This paper investigates the consensus control problem of multi-agent systems under intermittent communication and unmodeled external disturbances. The main contribution is to overcome the limitation of current synchronous intermittent framework and propose a novel asynchronous intermittent communication methodology on multi-agent systems. In this intermittent methodology, the state space is divided into three distinct regions by introducing both safety and intermittent boundaries, which enables effective monitoring of agent error dynamics.Furthermore, an asynchronous intermittent communication protocol is designed, where the activation and rest intervals are adjusted based on the real-time error states of the agents.By utilizing the distributed extended observer to observe the relative output information and unmodeled disturbances, the novel asynchronous intermittent consensus protocol with disturbance rejection is designed to realize the overall consensus of the multi-agent systems. The proposed spatial-segmentation-dependent intermittent communication methodology can adjust communication and non-communication time of each agent asynchronously according to the communication requirements, under which the multi-agent systems can tolerate more non-communication time and reduce the communication frequency. Finally, numerical simulations are performed to verify our results.

Multi-agent systems (MASs) in open networks face dual security threats: Byzantine attacks that steer malicious consensus and eavesdroppers that steal private information. Existing resilient consensus protocol isolates Byzantine attacks by relying on (2f+1)-robust networks, which imposes stringent topological constraints and fails to provide privacy preservation simultaneously. To address this issue, an improved resilient consensus protocol withf(IRCP-f) is proposed, via absolute values of relative states, to defend againstf-local Byzantine attacks. This protocol only requires that an undirected and connected graph is (f+ 1)-robust instead of (2f+ 1)-robust. The properties of the dynamic network processed by the IRCP-fare analyzed, and the graph conditions for achieving average consensus are consequently satisfied. A fully distributed differentially private event-triggered average consensus (DPETAC) control scheme is then developed. With the DPETAC control scheme, convergence analysis, Zeno behavior analysis, accuracy analysis and privacy analysis are presented for the MAS. Finally, a numerical simulation illustrates the feasibility and effectiveness of the proposed privacy-preserving average consensus control scheme.

This paper investigates a privacy-preserving consensus tracking problem for a class of nonstrict-feedback discrete-time multi-agent systems (MASs). An improved Liu cryptosystem is developed to alleviate the errors between encryption and decryption on the plaintext, which ensures satisfactory recovery of the plaintext information. A reinforcement learning (RL) technique is then employed to compensate for unknown dynamics and errors between true signals and decrypted ones. Based on the backstepping and graph theory, an RL-based privacy-preserving consensus tracking control strategy is further designed. By virtue of graph theory and Lyapunov stability theory, it is shown that the consensus tracking errors and all signals in the MAS are ultimately bounded. Finally, simulation examples are presented for verification of the effectiveness of the control strategy.

Long-term power load forecasting is critical for power system planning but is constrained by intricate temporal patterns. Transformer-based models emphasize modeling long- and short-term dependencies yet encounter limitations from complexity and parameter overhead. This paper introduces a novel Multi-Granularity Autoformer (MG-Autoformer) for long-term load forecasting. The model leverages a Multi-Granularity Auto-Correlation Attention Mechanism (MG-ACAM) to effectively capture fine-grained and coarse-grained temporal dependencies, enabling accurate modeling of short-term fluctuations and long-term trends. To enhance efficiency, a shared query-key (Q-K) mechanism is utilized to identify key temporal patterns across multiple resolutions and reduce model complexity. To address uncertainty in power load forecasting, the model incorporates a quantile loss function, enabling probabilistic predictions while quantifying uncertainty. Extensive experiments on benchmark datasets from Portugal, Australia, America, and ISO New England demonstrate the superior performance of the proposed MG-Autoformer in long-term power load point and probabilistic forecasting tasks.

