This paper investigates the fuzzy distributed reinforcement learning (RL) optimal resilient control problem for multiple unmanned surface vehicle (multi-USV) systems under denial-of-service (DoS) attacks. Firstly, the considered multi-USV systems are modeled by Takagi-Sugeno (T-S) fuzzy systems. Then, a resilient distributed formation observer is developed to estimate the leader’s states. A fuzzy optimal resilient formation control scheme is proposed by using the proposed resilient observer and game theory. Considering that the analytical solution of the optimized control is transformed into the game algebraic Riccati equations (GAREs), which are difficult to obtain analytically, a value iteration (VI) learning algorithm is designed to learn the approximate solutions of GAREs under a mild initial excitation (IE) condition. It is proved that the designed controller guarantees that multi-USV systems achieve the desired formation shape with DoS attacks. In addition, the proposed learning algorithm is demonstrated to be convergent and the persistence of excitation (PE) condition in the existing RL algorithms is relaxed. Finally, the simulation and comparison results confirm the feasibility of the proposed optimized control approach.

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.

This article studies the optimal cooperative tracking control problem of nonlinear multi-agent systems (MASs) in the presence of unknown dynamics and denial-of-service (DoS) attacks. It is more challenging to achieve the desired optimized performance under DoS attacks, especially when neural networks are utilized to identify the unknown dynamics online. Considering two types of DoS attacks (connectivity-maintained attacks and connectivity-broken attacks), the article presents a novel defense control strategy consisting of a resilient distributed observer and a neuro-adaptive optimal cooperative tracking controller. In specific, by introducing a label information algorithm, the resilient distributed observer for each follower agent is presented to reconstruct the leader's states under two types of DoS attacks. Subsequently, a neuro-adaptive optimal cooperative tracking controller is proposed under an identifier-critic-actor architecture in the presence of DoS attacks. It is proven that the output of all follower agents can synchronize with that of the leader under DoS attacks, while the local performance indexes reach the Nash equilibrium simultaneously. Finally, the simulation results show the effectiveness of the presented optimal cooperative tracking control methodology.

This study investigates the fixed-time distributed adaptive neural network (NN) hybrid optimized output-feedback formation control issue for multiple unmanned surface vehicle (multi-USV) systems. Under the differential graphical games theory, a novel fixed-time distributed adaptive NN hybrid optimal formation control strategy is developed via designing a NN state observer. The proposed distributed hybrid optimal control scheme consists of a distributed adaptive NN feedforward controller and a distributed error feedback optimized controller. The former is designed by adopting backstepping recursive control design algorithm to handle the nonlinear dynamics problem in multi-USV systems. The latter is developed based on differential graphical games to achieve the global optimization control performance. It is demonstrated that the proposed fixed-time distributed NN hybrid optimal formation control strategy can achieve the multi-USV systems formation control objectives. Meanwhile, it can obtain the global optimal control performance and reach Nash equilibrium in a fixed time. Finally, the computer simulation verified the validity of proposed fixed-time distributed optimal formation control strategy.

This article studies the distributed observer-based event-triggered (ET) optimal control problem for nonlinear multiagent systems (NMASs) over jointly connected digraphs. Since agents cannot get the leader under jointly connected digraphs, a distributed observer is constructed to estimate the unknown leader. At the same time, to enhance the efficiency of communication resources utilization between agents, an ET communication mechanism is developed to schedule the agent communication. Subsequently, neural networks (NNs) are adopted to handle the unknown nonlinearities, and an NN state observer is established to reconstruct the unmeasurable states. By utilizing the backstepping technique and adaptive dynamic programming theory, a distributed observer-based ET optimal control algorithm is developed, in which a critic network is designed with a proposed weight updating law to estimate the cost function. It is proven that the presented ET optimal control approach ensures that all signals of NMASs are uniformly ultimately bounded (UUB), and the cost function is minimized. At last, the theoretical results are applied to marine surface vehicles (MSVs) to validate the efficiency of the developed optimal control strategy.

