As an important long-range transportation carrier in the future Internet of Aerospace Things (IoAT), hypersonic flight vehicles (HFVs) will play a significant role in intelligent transportation systems (ITS). In IoAT architectures, HFVs function as intelligent edge nodes that must operate autonomously under severe uncertainties with limited onboard computational resources. However, strong coupling effects and unmodeled dynamics pose considerable challenges for the precise modeling and efficient control of HFVs. This paper proposes a novel framework for designing high-precision modeling strategies and efficient control algorithms for HFVs. The framework is named the Online-Enhanced Koopman (OE Koopman) Model Predictive Static Programming (MPSP) framework and is developed utilizing autoencoder neural networks. By leveraging the Koopman operator to lift nonlinear systems into high-dimensional linear spaces, the precise modeling associated with HFVs can be significantly simplified. Both the offline pre-training and online correction mechanisms are integrated into the OE Koopman-MPSP framework, which overcomes the issues of low precision in analytical modeling methods and insufficient data in deep learning methods. In the offline phase, autoencoder neural networks are utilized to construct the basic Koopman operator model. In the online phase, a few-shot-based Extended Dynamic Mode Decomposition (EDMD) method is employed to build compensatory operators for adapting to environmental changes. The proposed framework is specifically designed for resource-constrained IoAT edge devices, where computational efficiency and autonomous adaptation are critical. Experimental results demonstrate the effectiveness of the developed framework and specific algorithms.

Robotic arms serve as critical actuation edge nodes in Industrial Internet of Things (IIoT)-enabled intelligent manufacturing systems. In distributed industrial cyber-physical architectures, multiple robotic manipulators are required to perform autonomous and cooperative motion planning under obstacle-rich and dynamically coupled environments. However, existing multi-agent deep reinforcement learning approaches often exhibit limited scalability, redundant observation processing, inefficient experience utilization, and unstable convergence when deployed in high-dimensional cooperative scenarios. To address these challenges, this paper proposes an Attention-based Prioritized Trajectory Multi-Agent Deep Deterministic Policy Gradient (ATP-MADDPG) framework tailored for edge-coordinated multi-arm systems in IIoT environments. The proposed framework incorporates an adaptive attention mechanism to selectively emphasize critical interaction features while suppressing redundant sensory information, thereby enhancing decision efficiency at distributed edge nodes. A prioritized sequence experience replay (PSER) strategy is further introduced to improve the utilization of cooperative trajectory data and accelerate policy evolution. In addition, curriculum learning is employed to enable progressive training and scalable policy refinement for complex multi-arm tasks. Extensive simulations demonstrate that, compared with conventional MADDPG and representative baselines, the proposed ATP-MADDPG achieves higher task success rates, improved cumulative rewards, faster convergence, and enhanced policy stability. These results validate the effectiveness of the proposed framework for distributed cooperative motion planning in IIoT-oriented robotic systems.

Autonomous collision avoidance is essential for unmanned surface vehicles (USVs) in Maritime Internet of Things (MIoT) systems. Existing deep reinforcement learning (DRL) methods often suffer from poor exploration-exploitation balance and weak safety integration, which may lead to local optima and unsafe actions. To address these issues, a risk-aware role-differentiated dual-actor deep deterministic policy gradient framework (RADA-DDPG) is proposed. Abandoning homogeneous structures, a heterogeneous dual-actor design mitigates local optima by assigning distinct exploration and exploitation roles, dynamically balanced via a Q-value-based switching strategy. Additionally, an embedded risk-critic network directly shapes actions during end-to-end policy optimization, rather than serving merely as an external constraint. Extensive simulations demonstrate that RADA-DDPG outperforms baselines in learning efficiency, safety, and robustness. Furthermore, real-world field experiments with dynamic obstacles validate its feasibility.

Multiple mobile robot systems, as a dynamic type of the Internet of Things (IoT), have been gaining widespread attention. In this article, the prescribed-time (PT) formation control of nonholonomic mobile robots (NMRs) with uncertainties is investigated under the leader-follower architecture. First, the nonholonomic constraints of the mobile robots are sufficiently considered, and a transformation method is presented to convert the original nonholonomic system into an easy-to-handle Euler-Lagrange (EL) system. In addition, fuzzy logic systems (FLSs) and adaptive techniques are employed to deal with uncertainties, such as the damping matrix, so that the negative effects of approximation errors can be eliminated. By applying the sliding mode control (SMC) technique and PT stability theory, a sliding mode protocol is proposed to ensure that all states of the mobile robots can be driven onto the sliding surface and the formation errors converge within the prescribed time. Finally, simulations and experiments are conducted to demonstrate the effectiveness of the proposed method.

This paper investigates Nash equilibrium seeking for non-zero-sum games (NZSG) in internet of things systems. A resilient event-triggered control mechanism was proposed, which reduces false triggers under Denial-of-Service attacks while simultaneously lowering the communication and computational load of the system. Moreover, reinforcement learning is employed to seek the Nash equilibrium point within the NZSG framework, where both cooperative and competitive interactions among the distributed agents coexist. To enhance critic learning process, an experience replay method is introduced to relax the restrictive persistent excitation condition. Finally, the effectiveness of the proposed scheme is demonstrated through simulation studies conducted on microgrids.

This study addresses the multi-objectiveL-/L1fault detection filtering design for switched positive systems (SPSs) subject to a mode-dependent minimum dwell time (MD-MDT) constraint utilizing a dynamic event-triggered strategy (DETS). First, a novel linear copositive dynamic event-triggered condition is proposed for systems with positivity constraints. Next, sufficient and necessary conditions are derived to ensure that the designed fault detection filter provides a positive asymptotic estimation with anL-/L1performance index. To address the MDMDT constraint, a novel discretized linear copositive Lyapunov function (DLCLF) approach is developed to establish sufficient conditions for ensuring the corresponding augmented system is exponentially stable. Furthermore, by employing the matrix decomposition technology to design filter matrices, an effective mode-dependent piecewise design scheme is proposed for the fault detection filtering of SPSs in a linear programming (LP) form. The developed LP rather than linear matrix inequality (LMI) based scheme features a simpler structure, lower computational demands, and less conservativeness. Finally, three examples are exhibited to validate the achieved results.

This paper investigates neural networks-based state-dependent intermittent control (SDIC) from a data-driven perspective, considering unknown continuous-time linear systems subject to external disturbances. Instead of relying on precise system models, the proposed approach utilizes offline-collected data to develop a data-driven SDIC scheme. An ℓ1-norm-based convex optimization method is employed to estimate the domain of attraction (DOA), enabling the partitioning of the state space into certified control regions. This facilitates state-dependent control updates that reduce communication burden while preserving system stability. Compared with existing methods, the proposed scheme offers greater flexibility, as its triggering mechanism does not depend on prior model knowledge or a small estimated DOA. Furthermore, it is practically implementable: a neural feedback controller is constructed to satisfy Lyapunov-based stability conditions using only a data-driven linear matrix inequality (LMI), without requiring complex additional assumptions. The effectiveness of the proposed strategy is demonstrated through simulations on a real HVAC system. The learned DOA-based region partitioning allows the controller to adapt to varying environmental conditions while ensuring stability and energy efficiency. Comprehensive simulation results validate the practicality and performance of the proposed control framework.

This paper presents a prescribed time learning-based near optimal enclosing controller to ensure that unmanned aerial vehicles (UAVs) encircle around the specified target with prescribed performance constraints and minimum cost efforts. First, a basic enclosing controller is established to achieve the enclosing error stabilization and stable circumnavigation around a given target. Second, a new prescribed time behavior envelope that eliminates the availability on initial error is proposed. To render the satisfaction of performance constraints and optimal enclosing actions, a transformed enclosing error is obtained by enforcing state conversion on original error. Then, aiming at stabilizing the enclosing error to a prescribed accuracy within a prescribed time, a prescribed time learning-based near optimal enclosing controller under a critic-only adaptive dynamic programming (ADP) is explored, approximating the solution of a novel Hamilton-Jacobi-Bellman (HJB) equation via pursuing the minimum cost associated with transformed errors. Especially, a novel prescribed time learning rule driven by weight errors is elaborated by revisiting real-time and historical information, such that the convergence of weights is only determined by a user-defined time constant. The prominent merit is that the optimal enclosing with performance guarantees can be achieved by a prescribed time ADP. Lyapunov stability demonstrates that involved error variables are ultimately limited and resultant controller satisfies optimality. Finally, simulations verify the values and superiority of the proposed methodology.