This paper researches the event-triggered forward immersion and invariant (I&I) tracking control problem for a class of strict feedback nonlinear systems. A forward I&I-based control method is developed for the tracking problem with an dynamic event-triggered mechanism. Since I&I-based method does not require the introduction of Lyapunov functions in the controller design, the design complexity is greatly reduced. Since the I&I-based method can be used to decouple the design by constructing two manifolds separately, it avoids the need of the traditional backstepping method to combine the Lyapunov function coupled design control law of radial basis function neural networks (RBFNNs). I&I adaptive technique is introduced to improve the weight update in RBFNNs. It can improve the learning performance and convergence speed of neural networks under the event-triggered mechanism. Furthermore, finite-time technique is employed to improve the error convergence time of the event-triggered forward I&I control method. For stability analysis, an event-triggered control system is denoted as a nonlinear impulsive dynamical system, and a Lyapunov theorem is then used to represent the stability of the closed-loop system without Zeno behavior. Finally, the validity of the theoretical results is illustrated by simulation examples and experiments.Note to Practitioners—The motivation of this paper is to present an event-triggered forward I&I tracking control method in finite time for a class strict feedback nonlinear system. The use of I&I technique can reduce the complexity of control method design. To reduce the computational resources, the event-triggered mechanism is introduced in the forward I&I technique. The I&I technique is introduced to construct two manifolds separately and decouple the design of the control law and the RBFNNs weight update law. Moreover, the I&I adaptive technique with the event-triggered mechanism is employed to improve the approximation effect of RBFNNs. Finally, the finite-time technique is introduced to reduce the convergence time of the tracking error under the event-triggered mechanism. This proposed method can be simply and efficiently applied in industrial applications.

This paper addresses distributed formation tracking control for heterogeneous swarms consisting of quadrotor unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs). A hierarchical control framework is proposed to coordinate overall swarm formation. At the upper layer, a position-based control strategy is designed for UAVs, in which a virtual leader is introduced to facilitate coordinated aerial formation. At the lower layer, a bearing-based control strategy is employed for USVs, with selected UAVs serving as mobile leaders to guide the USV formation. Within this framework, optimized formation controllers for both UAVs and USVs are developed by integrating the backstepping method with a reinforcement learning algorithm based on the actor-critic architecture. Lyapunov-based stability analysis demonstrates that the proposed scheme ensures the desired formation performance of the swarm. Compared with existing studies that primarily address homogeneous UAV or USV formations, the proposed method achieves optimized formation tracking control for more complex heterogeneous swarms, without requiring precise knowledge of their dynamic models. The effectiveness and robustness of the proposed approach are further validated through numerical simulations.

Formation control is one of critical topics in cooperative control. In this paper, we design a prescribed-time bipartite formation control strategy for vehicle multi-agent systems with external disturbances and internal unknown dynamics. A prescribed-time extended state observer (PTESO) is developed to compensate for total disturbances in a prescribed time, and the convergence time can be set in advance for different initial conditions. In order to make the formation error converge in a prescribed time, two novel time functions are introduced and applied to the control strategy. A prescribed-time control strategy with PTESO is developed for bipartite vehicle formation, and the relationship of the convergence time between PTESO and formation error is illustrated. Stability analysis shows the observation error and bipartite formation error are steered to converge their prescribed time, respectively. Furthermore, simulations are conducted to demonstrate the effectiveness of the prescribed-time bipartite formation control strategy.Note to Practitioners—This paper presents a prescribed-time bipartite formation control strategy for vehicle multi-agent systems with external disturbances and internal unknown dynamics. The total disturbance of each agent is compensated by a prescribed-time extended state observer (PTESO). In this PTESO, the convergence time is adjustable in advance for different initial conditions, and the peak phenomenon, caused by large gains, is avoided owing to adjustable and smaller time-varying gains. Two novel prescribed-time functions are proposed for vehicle MASs. The proposed functions remove the requirement that calculating gains mathematically, and the issue of jumping variation, caused by modifying coefficients in traditional prescribed-time functions arbitrarily, is also addressed. This strategy provides a feasible strategy for industrial applications.