The multi-agent systems (MASs) exchange the communication information by the communication network, which is vulnerable to denial-of-service (DoS) attacks. DoS attacks can disrupt the communication channels and result in the collisions between agents, thus it is an important and challenging topic to study the collision avoidance formation control issue under DoS attacks. This paper investigates the asynchronous resilient collision-free formation control issue for nonlinear MASs with DoS attacks. An asynchronous resilient distributed observer is proposed to estimate the output information of leader under DoS attacks. Based on the designed distributed observer and by constructing two high-order filters, an asynchronous resilient collision-free formation control method is presented by backstepping control design theory. The presented formation control method can ensure that the formation tracking errors asymptotically converge to zero, and the collision avoidance objective is realized. Moreover, the non-differentiable problem of virtual controllers is solved. Finally, we apply the developed formation control method to multiple Euler-Lagrangian (EL) systems, the simulation and comparison results verify its effectiveness. (c) 2025 Published by Elsevier Ltd.

Since multi-agent systems (MASs) rely on communication networks to exchange information, which are vulnerable to denial-of-service (DoS) attacks. DoS attacks not only disrupt the communication channels but also lead to the instability of MASs. Thus, it is an important and challenging topic to study the resilient cooperative control problem under DoS attacks. This paper studies the fixed-time fuzzy resilient cooperative output regulation problem for nonlinear MASs over directed graphs under DoS attacks. Firstly, the considered nonlinear MASs are modeled by Takagi-Sugeno (T-S) fuzzy systems. Since the considered communication topology of the controlled systems is vulnerable to DoS attacks, the leader states cannot be obtained by agents, then a fixed-time fuzzy distributed resilient observer is developed to estimate the leader states. The developed fuzzy resilient observer can guarantee that the estimation errors converge to zero in a finite time interval. In control design, the controlled systems are transformed into the controllable canonical linear time-varying (LTV) MASs by using nonsingular Lyapunov transformations. Then, based on the designed fuzzy resilient observer, a fuzzy fixed-time distributed resilient regulator is proposed. It is proved that the proposed fuzzy fixed-time resilient cooperative output regulation scheme can ensure that regulated errors converge to zero in a finite time interval. Finally, we apply the developed fuzzy fixed-time resilient control method to multiple unmanned surface vehicle (USV) systems in maritime Internet of Things (IoT) systems, the simulation and comparison results verify the effectiveness of the developed fixed-time resilient control approach.

In this article, we study the reinforcement learning (RL) optimal output feedback control problem for Takagi-Sugeno (T-S) fuzzy systems with immeasurable states and disturbances. A fuzzy filtering observer is designed to estimate the immeasurable states, and then, based on the filtering observer, a fuzzy optimal output feedback control method is presented by employing zero-sum differential game theory. Since the analytical optimal control solutions are reduced to solving game algebraic Riccati equations (GAREs), which is difficult to obtain their analytical solutions, an output feedback model-free policy iteration (PI) learning algorithm is proposed. It is proved that the proposed algorithm is convergent and the proposed fuzzy RL optimal output feedback control approach can make the controlled systems be asymptotically stable and satisfy the disturbance attenuation condition. Finally, we apply the developed optimal control method to a mass-spring-damper system, and the simulation results verify the effectiveness of the developed method.

Multi-agent systems (MASs) exchange information through the network topology, which is prone to denial-of-service (DoS) attacks and detection delays. DoS attacks can interrupt communication channels, and detection delays may lead to asynchronization between the network topology and the controller, thereby making cooperative output regulation difficult to achieve. Thus, it is important to study the cooperative output regulation problem under DoS attacks and detection delays. This paper investigates the asynchronous resilient cooperative output regulation problem for uncertain nonlinear MASs subject to DoS attacks and detection delays. Asynchronous resilient distributed observers are proposed to estimate the exosystem’s matrix and state information, respectively. Based on the designed distributed observers, an asynchronous resilient cooperative output regulation control strategy is developed by using the backstepping control technique. The proposed control strategy is able to guarantee that the regulation errors converge asymptotically to zero even under DoS attacks and detection delays. Finally, a numerical example is given to check the effectiveness of the proposed observers and control strategy.