This paper investigates the predefined-time (PdT) formation control problem for heterogeneous wheeled mobile robots (WMRs) with complex nonlinear terms. To address the challenges arising from system heterogeneity and distributed coordination, a reference-tracking control framework is proposed. The first layer is a reference signal generation layer, where PdT formation trajectories are generated by signal generators, with local observers embedded in each agent to estimate the leader’s state when direct access is unavailable. The second layer is an agents tracking layer, where each WMR follows its assigned reference trajectories. By coordinating these two layers, the proposed framework enables distributed formation control within a predefined time. To achieve PdT tracking, a sliding mode control strategy enhanced with fuzzy logic control is developed in the tracking layer. Lyapunov-based analysis is conducted for both layers to ensure PdT stability and provide explicit convergence-time guarantees. Simulation results are presented to validate the theoretical analysis and demonstrate the effectiveness of the proposed method.

The article focuses on the design of event-triggered decentralized asynchronous (ETDA) control for positive interconnected switched systems (PISSs) subject to a mode-dependent minimum dwell-time (MDMDT) constraint. First, a novel 1-norm-based event-triggered mechanism (ETM) and a decentralized asynchronous control strategy (DACS) are proposed to facilitate the design of an ETDA control framework. Next, a sufficient positivity criterion is presented for PISSs in a closed-loop. Then, by constructing a newfangled discretized linear copositive Lyapunov function (DLCLF) for MDMDT switching, and utilizing the matrix decomposition approach for ETDA controller gains, a feasible mode-dependent ETDA control scheme with a tractable linear programming (LP) approach is presented for PISSs. Further, the provided ETDA control scheme can degenerate into three exceptional cases: event-triggered decentralized synchronous (ETDS) control, time-triggered decentralized asynchronous (TTDA) control, and time-triggered decentralized synchronous (TTDS) control. Finally, comparisons are conducted to exemplify the significance and feasibility of the designed control scheme.

Prescribed performance (PP) control is widely used in the construction of consensus protocols for multiagent systems (MASs) due to its property of ensuring that the variables of interest are constrained within the prescribed range during the control process. However, when unpredictable faults such as sudden sensor faults occur, or parameters such as the sampling interval are selected improperly, it can cause singularity problems and render the PP protocol ineffective. Introducing shear mapping into the PP mechanism can resolve the singularity problems, but it requires solving complex nonlinear equations, which may heavily occupy agents' computational resources. To address this issue, we propose a novel dynamic shear mapping mechanism, based on which an event-triggered PP consensus protocol is developed for a class of heterogeneous leaderless MASs. Specifically, by constructing a dynamic shear angle related to the constraint performance functions and variables of interest, the need to solve nonlinear equations is reduced, while the hard-soft transition of performance constraint in the control process is achieved. It is proven that, under the proposed protocol, the consensus errors can strictly satisfy the PP requirements during a prescribed stage, and ultimately converge to zero asymptotically. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

This article investigates the consensus problem of multiple heterogeneous-dimensional switched nonlinear systems (HDSNSs). Each HDSNS consists of nonlinear subsystems that may have distinct state dimensions, along with a rule governing the switching among them. Currently, the consensus problem of multiple HDSNSs remains unresolved, primarily due to the highly complex dynamic characteristics exhibited by multiple HDSNSs. This article addresses the specific practical output consensus problem for a class of multiple HDSNSs, thereby aiming to fill the corresponding research gap. Each subsystem of the considered agent system is described by a nonlinear strict-feedback system, and the switching signal of the agent system is subject to the minimum dwell-time constraints. The cooperative control goal for the multiple HDSNSs is accomplished through the proposed protocol, which requires only sampled-data output interactions between agents. A numerical example verifies the proposed theorem.

Autonomous berthing is a critical step in realizing the full autonomy of unmanned surface vehicles (USVs), which can essentially be regarded as a trajectory-tracking task. It can be further transformed into a problem of nonlinear systems with output constraints. This paper proposes a novel adaptive fixed-time backstepping control scheme based on the barrier Lyapunov function (BLF) for autonomous berthing of USVs. Firstly, a new barrier Lyapunov function is designed to solve the output asymmetric constraint requirement of the autonomous berthing system, and it is also adaptive to the unconstrained system without changing the control structure. Secondly, the convergence of adaptive fixed-time control and bounded tracking of BLF are combined to conquer the long convergence time and nonlinear system uncertainty. Finally, simulation and field tests are conducted to verify our proposed scheme’s superiority.

By proposing an optimal reference trajectory generator (RTG), the dynamic formation control problem for nonlinear multiagent systems (MASs) under an event-triggered mechanism (ETM) is addressed via reinforcement learning (RL). The introduction of the RTG enables the removal of several commonly used but stringent constraints while still ensuring that the desired control objectives are achieved. This broadens the applicability of the proposed control strategy. Leveraging actor-critic-identifier networks, each agent is able to optimally track the reference trajectory under the proposed ETM framework. The developed hybrid ETM reduces both interagent communication frequency and the computational burden on agents. An RL-based controller is designed using not only actor-critic-identifier networks but also a novel collision-avoidance function to ensure safe agent behavior. Using a Lyapunov-like function analysis, we prove the effectiveness of the proposed control strategy and the convergence of the actor-critic-identifier network weights. Finally, the effectiveness and superiority of the proposed approach are further validated through a numerical simulation case and a comparative study.

This article investigates the prescribed-time fault-tolerant formation (PTFTF) control problem for heterogeneous switched nonlinear multiagent systems (HSNMASs) with actuator faults. In particular, the system under consideration exhibits both heterogeneity and switching dynamics, and operates over a directed topology. A novel PTFTF protocol that includes two adaptive laws and an auxiliary system is proposed by introducing a time-varying function. It is noteworthy that the constructed auxiliary system can effectively address the heterogeneity and switching characteristics of the system. Fuzzy logic systems (FLSs) are utilized to approximate potentially unknown nonlinear functions that are not required to satisfy the specific growth conditions. Notably, the adaptive law, newly designed as a key part of the protocol, eliminates the adverse effects of fuzzy approximation errors, ensuring that formation errors converge to zero within any given time. Finally, the effectiveness of the proposed protocol is demonstrated through both numerical and comparative simulations.

This article investigates a distributed finite-horizon optimal leader-follower consensus for discrete-time multi-agent systems with prescribed performance. Each agent has a limited communication range. First, to maintain the topology connectivity and satisfy performance requirements, a segmented error transformation function is designed. In this case, the terminal cost function is designed to transform an infinite horizon optimal problem into a finite horizon optimal problem. Furthermore, the algorithm via adaptive dynamic programming is developed to optimize the performance index function. The convergence analysis of the iterative algorithm is provided. Since it is almost impossible to directly solve the Hamilton-Jacobi-Bellman (HJB) equation, the reinforcement learning method with neural networks is introduced. Finally, simulation results demonstrate the effectiveness of the proposed optimal control method.

The design, simulation, and testing of intelligent trajectory-tracking control in narrow waters are essential issues for unmanned surface vehicles (USVs). Due to limited actuators, spatial constraints, and obstacles in narrow waters, the reference trajectory for USVs has various curves. This presents significant challenges to the accuracy and computational load of trajectory tracking. Therefore, a novel event-triggered-based nonlinear model predictive control (NMPC) with an artificial reference trajectory (ENMPC-ART) method is proposed. The artificial reference decision variables are integrated into the quadratic trajectory planning of reference trajectory and motion control of USVs to reduce the cross-track error. An event-triggered mechanism is designed to improve NMPC’s efficiency. Further, a cyber-physical simulation test framework based on virtual reality is designed to verify the algorithm’s performance and enhance the immersion. Finally, the proposed ENMPC-ART shows significant improvements through virtual simulations and field tests, such as the maximum cross-track error being reduced by 16% and the computation time being reduced by 20.2%.

Autonomous collision avoidance technology is the core of unmanned surface vehicles (USVs). Deep reinforcement learning (DRL) is a new approach to avoid collision for USVs. However, most research is based on the assumption of a fixed number of obstacles and ignores the collision prediction to improve safety. To address this problem, a novel “prediction-decision” collision avoidance model based on the deep deterministic policy gradient (DDPG) is proposed. First, a radiation-shaped state space is designed to make the DDPG that can be used in time-varying scenarios with stochastic obstacles. Then, the velocity obstacle (VO) is combined with the state space for training to realize the collision prediction. Subsequently, reward functions are designed using a reward-shaping technique to improve training efficiency and safety. Finally, virtual simulation experiments based on Unity3D and field tests are conducted to verify the algorithm’s performance. The results show that it can take safe collision avoidance actions in unknown environments and with generalization ability.

An efficient formation-keeping strategy is essential for unmanned surface vehicles (USVs) to achieve complex cooperation missions in the Marine Internet of Things (MIoT) system. However, traditional methods make generating an efficient strategy to adapt to different formation patterns difficult in dynamic MIoT. To address this, we enhance the deep deterministic policy gradient (DDPG) algorithm and propose a novel formation control strategy generation approach. First, we design a generic reward mechanism based on the virtual leader–follower strategy to adapt to different formation patterns, simplify the design process, and optimize the formation control. Then, we adopt the intrinsic curiosity module (ICM) to alleviate the problem of sparse rewards and the prioritized experience replay (PER) mechanism to improve the utilization of experience and accelerate the learning rate. In addition, a Gaussian noise model is integrated into the DDPG approach to simulate various external disturbances, which can improve the robustness of the generated strategy. Finally, we built a virtual simulation environment based on Unity3D and conducted field tests to verify the feasibility and superiority of our approach.

