of simulation results confirm the effectiveness and superiority of the proposed control strategy.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

Existing studies on table-based fact verification generally capture linguistic evidence from claim-table subgraphs or logical evidence from program-table subgraphs independently. However, there is insufficient association interaction between the two types of evidence, which makes it difficult to obtain valuable consistency features between them. In this work, we propose heuristic heterogeneous graph reasoning networks (H2GRN) to capture the shared consistent evidence by strengthening associations between linguistic and logical evidence from two perspectives of graph construction and reasoning mechanism. Specifically, 1) to enhance the close connectivity of the two subgraphs, rather than simply connecting two subgraphs by the nodes with the same content (the constructed graph in this way has severe sparsity), we construct a heuristic heterogeneous graph, which relies on claim semantics as heuristic knowledge to guide the connections of the program-table subgraph, and in turn expands the connectivity of the claim-table subgraph through logical information of programs as heuristic knowledge; and 2) to establish adequate association interaction between linguistic evidence and logical evidence, we design multiview reasoning networks. In detail, we propose local-view multihop knowledge reasoning (MKR) networks to enable the current node to establish association not only with one-hop neighbors, but also with multihop neighbors, to capture context-richer evidence information. We execute MKR on heuristic claim-table and program-table subgraphs to learn context-richer linguistic evidence and logical evidence, respectively. Meanwhile, we develop global-view graph dual-attention networks (DAN) that execute on the entire heuristic heterogeneous graph, reinforcing global-level significant consistency evidence. Finally, the consistency fusion layer is devised to weaken the disagreement between the three types of evidence to assist in capturing consistent shared evidence for verifying claims. Experiments on TABFACT and FEVEROUS demonstrate the effectiveness of H2GRN.

In this article, we propose bionic swarm control based on second-order communication topology (SOCT) inspired by the migration of birds, which solves the difficulty in constructing communication topologies and high-computational complexity in controlling large-scale swarm systems. To realize bionic swarm control, there are three problems supposed to be solved. First, the adjacency matrix and the Laplacian matrix in traditional methods cannot be applied to SOCT directly, which should be redesigned. Second, sub-swarm systems formed based on 2-order communication topology (2-OCT) and independently distributed with each other also need to be put forward to reduce computational complexity. At last, the followers in 1-order communication topology (1-OCT) are set as the leaders of sub-swarm systems in 2-OCT. As a result, coupling in large-scale swarm systems would be reduced. The bionic swarm controller is designed through the backstepping method. In this case, the stability of bionic swarm controller is proven by the designed Lyapunov function. The simulations show the efficiency of the designed bionic swarm controller. And the tracking-containment control based on SOCT with 42 swarm members is realized.

In this article, we propose a complex continuous action iterated dilemma (CAID) with an incremental dynamic approach to overcome the limitations of traditional methods. In traditional CAID, the number of players was fixed. Consequently, when new players joined, computing resources were wasted due to repeated refreshes during the dynamic update process. To address these issues, we first propose a CAID model with an incremental dynamic approach. This model reflects the dynamic changes in the number of players, aligning more closely with real-world scenarios. Second, we propose an incremental updating method to prevent unnecessary refreshes of the original players’ states. When the number of players, denoted as$N$, increases, we update and expand the evolutionary dynamic model using incremental information. This allows for an incremental connection between the original and new players. We use a weighted adjacency matrix to represent the relationships among players. The incremental updating method then updates the state matrix and the adjacency matrix. Furthermore, an analysis based on the designed Lyapunov function is proposed to prove the convergence of the CAID with incremental dynamic. The simulation results reveal the effectiveness of our proposed method.

This article focuses on the singularity-free predefined time control design problem of the quantized nonstrict feedback (NSF) nonlinear systems. Radial basis function neural networks (NNs) are introduced to model the unknown nonlinear dynamics. With the property of the NN basis function, the algebraic loop problem posed by the NSF control structures is addressed. The input quantization is addressed by using the nonlinear decomposition technique. A nonlinear filter with predefined time stability is constructed to decrease the computational complexity. Further, by introducing the designed predefined time filter into the backstepping recursive framework, a predefined time dynamic surface control algorithm is developed, in which the improved adding power integration technique is introduced to prevent control singularities. The Lyapunov theory demonstrates the predefined time stability of the closed-loop quantized nonlinear systems. By the developed control algorithm, the controlled system can effectively track the specified command signal. Both the tracking and filtering errors can reach a small neighborhood around zero within the preset time. The validity and superiority of the proposed control algorithm are illustrated by an actual system simulation.

This article studies the adaptive fuzzy practical fixed-time control design for multi-input multi-output (MIMO) nonlinear systems with nonstrict feedback. The extant practical fixed-time stability criterion cannot obtain an accurate settling time upper bound or exists some constraints on parameters that lead to a conservative result. Thus, a novel practical fixed-time stability criterion is proved in this article to resolve the abovementioned problem and can obtain the precise value of the settling time upper bound. The control singular issue caused by the fixed-time stability criterion form is avoided by introducing adding power integration method. Compared with other approaches, this method is easy to apply in control design, and it is convenient to prove its effectiveness. And fuzzy logic system is adopted to approximate the unknown nonlinear items. Combining the proposed fixed-time stability criterion, traditional backstepping scheme, and fuzzy logic system, an adaptive practical fixed-time controller is proposed. The simulation of the actual physical system demonstrates the effectiveness of the controller and practical fixed-time criterion.