This article investigates the fuzzy distributed resilient formation control problem of Takagi-Sugeno (T-S) fuzzy multiagent systems (MASs) under DoS attacks and communication delays. Since the communication network among MASs is subject to DoS attacks and communication delays, the leader's states cannot be obtained continuously by each agent. A fuzzy distributed resilient estimator is first proposed to estimate the leader's state subject to DoS attacks and communication delays. By constructing a Lyapunov-Krasovskii functional, it is demonstrated that the estimation errors of the fuzzy resilient estimator exponentially converge to zero. Second, based on the formulated fuzzy distributed resilient estimator and parallel distributed compensation (PDC) algorithm, a fuzzy distributed resilient formation controller is developed. The presented fuzzy distributed resilient formation control strategy ensures that the controlled T-S fuzzy MASs remain stable and achieve the formation objective. Finally, the developed fuzzy distributed resilient formation control method is applied to the single-link robot arm systems, and the effectiveness is demonstrated by simulation and comparison results.

Inverse reinforcement learning optimal control is under the framework of learner-expert. The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function, so it can handle optimal control problems effectively. This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno (T-S) fuzzy systems. Based on learner systems, an expert system is constructed, where the learner system only knows the expert system's optimal control policy. To reconstruct the unknown cost function, we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known. The developed model-based learning algorithm is consists of two learning stages: an inner reinforcement learning loop and an outer inverse optimal control loop. The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy. Then, to eliminate the requirement that the system dynamics must be known, a data-driven integral learning algorithm is presented. It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable. Finally, we apply the proposed fuzzy optimal control to the truck-trailer system, and the computer simulation results verify the effectiveness of the presented approach.

Inverse reinforcement learning (RL) optimal control is under the framework of expert-learner, where the learner system can imitate expert system's trajectory and optimal solutions via an inverse RL algorithm and minimize the cost function, thus it can deal with optimal control problem effectively. This paper presents a fuzzy inverse RL optimal control approach for nonlinear system with partially unknown dynamics. Firstly, the controlled nonlinear system is modeled by Takagi-Sugeno (T-S) fuzzy system. Secondly, the fuzzy optimal controller and the worst-case disturbance input are given via a zero-sum game. To imitate expert system's demonstrated behavior and achieve optimization, an online adaptive inverse RL algorithm is developed. The presented algorithm consists of four synchronous neural networks (NNs): a critic NN, an actor NN, a rival NN and a state-penalty NN, which are used to reconstruct expert system's cost function, optimal controller, disturbance input and state-penalty weight. Moreover, the tuning law of critic NN is implemented by using experience replay technique, instead of persistent excitation (PE) condition. It is proved that the proposed online adaptive inverse RL algorithm can learn expert system's optimal solutions and imitate its behavior. And also the presented fuzzy inverse RL optimal control scheme can make the controlled fuzzy learner system be asymptotically stable and achieve Nash equilibrium solution. Finally, a continuous stirring tank reactor (CSTR) system is provided to illustrate the feasibility and superiority of the developed algorithm.

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.

This article studies the game-based fuzzy adaptive least-distance formation control problem for nonlinear multiagent systems (MASs) under event-triggered communication. Since agents cannot obtain the nonneighboring agents’ actions, and a subset of agents cannot access the moving target, distributed event-triggered observers are designed to estimate all agents’ actions and the moving target. Based on the designed distributed observers, a distributed time-varying Nash equilibrium (NE) seeking strategy is constructed such that the agents’ actions asymptotically converge to the NE. To overcome the nonexistence problem of high-order derivatives of the estimated signals arising from intermittent communication, three stage cascade filters are proposed to generate sufficiently smooth signals to replace the estimated signals. Then, a fuzzy least-distance formation controller is developed by utilizing the proposed cascade filters and the backstepping control theory. It is proven that the proposed formation control scheme can guarantee that all agents asymptotically achieve the least-distance formation. Finally, simulation and comparison results on marine surface vehicles (MSVs) verify the effectiveness of the proposed control scheme.

This article investigates the adaptive fuzzy distributed optimal control problem for nonlinear multiagent systems (MASs) under the predefined-time stability theory. The addressed controlled nonlinear MASs contain unknown dynamics, immeasurable states, and input saturations. To solve unknown dynamics and immeasurable states problems, fuzzy logic systems (FLSs) are used to model the uncertain nonlinear MASs, and an adaptive fuzzy distributed state observer is designed to estimate the unknown states. Then, based on the designed state observer and differential graphical game, a predefined-time distributed optimal output feedback controller is formulated. To implement the fuzzy distributed optimal output feedback controller, a fuzzy reinforcement learning algorithm is proposed to learn the solution of the Hamilton-Jacobi-Bellman equation, in which FLSs are used as a critical network, and its weights adaptive laws are designed by current and historical data. It is proven that the proposed adaptive fuzzy distributed optimal controller with reinforcement learning algorithm can guarantee the closed-loop system is asymptotically stable and reaches the Nash equilibrium within the given finite-time settling time without needing the restrictive persistent excitation condition. Finally, the computer simulation results and comparison with the existing optimal control method illustrate the effectiveness of the proposed distributed optimal control scheme.