Driven by the development of the smart Internet of Things (IoT), the consensus of heterogeneous multi-agents with nonholonomic chained-form dynamics is considered, where the order number and dynamics of each agent can be different. Firstly, a distributed adaptive observer is designed to estimate all states and inputs of a leader in a finite time. Then, a distributed finite-time consensus protocol is presented to track estimated states of the leader by integrating power integrator technique, which can address heterogeneous structure of multi-agent systems while achieving finite-time consensus tracking. Moreover, the consensus of systems is analyzed and proved by Lyapunov theory. Finally, a simulation example for multiple wheeled robots is provided to demonstrate the effectiveness of the protocol.

Heterogeneous multi-agent systems play a pivotal role in the Internet of Things (IoT) by enabling collaborative intelligence across diverse devices, yet they inherently struggle with discontinuous communication and inaccessible internal data across neighboring platforms. In this paper, a novel protocol design method, named target point traction method, for heterogeneous multi-agent systems is proposed. The method addresses protocol design for two types of heterogeneous multi-agent systems, with a focus on consensus which is a fundamental issue in cooperative control. It aims to overcome collaborative challenges caused by communication limits, mainly the non-interaction of continuous and internal information. First, multi-agent systems consisting of agents described by first-and second-order systems subject to disturbances are considered. Then, a more general heterogeneous nonlinear multi-agent system is investigated, where the order number and nonlinearities of each agent can be different. The existence of the protocol that can accomplish the given cooperative control task for the investigated multi-agent systems is discussed. The implementation of the protocols developed by the method only depends on the local sampled-data output interaction. Under the proposed control schemes, the system output evolution of each agent in the sampling instants is equivalent to the state evolution of a (perturbed) first-order differentiator, which can effectively reduce the conservatism in the selection of the sampling period. Finally, the validity of the developed method is verified by numerical examples.

This paper aims to establish a sampled-data framework to solve the consensus problem for multiple heterogeneous Euler-Lagrange systems (MHELSs). The systems under consideration have heterogeneous dynamics and limited communication range. Different from the existing works, the common requirement of not allowing edge disconnection has been relaxed. Firstly, a sampled-data virtual system is constructed to provide reference trajectory for the actual system. The virtual systems only exchange data at sampling instants, so that connectivity requirement only needs to be satisfied at these moments. Next, a prescribed performance controller is proposed to track the reference trajectory and ensure the systems satisfy the relaxed connectivity requirement. Furthermore, an event-triggered mechanism is developed to reduce the update frequency of the controller. To illustrate the effectiveness of the proposed framework, two numerical examples are provided. Note to Practitioners—This paper investigates the connectivity-preserving consensus problem for multiple heterogeneous Euler-Lagrange systems. The Euler-Lagrange system can effectively describe various practical systems, such as autonomous vehicles, robotic manipulators, and walking robots. The integration of virtual and physical systems enables the proposed algorithm to adapt well to heterogeneous multiagent systems. The sampling-data interaction mode of the virtual system ensures a reduction of communication pressure among agents in practice. The design of the direction selector and force limiter effectively maintains reliable communication. The introduction of event-triggering mechanisms reduces the update frequency of physical controllers and lowers the performance requirements of the robot actuators. It is worth mentioning that we relax the connectivity requirement of the topology for the first time. Therefore, it is permissible for the distance between two connected robots to exceed the maximum communication range.

This paper studies the optimal switching and control co-design for a class of continuous-time switched nonlinear systems. An event-triggered adaptive dynamic programming (ADP) algorithm is developed to obtain the optimal hybrid control policy. At the event-triggered instant, the switching controller determines which subsystem to activate and the input controller updates the system input. Compared with the time-triggered methods, the computation and communication are reduced. A critic neural network (NN) is applied to approximate the solution of the switched Hamilton-Jacobi-Bellman (HJB) equation. The proposed critic NN is tuned according to the HJB error in real time. A stability analysis of the closed-loop system is given by Lyapunov method. Moreover, the design of the event-triggered mechanism can also exclude Zeno behavior of the switching signal without fixing a minimum dwell time. Finally, the effectiveness of the developed algorithm is evaluated by a numerical simulation.Note to Practitioners—This paper is motivated by the great potential switched nonlinear systems have demonstrated in improving system dynamic performances. However, the existing results mainly focus on optimal control for discrete-time switched nonlinear systems. Moreover, fairly few researchers have investigated the optimal switching and control co-design for switched nonlinear systems. Therefore, this paper develops a novel event-triggered adaptive dynamic programming algorithm that can learn the optimal hybrid control policy online. The design of the event triggering mechanism can exclude Zeno behavior of the switching signal. It is noteworthy that the proposed control method is of great significance for many practical systems, such as automotive engine systems and single-link robot arm systems.

The canal waterways of China still play an important role in the logistics and transportation industry. Unmanned technology helps to reduce costs and improve the safety of navigation. Real-time environmental awareness is vital to making unmanned surface vehicles (USVs) come true. This paper proposes a new lightweight environmental awareness method based on deep convolutional neural networks (DCNN) and a mixed attention mechanism for USVs in canals, which can simultaneously perform ship detection, segmentation, and surface and background segmentation tasks. The features of the ships, surface, and background are extracted by a shared feature extraction backbone network and hybrid attention mechanism, which improves the efficiency of visual environmental awareness. In addition, a dataset namedUSV-Canalis constructed to enrich the features of canal waterways for environmental awareness, which contains typical canal scenes and 3443 ship objects. To improve the generalization, multiple public datasets are mixed with theUSV-Canaldataset to build an integrated dataset to train our model, which boasts diversity in scene types and ship classes. The comparative and field experiments’ results show that 40.9% ofmAP, 95.8% ofmIoU,and 5 frames per second (FPS) inference speed can be achieved, and have good generalization, which can meet the requirements of environmental awareness of low-speed ships in canal waterwaysNote to Practitioners—The trained and validated model can ultimately be deployed on unmanned surface vehicles, and the required hardware platform is NVIDIA’s Jetson Nano, which is used for real-time perception of surrounding ships and navigable surfaces during navigation. The information can be integrated into the guidance, navigation, and control (GNC) system of USVs, achieving obstacle avoidance and ensuring safe navigation. It is vital to make autonomous navigation come true.

This paper discusses the issue of achieving the prescribed-time formation (PTF) over a directed topology for nonlinear multi-Agent systems (NMASs). A novel PTF protocol framework is proposed through the incorporation of a time-varying function for NMASs. Fuzzy Logic Systems (FLSs) are used to approximate potentially unknown nonlinear functions within the system. It is crucial to note that incorporating the adaptive control technique into the proposed protocol framework eliminates the adverse impact stemming from fuzzy approximation errors. Consequently, the formation errors of each agent converge to zero within the prescribed time. Additionally, through the introduction of a novel adaptive law, the protocol framework is further expanded to the NMASs with disturbances. Both the benefits and efficacy of the presented protocol are shown through numerical examples. Note to Practitioners—This paper delves into the pivotal issue within the realm of NMASs concerning prescribed-time formation control. This paper is motivated by the observation that current practices utilizing fuzzy controllers may not achieve the convergence of system formation errors to zero within the user-defined time frame. To solve this, the introduction of a prescribed-time control methodology is advocated, poised to expedite the formation convergence. Furthermore, the incorporation of an adaptive fuzzy controller is proposed to address challenges stemming from inaccurate system modeling, thereby ensuring the stringent control accuracy. The proposed framework harbors considerable potential for application across diverse industrial contexts, encompassing the realms of mobile robotics, unmanned aerial vehicles, and vehicular traffic management systems. Subsequent research endeavors can delve deeper into refining this approach and investigating methodologies for attaining prescribed time control within switched multi-agent systems.

This paper proposes a comprehensive framework for prescribed-time optimal switching and control (PTOSC) in switched systems. First, a new performance index function is defined, which considers the system state, specified time and accuracy, and control costs. This effectively incorporates the prescribed time control into the optimal control framework. Following this, a switched Hamilton-Jacobi-Bellman equation is derived. An event-triggered (ET) PTOSC algorithm, via reinforcement learning, is subsequently presented to solve this equation, and then the optimal control policies are derived. At each event-triggering instant, the switched controller determines which subsystem to activate, and the input controller updates the system inputs. The proposed PTOSC algorithm guarantees the stability of the switched systems and ensures the system states converge to a specified range within a specified time, all while minimizing energy consumption. Furthermore, the devised ET mechanism significantly reduces the communication burden and effectively avoids Zeno behavior. Finally, a simulation is performed to validate the proposed PTOSC algorithms’ effectiveness.Note to Practitioners—This paper addresses the critical problem in the field of switched systems of achieving prescribed-time optimal switching and control. Current practices might not adequately balance convergence accuracy, settling time, and cost-saving, which is the motivation for this paper. The presented control method is of great significance for many practical processes, such as power systems, robot control, and water-air amphibious vehicles. The feasibility of this new approach is confirmed through simulation. Future research can further refine this approach and explore how to achieve the prescribed-time optimal control for multi-agent systems or multi-player non-zero-sum games.