For a class of uncertain nonlinear stochastic multiagent systems, a consensus control strategy is proposed with an adjustable-time-varying-gain-based event-triggered extended state observer (ATVG-ETESO) via dual-terminal event-triggered mechanism (DTETM). The ATVG-ETESO estimates internal uncertainties and external stochastic disturbances. Its adjustable time-varying gain avoids peaking phenomenon at the initial stage and accelerates estimation error convergence. A DTETM with an adaptive threshold reduce communication burdens on both the input and output channels of the ATVG-ETESO. Theoretically, both the ATVG-ETESO estimation errors and the state consensus errors are bounded. Finally, two illustrative simulation examples are given to illustrate the effectiveness of the control strategy.

Abstract Power load data frequently display outliers and an uneven distribution of noise. To tackle this issue, we present a forecasting model based on an improved extreme learning machine (ELM). Specifically, we introduce the novel Pinball-Huber robust loss function as the objective function in training. The loss function enhances the precision by assigning distinct penalties to errors based on their directions. We employ a genetic algorithm, combined with a swift nondominated sorting technique, for multiobjective optimization in the ELM-Pinball-Huber context. This method simultaneously reduces training errors while streamlining model structure. We practically apply the integrated model to forecast power load data in Taixing City, which is situated in the southern part of Jiangsu Province. The empirical findings confirm the method’s effectiveness.

Accurate short-term power forecasting (STPF) provides reliable support for the stable operation of power systems. However, due to the randomness of consumer behavior and energy properties, outliers inevitably exist in power series. Considering its negative influence, effectively extracting features from the power series with outliers has become a significant challenge in STPF. This paper develops a robust hybrid model to handle this issue. The proposed model utilizes the robust regression technique to handle outliers. An adaptive rescaled Huber loss is developed to approximate the complex distribution of the actual power series. Moreover, the proposed model applies autoregressive and bidirectional gated recurrent units to extract linear and nonlinear features of power series, respectively. Meanwhile, the attention mechanism extracts the temporal feature through the attention representation, which considers the correlations between different moments. The proposed model obtains the optimal coefficients of determination between predictions and observations on the wind power series as 0.9629 and power load series as 0.978, which indicates that the proposed model performs competitive robustness and generalization on the daily operation of renewable energy systems.

Abstract At present, the multi‐object tracking method based on transformer generally uses its powerful self‐attention mechanism and global modelling ability to improve the accuracy of object tracking. However, most existing methods excessively rely on hardware devices, leading to an inconsistency between accuracy and speed in practical applications. Therefore, a lightweight transformer joint position awareness algorithm is proposed to solve the above problems. Firstly, a joint attention module to enhance the ShuffleNet V2 network is proposed. This module comprises the spatio‐temporal pyramid module and the convolutional block attention module. The spatio‐temporal pyramid module fuses multi‐scale features to capture information on different spatial and temporal scales. The convolutional block attention module aggregates channel and spatial dimension information to enhance the representation ability of the model. Then, a position encoding generator module and a dynamic template update strategy are proposed to solve the occlusion. Group convolution is adopted in the input sequence through position encoding generator module, with each convolution group responsible for handling the relative positional relationships of a specific range. In order to improve the reliability of the template, dynamic template update strategy is used to update the template at the appropriate time. The effectiveness of the approach is validated on the MOT16, MOT17, and MOT20 datasets.

Abstract Wind power forecasting techniques have been well developed over the last half-century. There has been a large number of research literature as well as review analyses. Over the past 5 decades, considerable advancements have been achieved in wind power forecasting. A large body of research literature has been produced, including review articles that have addressed various aspects of the subject. However, these reviews have predominantly utilized horizontal comparisons and have not conducted a comprehensive analysis of the research that has been undertaken. This survey aims to provide a systematic and analytical review of the technical progress made in wind power forecasting. To accomplish this goal, we conducted a knowledge map analysis of the wind power forecasting literature published in the Web of Science database over the last 2 decades. We examined the collaboration network and development context, analyzed publication volume, citation frequency, journal of publication, author, and institutional influence, and studied co-occurring and bursting keywords to reveal changing research hotspots. These hotspots aim to indicate the progress and challenges of current forecasting technologies, which is of great significance for promoting the development of forecasting technology. Based on our findings, we analyzed commonly used traditional machine learning and advanced deep learning methods in this field, such as classical neural networks, and recent Transformers, and discussed emerging technologies like large language models. We also provide quantitative analysis of the advantages, disadvantages, forecasting accuracy, and computational costs of these methods. Finally, some open research questions and trends related to this topic were discussed, which can help improve the understanding of various power forecasting methods. This survey paper provides valuable insights for wind power engineers.