This article investigates the event-triggered predefined time output feedback control design problem for nonlinear interconnected systems with nonstrict feedback control structures. Compared with the existing event-triggered output feedback control design schemes, the most significant contribution of this article is that the system stability time can be preset directly. Fuzzy logic systems (FLSs) and FLSs-based state observer deal with unknown nonlinear dynamics and unmeasured states. Combining with dynamic surface control technology and event-triggered mechanism based on switching threshold strategy, an event-triggered predefined time decentralized output feedback control method is proposed, in which a predefined time filter is designed to solve the computational complexity problem. In addition, the algebraic loop problem and control singular problem are also solved, respectively, by applying the property of fuzzy basis function and L’Hospital’s rule. Utilizing the predefined time Lyapunov stability theory, the system stability analysis is given. Finally, the effectiveness and practicability of the proposed control method are verified by practical system simulation cases.

This article researches the adaptive fuzzy tracking control problem for uncertain nonlinear systems with multiple actuators and sensors faults. Compared with previous studies, all states of the system cannot be measured accurately in this article due to the existence of multiple sensors faults, and it brings significant difficulties to the design of the control scheme. Moreover, multiple actuators faults and external disturbance can also bring challenges to controller design. To solve these problems, we design different adaptive update laws to relieve the effects of unknown actuators faults, sensors faults, and external disturbance, respectively. Furthermore, the actual states can be estimated by combining sensors outputs with adaptive parameters. On this basis, the unknown nonlinear functions are approximated through the combining of fuzzy logic systems and the estimation of states. Then, a novel adaptive fuzzy tracking control algorithm is completed by the backstepping method. By employing the Lyapunov function, the presented novel fault-tolerant control algorithm can guarantee all signals of the system are bounded in spite of the occurrence of multiple faults. Finally, we verify the availability of the novel algorithm by comparing the control performance of the two algorithms.

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

In this article, a novel coverage algorithm is designed to realize dynamic tracking coverage of unmanned ground vehicles (UGVs) by unmanned aerial vehicles (UAVs) with quantity-adjustment behavior, which can adjust the quantity of UAVs to cover the moving UGVs. In traditional coverage control, the paths of UAVs are preplanned to achieve regional coverage. Additionally, the quantity of UAVs remains unchanged, resulting in a waste of resources and a lack of flexibility. To overcome these problems, we present a novel coverage algorithm. First, the tracking coverage algorithm is designed, in which the positions of the UGVs are sampled at a certain interval, and$k$-means is used to obtain the optimal expected positions of UAVs. Then, to realize the quantity-adjustment behavior of UAVs, an evaluation mechanism is proposed to determine whether the UAVs should be added or withdrawn. UAVs should reach the expected positions during the sample interval. As a result, a finite-time terminal sliding-mode controller is designed to drive the UAVs to follow expected positions. Furthermore, we design a Lyapunov function to prove the stability of the controller. Finally, three simulation examples are put forward, and the results demonstrate the effectiveness of the proposed algorithm and controller.

Reinforcement learning (RL) requires a lot of interactions with the environment, which is usually expensive or dangerous in real-world tasks. To address this problem, offline RL considers learning policies from fixed datasets, which is promising in utilizing large-scale datasets, but still suffers from the unstable estimation for out-of-distribution data. Recent developments in RL via supervised learning methods offer an alternative to learning effective policies from suboptimal datasets while relying on oracle information from the environment. In this article, we present an offline RL algorithm that combines hindsight relabeling and supervised regression to predict actions without oracle information. We use hindsight relabeling on the original dataset and learn a command generator and command-conditional policies in a supervised manner, where the command represents the desired return or goal location according to the corresponding task. Theoretically, we illustrate that our method optimizes the lower bound of the goal-conditional RL objective. Empirically, our method achieves competitive performance in comparison with existing approaches in the sparse reward setting and favorable performance in continuous control tasks.

This article deals with a practical distributed hybrid differentiation flowshop scheduling problem (DHDFSP) for the first time, where manufacturing products to minimize makespan criterion goes through three consecutive stages: 1) job fabrication in first-stage distributed flowshop factories; 2) job-to-product assembly based on specified assembly plan on a second-stage single machine; and 3) product differentiation according to customization on one of the third-stage dedicated machines. Considering the characteristics of multistage and diversified processing technologies of the problem, building new powerful evolutionary algorithm (EA) for DHDFSP is expected. To achieve this, we propose a general EA framework called distributed co-evolutionary memetic algorithm (DCMA). It includes four basic modules: 1) dual population (POP)-based global exploration; 2) elite archive (EAR)-oriented local exploitation; 3) elite knowledge transfer (EKT) among POPs and EAR; and 4) adaptive POP restart. EKT is a general model for information fusion among search agents due to its problem independence. In execution, four modules cooperate with each other and search agents co-evolve in a distributed way. This DCMA evolutionary framework provides some guidance in algorithm construction of different optimization problems. Furthermore, we design each module based on problem knowledge and follow the DCMA framework to propose a specific DCMA metaheuristic for coping with DHDFSP. Computational experiments validate the effectiveness of the DCMA evolutionary framework and its special designs, and show that the proposed DCMA metaheuristic outperforms the compared algorithms.