This article seeks the Nash equilibrium solutions for mixed zero-sum (MZS) games in unknown switched nonlinear systems. A new paradigm is presented, which offers a framework for analyzing strategic interactions of MZS games. To solve the coupled switching Hamilton–Jacobi equations, an event-triggered fuzzy reinforcement learning strategy is proposed. An identifier is designed to approximate the system's unknown nonlinear dynamics, and a critic is proposed to guide policy optimization. The proposed algorithm achieves Nash equilibrium while ensuring system stability. In addition, Zeno behavior is avoided, and the computational and communication loads are reduced. Finally, two simulation examples are provided to verify the effectiveness of the proposed method.

This paper proposes a decentralized adaptive fuzzy event-triggered fault-tolerant control scheme for nonlinear switched interconnected systems under arbitrary switchings. A novel state observer is crafted to estimate unmeasured states by using the faulty output signal. Interval type-2 fuzzy logic systems are adopted to deal with uncertain nonlinearities. The Nussbaum gain technique and a novel fault compensation mechanism are utilized to deal with actuator and sensor faults. A switching threshold event-triggered control strategy is developed to guarantee that all closed-loop signals are bounded, meanwhile the Zeno behavior is excluded. Eventually, a practical simulation illustrates the validation of the theoretical findings.

This article investigates the consensus problem of multiple heterogeneous uncertain Euler–Lagrange systems with limited communication range and input saturation. Due to the heterogeneity of the system, it is difficult to directly design a protocol to achieve consensus. To deal with it, a virtual system framework is proposed such that the consensus problem can be decoupled into two simpler subproblems: consensus among virtual systems and tracking of virtual states by actual agents. Since two agents will lose connection when their distance is greater than limited communication range, large control inputs are required to maintain topological connectivity. However, in practical applications, the existence of input saturation constraints may cause insufficient torque generation and potential connectivity loss. To address this issue, virtual system interaction protection rules are further proposed. The requirements on the connectivity maintenance can be relaxed by allowing temporary disconnections between agents. Finally, a numerical example is provided to verify the effectiveness of the proposed protocol.

This article investigates the optimal consensus problem for a class of nonlinear multiagent systems (MASs) under an event-triggered mechanism (ETM) and switching topologies. By employing an adjusted backstepping technique, a more specific form of the backstepping optimal consensus protocol is presented, enabling the designed actor–critic networks to approximate an explicit target. Due to the incomplete knowledge of the system dynamics, a novel adaptive identifier is developed to approximate unknown nonlinear functions. Moreover, the energy of the MAS is taken into account when designing the dynamic thresholds. Specifically, two novel thresholds are introduced, which update alternately and correspond to fast and slow time scales, respectively. These specialized designs ensure the prevention of Zeno behavior and enable events to be triggered more adaptively. The optimal consensus of the MAS is guaranteed through a mathematical proof using a common Lyapunov function, ensuring that Zeno behavior is avoided. Finally, a simulation is provided to validate the effectiveness of the proposed control strategy.

Considering total disturbances, i.e., parameter variation, model error, and load mutation, an adaptive active disturbance rejection control (adaptive ADRC) method is proposed to regulate the speed of permanent magnet synchronous motor system (PMSMs) in this article. First, a tracking state space model of a PMSMs is structured with adaptive parameter estimation of inertia and flux. Second, a nonlinear extended state observer (ESO) based on an adaptive law is designed to estimate the total disturbances for feedforward compensation. A finite time bounded stability theory is established to analyze the proposed nonlinear ESO. In addition, the stability of the closed-loop system is proved by a Lyapunov stability theory based on a proposed positive definite scalar function. Finally, the speed regulation and antidisturbance performances of the proposed adaptive ADRC controller are verified by an experimental platform based on DSPF28335 and MATLAB/SIMULINK. The reliability and superiority of the proposed controller are verified by simulation and experiment results.

Low-cost heading sensors and environmental interference lead to significant heading measurement error (HME) in Autonomous Surface Vehicles (ASVs), necessitating compensation to enhance path-following accuracy. To address this, we propose a compensated event-triggered line-of-sight (CET-LOS) guidance law. The core objective is to rapidly estimate and compensate for HME using an exponential estimation model. Specifically, the exponential model enables fast HME estimation, while an event-triggered mechanism, based on the convergence state of the cross-track error, ensures accurate error estimation. Additionally, the integral term from the integral LOS (ILOS) is utilized to refine the error estimation further. Experimental comparisons of CET-LOS with LOS, ILOS, and adaptive LOS (ALOS) demonstrate its effectiveness. For straight-line paths, the average cross-track error is reduced by 72.3%, 34.5%, and 62.3%, respectively. For complex paths, the reductions are 43.8%, 34.0%, and 29.2%, respectively. These results highlight the superiority of the proposed method.

This article addresses the data-based optimal switching and control codesign for discrete-time nonlinear switched systems via a two-stage approximate dynamic programming (ADP) algorithm. Through offline policy improvement and policy evaluation, the proposed algorithm iteratively determines the optimal hybrid control policy using system input/output data. Moreover, a strict proof of the convergence is given for the two-stage ADP algorithm. Admissibility, an essential property of the hybrid control policy must be ensured for practical application. To this end, the properties of the hybrid control policies are analyzed and an admissibility criterion is obtained. To realize the proposed Q-learning algorithm, an actor-critic neural network (NN) structure that employs multiple NNs to approximate the Q-functions and control policies for different subsystems is adopted. By applying the proposed admissibility criterion, the obtained hybrid control policy is guaranteed to be admissible. Finally, two numerical simulations verify the effectiveness of the proposed algorithm.

This article investigates cluster synchronization (CS) of individuals during an epidemic using a coupled nonlinear network that integrates diffusion-coupled nonlinear systems with an susceptible-infected-recovered (SIR) virus model. To better reflect real-life scenarios, individuals are grouped into clusters, and the model incorporates recovery rates that vary according to collective behavior patterns. The study focuses on analyzing the relationship between CS behavior and the progression of virus transmission within the network. By ensuring that the directed graph satisfies the cluster input equivalence condition and that the system’s Jacobian matrix remains bounded, contraction analysis is employed to establish conditions for achieving CS, which are influenced by the virus’s state. Furthermore, the impact of CS on epidemic dynamics is explored. Numerical simulations validate the theoretical findings.

This article investigates Nash equilibrium seeking for nonzero-sum games of switched nonlinear systems. A novel cost function is presented that measures the system state cost and control cost while considering the dynamics under different switching modes. Then, a new coupled switching Hamilton-Jacobi (HJ) equation is derived. To address the challenge of directly solving the HJ equation, an event-triggered two-stage reinforcement learning strategy is proposed. Upon event triggering, each player’s switching law determines the optimal subsystem to switch to by minimizing the HJ equation. Subsequently, the corresponding learning law for each player updates its respective input via the determined optimal subsystem. The proposed algorithm achieves Nash equilibrium while ensuring system stability. Furthermore, Zeno behavior is avoided, and the computational and communication loads are reduced. Finally, the proposed algorithm’s efficacy is substantiated through two simulation examples.

The subject of this study is fuzzy predefined-time control for a class of switched nonlinear systems with multiple faults. In comparison to existing research on predefined-time control, this study delves into the realm of switched nonlinear systems, encompassing switched linear sensor faults and switched nonaffine faults. The difficulty in the controller design lies in following the backstepping technique, as taking the derivative of fractional power virtual control laws would trigger singularity issues at equilibrium states or coordinate transformation origins. The study utilizes the unique characteristics of switching and fuzzy logic systems to introduce a continuous piecewise predefined-time controller with a fault-tolerant compensation mechanism to avoid singularity problems. By adjusting a predefined parameter in the developed controller, the system could achieve the objectives of adaptive stability and adaptive tracking within a predefined time, as desired by the user. Moreover, the application of the proposed algorithm to practical systems is presented.

This paper investigates the predefined-time consensus for a class of second-order nonlinear multi-agent systems via sliding mode technique. Fuzzy logic systems are utilized to estimate unknown continuous functions. Sliding mode control is employed to address the estimation errors generated by the estimation process and terms caused by unmodeled dynamics. By incorporating hyperbolic tangent functions into the protocol and utilizing their properties, singularity issues are avoided. A predefined-time fuzzy protocol is designed to ensure that the consensus error reaches a small neighborhood near zero within the predefined time. The effectiveness of the proposed approach is demonstrated through a simulation example.