An attitude control issue is concerned for a quadrotor with external disturbances in this paper. For unknown system dynamics, predictor-based neural networks (NNs) are introduced, where prediction errors, angular velocities, are constructed, instead of tracking errors, for updating NNs' weights. This replacement reduces the occurrence of high-frequency oscillations in NNs' approximation. With this improved NNs, a predictorbased NN disturbance observer is then developed for compensation for external disturbances and NNs' approximation errors, and a normalization learning technique is employed for reduction of the number of learning parameters. A predictor-based neural attitude control strategy is proposed for a quadrotor with external disturbances. Furthermore, measurement noise are taken into account in our predictor-based neural attitude control strategy. The Lyapunov-based stability analysis shows that all closed-loop signals in the designed attitude system are semiglobally bounded. A numerical simulation and a hardware-in-loop experiment as well as outdoor flight verify the effectiveness of the proposed anti-disturbance attitude control strategy.

This article is concerned with resilient consensus control for a heterogeneous multiagent system (HMAS) in the presence of malicious attacks on sensors. Most existing strategies are dependent on compensation principle resulting in bounded consensus error. To address this issue, a multiround attack detection and isolation (MR-ADI) algorithm is presented, and, with this algorithm, a resilient isolation-based control strategy is developed to achieve output synchronization. In detail, via output regulator equations, heterogeneous followers are transformed into a virtual layer with same output matrices. With the transformation information from neighbors, a distributed attack monitor is constructed for generating feature signals. With the help of such signals from monitors, a centralized MR-ADI algorithm precisely locates paralyzed followers via a supervisory center, and a distributed MR-ADI algorithm is further proposed only with local and neighbor information. In theory, it is proven that the convergence of output consensus error is ensured. Simulation examples are presented to demonstrate the availability of our theoretical results.

An optimal tracking control problem is critical for marine surface vessels (MSVs) with full state constraints, input constraints, external disturbances, and model uncertainty terms. For solving an MSV’s position and velocity constraints, a barrier Lyapunov function (BLF) and control barrier function (CBF) are introduced and combined with prescribed performance functions, and then, an adaptive dynamic programming (ADP) optimized tracking control strategy is presented based on the two functions. A dynamic event-triggered mechanism is employed, which reduces the number of triggers by tracking the intermittent transmission of error signals, thus avoiding actuator wear and excessive consumption of communication resources. The experience replay method is brought in the gradient descent method for improvement of the weight learning efficiency. The Lyapunov-based stability analysis shows that the designed tracking control strategy ensures that all signals and weights in the closed-loop system are semi-globally bounded with Zeno-free behavior. Numerical comparison simulation verifies the effectiveness and superiority of the strategy.

A finite-time output consensus control problem is investigated in this article for an uncertain nonlinear high-order multiagent systems (MASs). For this class of MASs, the order of individual follower is reduced gradually by implementing the immersion and invariance (I&I) control theory repeatedly, and a requirement of solving partial differential equations (PDEs) in I&I control theory is obviated. Furthermore, an I&I-based radial basis function neural network (RBFNN) approximator is developed, where an extra cross term is added in the approximation mechanism, and the form of an update law for weights is transformed into a proportional and integral one. This I&I-based RBFNN approximator does not rely on a cancellation of the perturbation term, and these uncertainties are reconstructed by the I&I manifold adaptively, which is for improvement of approximation behaviors of traditional RBFNNs. On this basis, a distributed adaptive forwarding finite-time output consensus control strategy is proposed by combining a sign function, and the convergence time of the MAS can be adjusted with appropriate finite-time parameters. Finally, two illustrative examples verify the effectiveness of the theoretical claims.

