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.

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.

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.

In this paper, the consensus problem for a class of multi-agent systems is investigated, where each agent is described by an Euler-Lagrange system and only sampled-data output interaction among agents is allowed. In addition, the Euler-Lagrange system considered possesses a higher degree of uncertainty; specifically, the regression matrix is also unknown. The intricate heterogeneity, inherent uncertainties, and stringent constraints of information interactions compel us to develop a new protocol. The protocol is synthesized by organically integrating theories and techniques such as graph theory, sampled-data cooperative control, fixed-time control, and fuzzy approximation. Each agent is equipped with a first-order difference trajectory generator that updates exclusively at sampling instants using the output information received from its neighbors. The virtual trajectory serves as the tracking target for the corresponding agent systems output. A fixed-time fuzzy adaptive tracker is proposed for each agent to track the generated trajectory. The problem of analyzing the protocol's effectiveness is deconstructed into two coupled subproblems: a synchronization problem for a perturbed first-order differentiator and a practical fixed-time tracking problem for a single Euler-Lagrange system. This problem is adequately addressed primarily based on the Lyapunov function method. Finally, the effectiveness of the proposed protocol is validated through numerical simulation and ROS experiment. Code is available at:https://github.com/Consensus-EL-output/tfs.

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.

In this paper, an output feedback adaptive fuzzy leader-following event-triggered consensus (ETC) problem for switched nonlinear multi-agent systems (SNMASs) is investigated. In the considered systems, only outputs of leader and followers are measurable at sampling instants. To deal with this problem, a novel auxiliary system and observers are employed. Then, corresponding error systems are established and the consensus problem is transformed into a stabilization problem. To achieve better approximation ability for nonlinear uncertainties, the interval type-2 fuzzy logic systems (IT2FLSs) are utilized. In order to reduce the wastage of communication resources (WCRs), an adaptive fuzzy ETC protocol with a discrete-time switching threshold event-triggering mechanism (ETM) which is monitored only at sampling instants is provided. It is proved that the output feedback adaptive fuzzy ETC protocol enables the realization of the consensus target. Finally, to verify the effectiveness of the proposed scheme, the ETC protocol is applied to a practical example.

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.

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 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.

Most visual SLAM systems are based on static scene assumption, what causes them to fail in dynamic scenes and greatly limits their industrial applications. To overcome this challenge, we introduce SGD-SLAM, an innovative RGB-D visual SLAM system that integrates semantic, geometric, and depth information for robust dynamic feature rejection. Depth information is used to compute the average depth of the detected objects to make the segmentation results of target detection more accurate. The introduction of moving confidence can effectively remove high-dynamic regions while preserving low- dynamic regions, greatly improving performance in low-dynamic environments. Our experimental results, conducted on both datasets and real-world scenarios, demonstrate SGD-SLAM's superior performance in dynamic scenes, particularly excelling in low-dynamic environments. To our knowledge, SGD-SLAM represents one of the most robust real-time SLAM solutions for low-dynamic environments, paving the way for broader industrial applications of visual SLAM technology.

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.

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 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 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.

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.

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.

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.

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.

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 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.