This article investigates multiasynchronous control for asymptotic stabilization (AS) in mean-square and nonweighted$\mathcal {L}_{2}$-gain for a class of switched Takagi–Sugeno fuzzy systems with both time-varying delay and infinite-time distributed delay (mixed delays) as well as cyber-attacks. The proposed event-triggered controller not only is mode-dependent but also excludes Zeno behavior automatically with two tunable parameters to adjust the event-triggering (ET) number. A novel Lyapunov–Krasovskii functional (LKF) with a negative term is established to greatly reduce the conservatism and simplify the analysis of nonweighted$\mathcal {L}_{2}$-gain by ensuring its increment at switching instants be smaller than one. Three main results are provided to guarantee the AS in mean-square and design the control gains and weights of the ET mechanism, as well as the optimal nonweighted$\mathcal {L}_{2}$-gain. Compared with existing results, the new asynchronous control techniques eliminate the limitation of divergence in mismatched intervals for LKF. Numerical simulations demonstrate the merits of the theoretical analysis.

Addressed in this paper is the problem of observer-based periodic event-triggered (PET) adaptive fuzzy control for a class of nonlinear systems adopting a predictor approach. In most existing results on PET output- feedback control, only the system output at sampling instants is available for observer design. For the use of more effective information in observer, a predicted signal of the continuous system output is generated by a predictor and used for the construction of observer. Then, a dynamic gain is introduced to the construction of Lyapunov function to ensure the decreasing property of the developed Lyapunov function at sampling instants. Owing to this good property, the PET adaptive controller can be designed using adaptive fuzzy control and backstepping techniques. It is proved that the system states are locally bounded and converge to a small neighborhood of the origin under given sampling period and controller. Finally, two examples are provided to verify the effectiveness and advantage of the proposed control method.

This article focuses on finite-time$\mathcal {L}_{2}$stabilization of T–S fuzzy systems with time delays and parameter uncertainties via intermittent control. To cope with the effects of parameters uncertainties, time delays, and intermittent divergence simultaneously, a new finite-time stability lemma for intermittently controlled systems is presented. Then, a weighted 2-norm Lyapunov–Krasovskii functional (LKF) is established, which has the advantage that it is convenient to derive less conservative linear matrix inequality sufficient conditions and to overcome the difficulty in analyzing$\mathcal {L}_{2}$performance under intermittent control frameworks. Another advantage of our result over existing results is that the growth increment of the LKF on the noncontrolled interval can be larger than the decreasing magnitude on the controlled interval. The merits of the theoretical results are examined by a numerical example and a coupled Chua's circuit.

This article investigates the optimal tracking problem for discrete-time autonomous nonlinear switched systems with the switching cost. To avoid excessive switching frequency, the switching cost between modes is considered in the performance index, which means that the optimal switching policy is not only related to the tracking error but also the mode applied at the previous instant. The objective is to make the system state track the reference signal while minimizing the defined performance function. A model-free Q-learning algorithm that learns the optimal switching policy from real system data is developed. Furthermore, it is proved by mathematical induction that the iterative Q-functions generated by the proposed Q-learning algorithm will converge to the optimum. To implement the Q-learning algorithm, fuzzy logic systems (FLSs) are applied to approximate the iterative Q-functions. A novel structure of FLSs is designed to ensure the validity of Q-function approximation. Finally, simulation results demonstrate the effectiveness and advantages of the algorithm.

A collision-free formation control problem for multiple unmanned aerial vehicles (UAVs) with directed switching topologies and disturbances is investigated. A novel distributed control algorithm that uses UAVs local directed switching information is proposed for achieving the required flight formation and ensuring a safe distance between UAVs; the algorithm involves the incorporation of the APF method in the virtual leader formation scheme. Two command signals generated by the virtual position controller are transmitted to the attitude subsystem. For each UAV, an adaptive composite controller is designed by combining a fuzzy system and fast terminal sliding mode control technique to guarantee that tracking errors converge to a stable area around zero. Finally, the feasibility of the proposed composite control algorithm is demonstrated through a simulation.

The prescribed-time optimal control problem for nonlinear systems is investigated in this article. First, a transformation function is constructed, which includes the system state and a strictly decreasing auxiliary function related to the prescribed time and accuracy. Second, the control input and the transformation function are incorporated into a new performance index function. This encodes the prescribed-time control into the optimal control problem. Subsequently, a new Hamilton–Jacobi–Bellman (HJB) equation related to the prescribed time and accuracy is derived. To find a solution to the HJB equation, a fuzzy reinforcement learning algorithm is proposed. This algorithm successfully approximates the optimal cost and control policy while ensuring the system stability. Additionally, the system state can converge to a preassigned residual set within a prescribed time. Finally, an example of an electromechanical system is used to illustrate the efficacy of the suggested algorithm.

This article investigates the Nash equilibrium seeking issue in$N$-player nonzero-sum (NZS) games. First, prescribed-time control is a priori encoded into the framework of$N$-player NZS games by defining a cost function that considers the interactions between multiple players and prescribed-time performance requirements. To tackle the complex challenge of solving the coupled Hamilton–Jacobi (HJ) equation, a fuzzy adaptive learning algorithm within the prescribed-time frame is proposed. An identifier is constructed to address the lack of prior knowledge about the system's nonlinear dynamics. Critic and actor-tuning laws are designed to approximate optimal value functions and Nash equilibrium strategies. The proposed algorithm achieves Nash equilibrium and ensures the system state converges to a prescribed range within a specified time. Finally, the feasibility of the proposed algorithm is substantiated through a simulation example involving three-player games.

In this article, we investigate the prescribed-time fuzzy optimal tracking control for autonomous surface vehicles (ASVs). A monotonically decreasing boundary function that incorporates the settling time and tracking accuracy is proposed. A coordinate transformation on the boundary function and tracking error is proposed, and then an augmented system is defined. Subsequently, a new performance index function is presented that considers both the prescribed performance costs and control input costs. Given the inherent difficulties when directly resolving the Hamilton–Jacobi–Bellman equation within the prescribed-time framework, a new fuzzy optimal control scheme is proposed via integral reinforcement learning. This scheme does not require knowledge on the drift dynamics in the designed control policy and tuning laws, guarantees the simultaneous approximation of the optimal value function and control policy, ensures the stability of the ASV system, and allows users to specify the settling time and tracking accuracy. Finally, the presented strategy's effectiveness is validated by simulation.

This article is devoted to solving an adaptive finitetime sampled-data stabilization problem for a class of fractionalorder nonlinear systems (FONSs). By taking advantage of type-2 fuzzy logic systems (FLSs), the uncertainties existed in considered system are able to be approximated, and one adaptive fuzzy finitetime sampled-data stabilizer (AFFSS), which possesses switching dynamics, is developed by following backstepping approach. By the crucial effects of those switching dynamics, the “singularity phenomenon” which is happened in taking the derivative of such AFFSS at equilibrium state can be efficiently avoided. In addition, when such stabilizer with allowable design scalars and sampling period is imposed on the considered FONS, the closed-loop system under consideration can reach practically finite-time stable (PFS), it can be verified with the aid of the selected Lyapunov function candidate (LFC). In the end, the developed stabilization scheme is respectively applied for a numerical and an engineering examples to verify its effectiveness.

The collision avoidance in real-time is crucial for unmanned surface vehicles (USVs) in a complex environment. Traditional methods make it hard to ensure the balance of control decisions. To balance safety and practicality, a collision avoidance algorithm based on deep reinforcement learning (DRL) and a two-level incentive reward based on the principle of complementarity is proposed. To address the vital sparse reward problem of Deep Deterministic Policy Gradient (DDPG), the trajectory evaluation function of the dynamic window algorithm (DWA) is referred to construct the primary reward strategy, and a secondary incentive reward is constructed based on velocity obstacle (VO) to eliminate potential collision risks. To improve the efficiency of training, the electronic chart (EC) and Unity3D are used to build an immersive simulation platform. Based on it, simulations are made to verify the performance. In addition, field experiments are first conducted in various encounter scenarios to verify the effectiveness. The results show that it can take safe collision avoidance actions and get practical paths in various situations.

This article considers the connectivity-preserving consensus for a class of multiagent systems under the event-triggered mechanism (ETM). By employing the topology hierarchical decomposition method, unnecessary communication interactions can be reduced. Each agent receives state information from one specific agent and sends messages to some other agents. A hybrid ETM is proposed to reduce communication costs and save computational resources for agents. Additionally, distributed state observers are designed to estimate the information of other agents under the ETM. Moreover, a novel connectivity-preserving error function is designed to maintain the connection between two neighboring agents. With the help of this function, a fully distributed connectivity-preserving consensus protocol for the considered multiagent system under directed graphs is proposed. The update of the protocol relies on the designed observer under the ETM. Finally, one example is presented to verify the efficiency of the theoretic designs.