Neural dynamic surface control (NDSC) is an effective technique for the tracking control of nonlinear systems. The objective of this article is to improve closed-loop transient performance and reduce the number of learning parameters for a strict-feedback nonlinear system with unknown control gains. For this purpose, a predictor-based NDSC (PNDSC) approach is presented. It introduces Nussbaum functions and predictors into the traditional NDSC for nonlinear systems with unknown control gains. Unlike NDSC that uses surface errors to update the learning parameters of neural networks (NNs), the PNDSC employs prediction errors for the same purpose, leading to improved transient performance of closed-loop control systems. To reduce the number of learning parameters, the PNDSC is further embedded with the technique of the minimal number of learning parameters (MNLPs). This avoids the problem of the "explosion of learning parameters" as the order of the system increases. A Lyapunov-based stability analysis shows that all signals are bounded in the closed-loop systems under PNDSC embedded with MNLPs. Simulations are conducted to demonstrate the effectiveness of the PNDSC approach presented in this article.

An event-triggered output feedback control approach is proposed via a disturbance observer and adaptive dynamic programming (ADP). The solution starts by constructing a nonlinear disturbance observer, which only depends on the measurement of system output. A state observer is then developed based on approximation information of system dynamics via neural networks. In order to avoid continuous transmission and reduce the communication burden in the closed-loop system, an event-triggered mechanism is introduced such that the control signal is updated only at a specific instant when a triggered condition is violated. By virtue of the disturbance observer and state observer, an output-feedback ADP control approach then is developed, where only a critic network is employed to estimate the value function. Based on the Lyapunov stability theory, the stability of the closed-loop system is rigorously analyzed, and the effectiveness of the proposed control approach is verified by two simulation examples.

In time series forecasting with outliers and random noise, parameter estimation in a neural network via minimizing the$l_{2}$loss is unreliable. Therefore, an adaptive rescaled lncosh loss function is proposed in this article to handle time series modeling with outliers and random noise. It overcomes the limitation of the single distribution of traditional loss functions and can switch among$l_{1}$,$l_{2}$, and the Huber losses. A tuning parameter in the loss function is estimated by using a “working” likelihood approach according to estimated residuals. From the proposed loss function, a robust adaptive rescaled lncosh neural network (RARLNN) regression model is developed for highly accurate predictions. In the training phase of the model, an iterative learning procedure is presented to estimate the tuning parameter and train the neural network in iterations. A new prediction interval construction method is also developed based on quantile theory. The proposed RARLNN model is applied to two groups of wind speed forecasting tasks. The results show that the proposed RARLNN model is more conducive to enhancing forecasting accuracy and stability from the perspectives of noise distribution and outliers.

For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system.

Information exchanges among interacting agents play a significant role in guaranteeing successful completion of the desired coordinated control tasks for a multi-agent system (MAS). Furthermore, these information exchanges are often performed over some open and resource-constrained communication networks, thereby making security and resource efficiency vitally important for various multi-agent coordinated control problems. This paper addresses a secure dynamic event-trigger-based resilient consensus control problem for an MAS in the presence of both sensor and actuator attacks. First, a distributed adaptive compensator is introduced for prediction of unavailable system states. Due to the existence of sensor and actuator attack signals, a secure dynamic event-triggered mechanism is then proposed, and a resilient control strategy is further devised for the paralyzed MAS. It is theoretically proved that the controlled MAS is asymptotically stable and asymptotic consensus is eventually achieved among the coordinated agents regardless of the attacks and constrained resources. Finally, three examples are provided to illustrate the effectiveness of the proposed strategy.