This paper investigates the predefined-time optimal control problem for nonlinear systems with unknown dynamics. A predefined-time optimal controller is formulated based on the predefined-time stability theory and neural networks (NN) approximation techniques. Since the nonlinear system dynamics are unknown, an integral learning algorithm is formulated to model the uncertain nonlinear systems. To implement the predefined-time optimal controller, a NN data-driven reinforcement learning (RL) value iteration (VI) algorithm is developed to learn the solution of the Hamilton-Jacobi-Bellman (HJB) equation and the predefined-time optimal controller. It is proven that the proposed algorithm is convergent, and the proposed NN data-driven predefined-time optimal control approach can ensure that the closed-loop system is predefined-time stable and optimizes within the given finite settling time. Finally, the computer simulation results and comparison illustrate the effectiveness of the proposed optimal control scheme.

In the cruising mission of the unmanned surface vessel-unmanned aerial vehicle (USV-UAV) cooperative plant, although the UAV is capable of executing aerial maneuvers, it still faces inevitable obstacle avoidance and control challenges in narrow waterways and cross-bridge scenarios. As such, this study proposes a variable-speed multi-port segmented threshold event-triggered cooperative collision avoidance control algorithm based on the geometric velocity obstacle method (GVO). In the guidance module, first define the obstacle zone based on the detected bridge dimensions. Then, by setting safety thresholds and target points, implement a bridge collision avoidance guidance function with an automatic selection mechanism for the narrow waterway navigation mission. In the control module, in the presence of bridge obstacles, a variable-speed multi-port segmented threshold event triggering mechanism (MSETM) is designed for path tracking and collision avoidance missions to ensure the coordination of the USV-UAV cooperative plant at the beginning and end of collision avoidance. Furthermore, a multi-layer neural networks (MNNs) is adopted to approximate the system's nonlinearities, achieving high approximation accuracy and computational efficiency. Stability of the algorithm is proven using Lyapunov stability theory, and its effectiveness is validated through simulation experiments. Note to Practitioners-As maritime mission requirements grow increasingly complex, effectively controlling the unmanned surface vessel-unmanned aerial vehicle (USV-UAV) cooperative plant has become crucial for leveraging its unique advantages across different scenarios. Within complex bridge zone environments, the USV-UAV cooperative system faces potential threats from obstacles and various unexpected situations. To address the challenge of autonomous obstacle avoidance for the cooperative plant, this paper proposes the Geometric Velocity Obstacle (GVO) method. Additionally, to address actuator wear issues, a variable-speed multi-port segmented threshold event-triggering mechanism (MSETM) has been designed. Simultaneously, to achieve energy conservation, reduce consumption, and minimize communication resource usage, an adaptive control algorithm for multi-layer neural networks (MNNs) has been developed.

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 paper proposes a formation cooperative tracking control strategy for unmanned surface vehicles (USVs) considering the effects of communication delays, output constraints, and a quantization-based event-triggered mechanism. The proposed method ensures that each follower USV rapidly forms a formation and accurately tracks the desired trajectory of the virtual leader. In terms of design, a time-delayed distributed event-triggered extended state observer (ESO) is constructed to accurately estimate the position and velocity of the virtual leader under communication delays, while a reduced-order ESO is introduced to compensate for system uncertainties and external disturbances. Moreover, an asymmetric Barrier Lyapunov Function (BLF) is integrated within the backstepping scheme, guaranteeing that the output constraints remain strictly enforced during the entire control procedure. Furthermore, in view of the limited bandwidth of maritime communication, an event-triggering mechanism is designed based on input quantization. In terms of theoretical analysis, the stability of the proposed control system is rigorously established in the sense of uniform ultimate boundedness (UUB) based on Lyapunov theory and the stability properties of closed-loop systems, while the occurrence of Zeno behavior is explicitly excluded. Finally, simulation experiments demonstrate the effectiveness and feasibility of the proposed method, further highlighting its application potential in complex marine environments.