The leader-following formation control is investigated for heterogeneous multiple unmanned surface vehicles with unknown upper bound disturbances and uncertain parameters in this article. Each vehicle has a limited communication range, restricting the information exchange between neighboring vehicles to a specified radius. Due to the limitations of sensors and communication components, the communication frequency between vehicles is taken into account. First, a novel hybrid event-triggered virtual trajectory generation protocol is proposed. In such a protocol, each vessel generates its reference states in real-time without requiring real-time information from its neighbors. Then, by designing error-constrained tracking controller and connectivity-preserving potential function, the initial connectivity of the topology is maintained. Furthermore, fuzzy logic approximation and adaptive control techniques are combined in order to tackle the issues of disturbances and uncertain parameters. Through the Lyapunov method, it is proven that formation errors converge to zero as time approaches infinity. Finally, the effectiveness of the proposed protocol is verified through a simulation involving a cluster of seven vehicles.

This article studies sampled-data stabilization for a class of fractional-order switched nonlinear systems (FOSNSs) with arbitrary switching. The feasibility of using a fuzzy-logic system (FLS) to approximate the fractional-order systems (FOSs) is proved. Using backstepping method, the fractional-order adaptive update laws and sampled-data controller for the discussed FOSNSs are designed based on the FLS. Under the proposed sampled-data control scheme, it is proved that solutions of the studied FOSNSs are semi-globally uniformly ultimately bounded (SGUUB). Two examples are given to verify the effectiveness of the proposed sampled-data control scheme.

This article investigates an adaptive event-triggered fixed-time fault-tolerant consensus control for a category of multiagent systems (MASs). First, radial basis function (RBF) neural networks (NNs) are applied to handle unknown nonlinear terms. Furthermore, the backstepping technique is employed to construct the fixed-time event-triggered consensus control scheme by utilizing the command filter technique. The proposed scheme can guarantee the boundedness of all signals in the closed-loop system and the fixed-time convergence of consensus error. Additionally, a simulation example is presented to verify the validity of the presented results.

This article presents a positivity analysis and exponential stabilization design for singular switched positive systems (SSPSs) with actuator saturation under a mode-dependent minimum dwell time (MDMDT) constraint. First, a necessary and sufficient positivity criterion is proposed for SSPSs using the singular value decomposition approach. Then, an exponential stability condition is provided for the closed-loop SSPSs via the mode-dependent state-feedback control using a novel discretized linear copositive Lyapunov function technique. Furthermore, by applying the matrix decomposition technique to the controller gain matrix and controller auxiliary gain matrix, an effective mode-dependent design scheme for a saturation controller in the solvable linear programming (LP) form is proposed for the SSPSs. For singular positive systems, an effective saturation control scheme in the solvable LP form can be obtained accordingly. Finally, three examples are provided to validate the results.

This article puts forward an observer-based finite-time sampled-data stabilization scheme for a nonlinear time-delay system. To overcome the difficulties of stabilizing such nonlinear system under consideration, a reduced-order observer, whose role lies in estimating unavailable states, is formulated by relying on detectable sampled output, subsequently, a finite-time sampled-data output-feedback stabilizer (FSOS), which possesses suitable scalars and sampling period, can be developed with the help of adding a power integrator (AAPI) technique, such stabilizer can drive the formulating closed-loop system to be globally practically finite-time stable (GPFS) in the presence of uncertain time delays, which requires to be verified by means of established Lyapunov-Krasovskii functionals (LKFs). The availability of the developed scheme can be reflected by two simulations in the end.

The current paper is devoted to studying global asymptotic$H_{\infty }$drive-response synchronization for a kind of switched nonlinear time-delay systems with output random injection attacks (IAs). An attack-decomposition method is proposed to derive an attack-free signal, by which an observer is designed to estimate the state of the driving system. Then, two mode-dependent event-triggering mechanisms (MDETMs) are respectively designed for observer-controller (O-C) and controller-actuator (C-A) channels to save the communication resources as much as possible. In order to analyze the effects of the switching on the$H_{\infty }$performance, a mode-dependent discretized Lyapunov-Krasovskii functional (LKF) is developed, which has the merit of monotone decreasing on any time-interval and switching instants. Sufficient criteria are given to ensure the$H_{\infty }$synchronization with non-weighted$\mathcal {L}_{2}$-gain, whether the attack is related to the output or not. Numerical simulations are provided to verify the non-weighted$\mathcal {L}_{2}$-gain performance with low conservatism.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

In this study, the sampled-data consensus problem is investigated for a class of heterogeneous multiagent systems (MASs) in which each agent is described by a second-order switched nonlinear system. Owing to the heterogeneity and the occurrence of dynamic switching in the MASs, the sampled-data consensus protocol design problem is challenging. In this study, two periodic sampled-data consensus protocols and an event-triggered consensus protocol are developed. Here, we first propose a new periodic sampled-data consensus protocol that involves the local objective trajectory interaction among agents. The protocol is then improved by applying the finite-time control and sliding-mode control techniques. Notably, the improved protocol can be implemented without the transmission of constructed auxiliary dynamical variables, which is a major feature of the present study. It is shown that complete consensus of the underlying MASs can be achieved by the two proposed protocols with only sampled-data measurements. To further reduce the communication load, we introduce an event-triggered mechanism to obtain a new protocol. Finally, the effectiveness of the given schemes is demonstrated by considering a numerical example.

The adaptive fuzzy predefined-time tracking control problem for a class of nonlinear systems with output hysteresis is investigated in this article. An inverse model is utilized to capture the output hysteresis phenomenon, and then, the Nussbaum-type function technique is utilized to overcome the difficulty of unknown time-varying control gain caused by output hysteresis. An adaptive fuzzy control scheme under the backstepping framework is developed using the predefined-time stability criterion. Different from the existing predefined-time design approaches, the adaptive law designed in this article is represented as a nonlinear differential equation. Theoretical analysis demonstrates that all signals of the closed-loop systems are bounded, and the tracking error can converge to the neighborhood near the origin within an expected settling time. The developed scheme's feasibility is verified by an example of an electromechanical system.

This article focuses on developing an adaptive output feedback fault-tolerant fixed-time tracking control strategy for a class of switched nonlinear systems with nonaffine faults. To approximate the unmeasurable states, a mode-dependent state switched fuzzy observer is generated using fuzzy logic systems and a Butterworth low-pass filter. Next, an adaptive fixed-time tracking control strategy is developed by combining dynamic surface technology with the backstepping method. An improved mode-dependent average dwell-time switching rule is also introduced to ensure the stability of switched nonlinear systems with unstable subsystems. A stability analysis proves the effectiveness of the proposed control scheme in stabilizing the switched nonlinear system under mode-dependent average dwell-time switching, ensuring that the tracking error reaches the residual set within a derived settling time. Finally, a switched resistor–inductor–capacitor circuit example is provided to demonstrate the validity of the proposed strategy.

This article investigates the adaptive fixed-time fault-tolerant tracking fuzzy control issue for nonlinear switched systems with dynamic uncertainties. Actuator faults considered in this article simultaneously contain the loss of effectiveness and time-varying bias fault depending on the switching signal. The generated scheme extends the fixed-time convergence to switched nonlinear systems with unmodeled dynamics. An improved adaptive fixed-time fault-tolerant controller is proposed by employing the backstepping method and fuzzy logic estimator. In particular, the presented framework removes the singularity, and the convergence time is assignable for any initial condition. Finally, a numerical simulation example and a resistor-capacitor-inductor circuit system example are given to prove the system output can converge to a desired trajectory within a fixed time.

This article investigates a distributed fuzzy adaptive formation control for quadrotor multiple unmanned aerial vehicles (UAVs) under unmodeled dynamics and switching topologies. The UAVs dynamics model is described by the Newton–Euler formula, and the actuator faults are considered in the system model in the form of multiplicative factors and additive factors. Due to the underactuated characteristics of the UAVs, two objective attitude commands are generated by designing a virtual control signal, which are transmitted to the attitude subsystem, and then the position controller is solved. By constructing a distributed communication mechanism between UAVs, an adaptive formation control strategy is proposed, which can enable UAVs to update their position and speed online according to their neighbor information, and then achieve the required formation. In addition, a fuzzy adaptive sliding mode controller is designed to ensure that the tracking errors of UAVs converge to the neighborhood of the origin. Finally, the simulation results verify the effectiveness of the proposed control strategy.