This article proposes the fuzzy swarm control based on sliding-mode strategy with self-organized omnidirectional mobile robots (OMRs) system. In previous work, swarm control is realized by using sliding-mode strategy. However, chattering in the OMRs system is very serious. To overcome this drawback, a new fuzzy swarm control for OMRs system is designed, which introduces the fuzzy logic to replace switching control in traditional sliding-mode control (SMC). The fuzzy SMC (FSMC) can weaken chattering for sliding-mode strategy in the OMRs system. However, it is difficult to design swarm control law for OMRs because of model uncertainties, external disturbance and the introduction of fuzzy logic. The FSMC is proposed in this article and its stability is analyzed. Simulation and experiment results show that the fuzzy swarm control based on sliding-mode strategy with self-organized OMRs system can realize stability asymptotically and chattering is weakened.

In this article, an adaptive swarm control within saturated input based on the nonlinear coupling degree is proposed. Swarm control is a forward study in kinematics and dynamics of the swarm system. However, the coupling degree in the previous work can only manifest whether the agents in the swarm being connected or not, ignoring the connection strength. As a result, the nonlinear coupling degree is proposed, which is more suitable for practical engineering than the previous coupling degree. Based on the nonlinear coupling degree, we put forward novel swarm kinematics and dynamics. Besides, the effects of input saturation and nonlinear dynamics should be considered for this novel swarm control based on the nonlinear coupling degree. Therefore, we introduce the backstepping method to design an adaptive swarm controller. With this controller, the input saturation auxiliary system is designed to reduce the effects of input saturation, and a radial basis function neural network (RBF-NN) is introduced to approximate the nonlinear dynamics. To overcome the differential explosion in the backstepping method, a command filter is put forward to reduce the amount of calculation and reduces the difficulty of the controller design. It is proved that the proposed controller ensures stability based on the Lyapunov stability theory. Finally, the simulation results of a multiagent system composed of six omnidirectional mobile robots illustrate the validity of the proposed controller.

This paper presents the generation strategy, motion planning, and switching topologies of a distance-based leader-follower relation-invariable persistent formation (RIPF) of multiagent systems (MASs). An efficient algorithm is designed to find out if a persistent formation can be generated from a rigid graph. Derived from the properties of a rigid graph, the algorithm to generate RIPF from any initial location is presented. In order to generate different RIPFs in the switching topology, state and transition matrices are introduced. To achieve the minimum agent-movement among RIPFs, a downward-tree combinatorial optimization algorithm is presented. In the end, with the selected minimum agent-movement RIPF, a control law is designed to drive initial RIPF to desired RIPF with given distances among agents. Simulation results show the proposed generation method, control law, and downward-tree are effective to realize the desired formation.

In this article, we propose the swarm control for a self-organized system with fixed and switching topology, which can realize aggregation, dispersion, or switching formation when swarm moves. The self-organized system can automatically construct the communication topology for intelligent units in swarm. Swarm control can realize aggregation and dispersion of intelligent units based on its communication topology when swarm moves. The proposed swarm control, in which distances between the related intelligent units are time varying, is different from traditional swarm consensus or swarm formation maintenance. To design swarm control, we define the normalization adjacency matrix and normalization degree matrix based on communication topology. The communication topology is automatically generated based on relation-invariable persistent formation. Depending on whether the communication topology changes or not, the swarm control can be classified as fixed topology and switching topology. Then, the swarm control with fixed and switching topology is designed and analyzed, respectively. The swarm control can realize stability asymptotically when topology is fixed and realize stability in finite time when topology is switched. The simulation results show that the proposed approaches are effective.

In this article, we propose a smooth transition in communication for swarm control with formation change. The communication topology in a swarm is automatically constructed by the relation-invariable persistent formation, which is a method of a self-organized system. Based on the communication topology, intelligent units in swarm systems can solve difficult tasks which would be hardly completed by a single intelligent unit. Intelligent units in the swarm are controlled to realize swarm behaviors, such as aggregation, dispersion, and switching formation when the swarm moves. The switching function in the traditional swarm control with formation change is step function and the transient switching may result in communication failure, transient velocity change, energy waste, and actuator damage. To overcome transient switching in traditional methods, we design smooth transition in communication. The proposed method guarantees the intelligent units could be connected in the communication, which can ensure the communication security of swarm system during the process of communication topology changing. Introduction of smooth switching function in swam control makes it difficult to design the controller. The swarm control with smooth transition in communication, which is based on sliding mode control, is designed and analyzed. Finally, a simulation is carried out to verify the effectiveness of the proposed approaches.