This article concerns optimal prescribed-time formation control for a class of nonlinear multiagent systems (MASs). Optimal control depends on the solution of the Hamilton–Jacobi–Bellman equation, which is hard to be calculated directly due to its inherent nonlinearity. To overcome this difficulty, the reinforcement learning strategy with fuzzy logic systems is proposed, in which identifier, actor, and critic are used to estimate unknown nonlinear dynamics, implement control behavior, and evaluate system performance, respectively. Different from the existing optimal control algorithms, a new performance index function considering formation error cost and control input energy cost is constructed to achieve optimal formation control of MASs within a prescribed time. The presented control strategy can ensure that the formation error converges to the desired accuracy within a prescribed time. Finally, the validity of the presented strategy is verified via a simulation example.

The problem of neural adaptive distributed formation control is investigated for quadrotor multiple unmanned aerial vehicles (UAVs) subject to unmodeled dynamics and disturbance. The quadrotor UAV system is divided into two parts: the position subsystem and the attitude subsystem. A virtual position controller based on backstepping is designed to address the coupling constraints and generate two command signals for the attitude subsystem. By establishing the communication mechanism between the UAVs and the virtual leader, a distributed formation scheme, which uses the UAVs' local information and makes each UAV update its position and velocity according to the information of neighboring UAVs, is proposed to form the required formation flight. By designing a neural adaptive sliding mode controller (SMC) for multi-UAVs, the compound uncertainties (including nonlinearities, unmodeled dynamics, and external disturbances) are compensated for to guarantee good tracking performance. The Lyapunov theory is used to prove that the tracking error of each UAV converges to an adjustable neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.

In this article, an adaptive finite-time tracking control scheme is developed for a category of uncertain nonlinear systems with asymmetric time-varying full-state constraints and actuator failures. First, in the control design process, the original constrained nonlinear system is transformed into an equivalent "unconstrained" one by using the uniform barrier function (UBF). Then, by introducing a new coordinate transformation and incorporating it into each recursive step of adaptive finite-time control design based on the backstepping technique, more general state constraints can be handled. In addition, since the nonlinear function in the system is unknown, neural network is employed to approximate it. Considering singularity, the virtual control signal is designed as a piecewise function to guarantee the performance of the system within a finite time. The developed finite-time control method ensures that all signals in the closed-loop system are bounded, and the output tracking error converges to a small neighborhood of the origin. At last, the simulation example illustrates the feasibility and superiority of the presented control method.

In this article, a hybrid event-triggered control protocol is proposed to solve the consensus problem for a class of multiple uncertain Euler–Lagrange systems with limited communication range. The limited communication range will cause the system topology to be time varying. A novel connectivity-preserving mechanism based on the potential function is designed to guarantee the connectivity of initial edges. Then, we introduce an event triggering mechanism to save communication resources. It is noted that connectivity-preserving control often requires continuous communication as the system states needs to be monitored in real time to ensure that the connection will not be destroyed. Thus, it is difficult to combine event-triggered control with connectivity-preserving control. In this article, we design a novel event-triggered hybrid condition without the real-time neighbors’ information and we exclude Zeno behavior. Finally, a numerical example is given to verify the effectiveness of the protocol.

This article develops a global finite-time stabilization algorithm for a type of upper-triangular nonlinear systems, and the controlled system under consideration covers the input delay. A reduced-order observer (ROO) is established by relying on the sampled detection of the output to realize the state evaluation. By the stabilizer establishment method of backstepping, together with adding a power integral technique, a finite-time sampled-data stabilizer is established under output feedback framework, and with the aid of the proper Lyapunov–Krasovskii functionals (LKFs), the unstable dynamics covered in the existed delays can be efficiently restrained through the developed stabilizer with the reasonable design scalars and sampling period, the corresponding closed-loop system can be further regulated to meet practically finite-time stable in global sense. In the end, a simulation example for a circuit system is presented to check the raised algorithm.

In this study, an adaptive fuzzy decentralized dynamic surface control (DSC) problem is investigated for switched large-scale nonlinear systems with deferred asymmetric and time-varying full-state constraints. Due to the existence of additional general nonlinearities, complicated output interconnections, and full-state constraints, it is difficult to address the above control problem using existing methods. Fuzzy-logic systems are, therefore, utilized to approximate the unknown nonlinear functions, and the DSC technique is adopted to overcome the "curse of dimensionality" problem. A novel fuzzy adaptive decentralized controller design is presented using the proposed convex combination technique. Furthermore, it is proven that under the proposed controller and state-dependent switching law, all states of the closed-loop system are bounded and deferred asymmetric, and the time-varying full-state constraints are strictly obeyed. The simulation results are presented to demonstrate the effectiveness of the proposed method.

A decentralized adaptive fuzzy sampled-data control problem for switched large-scale nonlinear systems with time-varying delays is considered in this article. Fuzzy logic systems are applied to handle unknown nonlinear terms. A novel fuzzy adaptive law is proposed utilizing only the information of the system states at sampling instants. Moreover, a proper CLF and a new decentralized adaptive sampled-data control law are constructed to ensure that all states of the CLS are bounded. The developed strategy’s effectiveness is verified with two examples.

This article focuses on an adaptive fuzzy dynamic event-triggered tracking control for nonlinear time-delay systems with unmodeled dynamics via a command filter method. Fuzzy logic systems are utilized to address the unknown nonlinear functions. The upper bound of the approximation error is allowed to be unknown and can be compensated by skillfully introducing a hyperbolic tangent function to the design of the adaptive laws. Meanwhile, without requiring any assumptions, time delays can be handled by appropriately incorporating the delayed nonlinear functions into the Lyapunov–Krasovskii functional. Then, a dynamic event-triggered control mechanism is designed to dynamically adjust the threshold parameter. Finally, a new adaptive controller is constructed such that all states of the closed-loop system are bounded. The system output is demonstrated to follow the desired signal. Two examples are given to illustrate the validity of the presented method.

This article presents a decentralized fuzzy adaptive event-triggered command-filtered control scheme for switched large-scale nonlinear systems with input delay. Fuzzy logic systems are employed to approximate uncertain nonlinearities and a novel observer is constructed to estimate unmeasured states. The “explosion of complexity” defect inherent in the backstepping approach is overcome by employing command filter technology. An auxiliary system is designed to compensate for the effect of input delay, and a novel event-triggered decentralized controller is derived based on the common Lyapunov function method. This article shows that the presented strategy guarantees that all closed-loop variables are semiglobally uniformly ultimately bounded. Finally, simulation results are shown to further confirm the presented strategy’s validity.

In this article, a decentralized adaptive neural network (NN) event-triggered sensor failure compensation control issue is investigated for nonlinear switched large-scale systems. Due to the presence of unknown control coefficients, output interactions, sensor faults, and arbitrary switchings, previous works cannot solve the investigated issue. First, to estimate unmeasured states, a novel observer is designed. Then, NNs are utilized for identifying both interconnected terms and unstructured uncertainties. A novel fault compensation mechanism is proposed to circumvent the obstacle caused by sensor faults, and a Nussbaum-type function is introduced to tackle unknown control coefficients. A novel switching threshold strategy is developed to balance communication constraints and system performance. Based on the common Lyapunov function (CLF) method, an event-triggered decentralized control scheme is proposed to guarantee that all closed-loop signals are bounded even if sensors undergo failures. It is shown that the Zeno behavior is avoided. Finally, simulation results are presented to show the validity of the proposed strategy.

This article is concerned with the stochastic stability and$l_{1}$-gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact$l_{1}$-gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the$l_{1}$-gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal$l_{1}$-gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples.

This work discusses the fault detection problem for two-dimensional (2-D) positive systems (PSs) with distributed delays. First, a systematic method is proposed for the computation of exact values of $\ell _{1}$ -gain and $\ell _{-}$ index for delay-free systems, and the dimension expansion technique is used to transfer the computation of $\ell _{1}/\ell _{-}$ index for 2-D delayed PSs to one of the delay-free systems. Second, necessary and sufficient conditions are established such that the 2-D delayed PSs are asymptotically stable with a desired $\ell _{1}/\ell _{-}$ performance level (PL) $\gamma /\beta $ . Third, based on the above results, some NCSs are established such that the disturbance and the fault impact on the output signal are minimized and maximized, respectively. An algorithm (iterative) is formulated for the solution of the convex optimization problem. Finally, the potency and accuracy of the developed theoretical results are exhibited by an example.

This article presents a stabilization achievement for a switched nonlinear time-delay system through output-feedback control under the sampled-data and global senses. An observer with the sampled output measurement is constructed to evaluate the unavailable states, and then a controller formed from the sampled observer states is given. For the stability analysis, a merging virtual switching signal (MVSS) is created to express the asynchronous switching mechanism in the resultant closed-loop system. Through designating a positive-definite function as the Lyapunov function candidate, a proof is conducted to reveal that global stability can be ensured for the considered systems which work under the time-varying delay case and the developed sampled-data controller with a switching restriction. Finally, two examples are provided in this article to indicate the given control strategy usefulness.

We study the containment control problem for high-order heterogeneous nonlinear multi-agent systems under distributed event-triggered schemes. To achieve the containment control objective and reduce communication consumption among agents, a distributed event-triggered control scheme is proposed by applying the backstepping method, Lyapunov functional approach, and neural networks. Then, the results are extended to the self-triggered control case to avoid continuous monitoring of state errors. The developed protocols and triggered rules ensure that the output for each follower converges to the convex hull spanned by multi-leader signals within a bounded error. In addition, no agent exhibits Zeno behavior. Two numerical simulations are finally presented to verify the correctness of the obtained results.

This study considers an adaptive neural-network (NN) periodic event-triggered control (PETC) problem for switched nonlinear systems (SNSs). In the system, only the system output is available at sampling instants. A novel adaptive law and a state observer are constructed by using only the sampled system output. A new output-feedback adaptive NN PETC strategy is developed to reduce the usage of communication resources; it includes a controller that only uses event-sampling information and an event-triggering mechanism (ETM) that is only intermittently monitored at sampling instants. The proposed adaptive NN PETC strategy does not need restrictions on nonlinear functions reported in some previous studies. It is proven that all states of the closed-loop system (CLS) are semiglobally uniformly ultimately bounded (SGUUB) under arbitrary switchings by choosing an allowable sampling period. Finally, the proposed scheme is applied to a continuous stirred tank reactor (CSTR) system and a numerical example to verify its effectiveness.

The adaptive fuzzy finite-time tracking control problem of a class of switched nonlinear systems is investigated in this study. Fuzzy logic systems are introduced to handle the unknown nonlinear terms in the considered system. To overcome the drawback in the recursive design method, a finite-time command filter is employed. By constructing a new state-dependent switching law and adaptive fuzzy control signal, the existing restrictions on subsystems of switched systems are relaxed, all subsystems of the considered system are allowed to be unstabilizable. To avoid the Zeno behavior, a new hysteresis switching law is derived. It is proven that all states of the closed-loop system are bounded in finite time under the proposed fuzzy finite-time control scheme. Additionally, the proposed control method is extended to a class of more general switched large-scale nonlinear systems. Finally, two examples are provided to verify the developed method's effectiveness.

In this article, the distributed fault-tolerant consensus tracking control problem is investigated for a class of nonlinear multiagent systems, where the dynamics of agents are heterogeneous and switched. For the subsystems of each agent, nonlinear terms are not required to satisfy any growth conditions and fuzzy logic systems are employed to approximate unknown functions. In the protocol design, information on the interaction topology and the number of agents cannot be used. Since the underlying multiagent systems are heterogeneous and have switching characteristics, and the topology information is unknown, it is rather difficult to solve the consensus tracking problem using existing algorithms. In this article, a novel distributed consensus tracking protocol is developed. By using the graph theory, Lyapunov functional method and fuzzy logic systems approximation technique, it is proven that the consensus tracking control objective can be achieved for multiagent systems suffering from actuator faults and arbitrary switchings. Finally, to demonstrate the validity of the developed methodology, a numerical simulation is presented.

The global output feedback stabilization problem is investigated in this paper via sampled-data control for switched nonlinear systems in the p-normal form. First, a reduced-order state observer is designed. Then, an output feedback sampled-data controller is constructed with the relaxation of some restrictions of switched nonlinear systems. The proposed controller can ensure that all states of the corresponding closed-loop system can converge to the origin. Simulation results are given to show the effectiveness of the proposed scheme.

This article investigates the sampled-data stabilization problem of a class of switched nonlinear systems. All subsystems of the considered system are allowed to be unstabilizable. To relax the restrictions on unknown nonlinear functions in some existing results, we use the nonlinear approximation ability of radial basis function neural networks. Novel mode-dependent adaptive laws and sampled-data control laws are constructed by only using the system states' information at sampling instants. A novel sampled-data switching condition is derived, which can avoid Zeno behavior effectively. To guarantee that all states of the closed-loop system (CLS) are bounded, a new allowable sampling period is deduced. Finally, we demonstrate the proposed method's effectiveness through two examples.

In this paper, the consensus tracking problem is investigated for a class of continuous switched stochastic nonlinear multiagent systems with an event-triggered control strategy. For continuous stochastic multiagent systems via event-triggered protocols, it is rather difficult to avoid the Zeno behavior by the existing methods. Thus, we propose a new protocol design framework for the underlying systems. It is proven that follower agents can almost surely track the given leader signal with bounded errors and no agent exhibits the Zeno behavior by the given control scheme. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the new design techniques.

In this brief, the practical finite-time consensus (FTC) problem is investigated for the second-order heterogeneous switched nonlinear multi-agent systems (MASs), where the subsystems and the switching signal for each agent are different. Mainly due to that agents' dynamics are switched and the unknown nonlinearities in the systems are more general, the practical FTC problem of the MASs is rather difficult to be solved by existing methods. As such, a new protocol design framework for the FTC problem is developed. Then, a novel adaptive protocol is proposed for the switched nonlinear MASs based on the developed design framework and the neural network method. The sufficient conditions for the practical FTC of nonlinear MASs under arbitrary switching are given. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control scheme.

This paper considers the problem of sampled-data adaptive output feedback fuzzy stabilization for switched uncertain nonlinear systems associated with asynchronous switching. A state observer is designed to estimate the unmeasured states and fuzzy logic systems are employed to deal with the unknown nonlinear terms. Sampled-data controller and novel switched adaptive laws are constructed based on the recursive design method and an average dwell time constraint is given to ensure that the closed-loop system is stable. The proposed scheme is employed in a mass-spring-damper system to demonstrate its effectiveness.

This paper considers the global stabilization problem via sampled-data control for a class of switched nonlinear systems meanwhile taking into account asynchronous switching. First of all, a state feedback sampled-data controller is constructed by backstepping design method. Then, a relationship between the sampling period and the average dwell time is derived, which can guarantee that the closed-loop system is globally asymptotically stable. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed method.

This paper investigates an adaptive consensus problem of a class of nonlinear multiagent systems in which the states are unmeasurable and the dynamics of all agents are supposed to be in strict-feedback form with unknown time-varying control coefficients. Due to the presence of uncertain nonlinearities in agents' dynamics, radial basis function neural networks are used to approximate the unknown nonlinear functions, and a neural-network-based observer is designed to estimate the unmeasured states. The adaptive observer-based protocols are based on the relative output information of neighbors, and are constructed by adopting the dynamic surface control technique. It is proved that practical consensus of the system can be achieved with the proposed protocols. A simulation example is given to show the effectiveness of the proposed method.

This paper focuses on the mean square practical leader-following consensus of second-order nonlinear multiagent systems with noises and unmodeled dynamics, where all agents are influenced by noises emerging from the input channels. We present a new distributed protocol, which contains a designed signal to dominate the effects of unmodeled dynamics, to solve the mean square leader-following consensus problem for the nonlinear multiagent systems. The protocol is designed without using any global information, even the eigenvalues of the Laplacian matrix. The Lipschitz constant of the nonlinear function is also unknown to all followers. Using the Lyapunov functional approach and the stochastic theory, it is proven that the mean square practical leader-following consensus is achieved by the designed protocol. Finally, two examples are provided to illustrate the effectiveness of the designed algorithm.

This paper addresses the aggregation issues of competitive multiagent systems (CMASs) consisting of competitive agents with multimodes and saddle points. In such CMASs, due to existing mutual competitions, every agent is equipped with finite multimodes, and every mode in any agent is described as a second-order linear time-invariant (LTI) control system. When the origin is the same saddle point of all modes of agents, to investigate aggregation of the CMASs with switching strategies, we first use switched LTI systems with saddle points to formulate such CMASs. Then, two new stability concepts, called initial-state-dependent (ISD) stability and initial-state-independent (ISI) stability, are defined for the CMASs. Based on these new stability concepts, a practical criterion of local/global ISI asymptotic aggregation is proposed for the CMASs. A local/global ISD/ISI asymptotical-stabilizing-control observed as distributed controls of multimodes, stabilizing-switching-paths, and a corresponding algorithm are all designed for local/global aggregation of such CMASs with switching delays. Finally, a numerical example illustrates the effectiveness and practicality of our new results.

This paper investigates the adaptive practical finite-time stabilization for a class of nonstrict feedback nonlinear systems. The nonlinear systems under consideration contain unknown nonlinearities and control coefficients, and unknown deadzone and saturation input nonlinearities. Without imposing any conditions on the unknown nonlinearities, neural networks are utilized as the approximators to cope with these unknown nonlinear functions. The adding a power integrator technique is employed to construct controller and adaptive laws. The stability of the corresponding closed-loop system is proved with the help of the finite-time Lyapunov theory. Finally, two simulation examples are provided to show the validity of the proposed design method.