Abstract As unsupervised learning algorithm, clustering algorithm is widely used in data processing field. Density-based spatial clustering of applications with noise algorithm (DBSCAN), as a common unsupervised learning algorithm, can achieve clusters via finding high-density areas separated by low-density areas based on cluster density. Different from other clustering methods, DBSCAN can work well for any shape clusters in the spatial database and can effectively cluster exceptional data. However, in the employment of DBSCAN, the parameters, EPS and MinPts, need to be preset for different clustering object, which greatly influences the performance of the DBSCAN. To achieve automatic optimization of parameters and improve the performance of DBSCAN, we proposed an improved DBSCAN optimized by arithmetic optimization algorithm (AOA) with opposition-based learning (OBL) named OBLAOA-DBSCAN. In details, the reverse search capability of OBL is added to AOA for obtaining proper parameters for DBSCAN, to achieve adaptive parameter optimization. In addition, our proposed OBLAOA optimizer is compared with standard AOA and several latest meta heuristic algorithms based on 8 benchmark functions from CEC2021, which validates the exploration improvement of OBL. To validate the clustering performance of the OBLAOA-DBSCAN, 5 classical clustering methods with 10 real datasets are chosen as the compare models according to the computational cost and accuracy. Based on the experimental results, we can obtain two conclusions: (1) the proposed OBLAOA-DBSCAN can provide highly accurately clusters more efficiently; and (2) the OBLAOA can significantly improve the exploration ability, which can provide better optimal parameters.

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

Formation tracking is a critical issue in the consensus control of multiagent systems (MASs). This article presents a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs connected through a directed topology. The nonaffine nonlinear MASs are transformed into affine nonlinear ones with uncertainties via the idea of active disturbance rejection control (ADRC). The uncertainties in the MASs are approximated and compensated by extended state observers (ESOs) in real time. Tracking differentiators (TDs) are introduced to reduce the complexity in the computation of the derivatives of virtual control variables. Employing funnel variables, our strategy guarantees the formation of tracking errors to stay within the desired ranges, thus improving the control performance of the closed-loop system. It is proved that all signals of the system are bounded and the formation errors can be made arbitrarily small within a residue around the origin by appropriate choices of control parameters. Case studies are carried out to demonstrate the effectiveness of the proposed control strategy.Note to Practitioners—The motivation of this article is to present a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs within a directed topology. To simplify the process of solving the formation tracking problem, the presented strategy incorporates ADRC with the backstepping technique. Employing ADRC, our strategy approximates the uncertainties of the MAS followers via ESOs. The uncertainties are then compensated through real-time estimations of extended states. Moreover, with ADRC, TDs are used to estimate the derivatives of complex nonlinear functions, eliminating the requirement of the operations of higher order derivatives of virtual control variables. It provides a feasible strategy for industrial applications.

Consensus control of multiagent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to various cyberattacks, such as denial of service (DoS). Efforts have been made in the development of both time- and event-triggered consensus control of MASs. However, there is a lack of precise calculation of control input during the attacking periods. To address this issue, a distributed secure consensus control with event triggering is developed for linear leader-following MASs under DoS attacks. It is designed with a dual-terminal event-triggered mechanism, which schedules information transmission through two triggered functions for each follower: one on the measurement channel (sensor-to-controller) and the other on the control channel (controller-to-actuator). To deal with DoS attacks, the combined states in the triggered functions are replaced by their estimations from an observer. Sufficient conditions are established for the duration and frequency of DoS attacks. To remove continuous monitoring of the measurement errors, a self-triggered secure control scheme is further developed, which combines the system states and other information at past triggered instants. Theoretical analysis shows that the followers in MASs under DoS attacks are able to track the leader and meanwhile the Zeno behavior is excluded. Case studies are conducted to demonstrate the effectiveness of our distributed secure consensus control of MASs.

Containment control is an important issue in the consensus problem of multiagent systems (MASs). This article presents an output-based containment control strategy for a class of nonaffine nonlinear MASs with uncertainies and directed topology. With the help of differential homeomorphism transform and the idea of active disturbance rejection control (ADRC), a nonaffine nonlinear MAS is transformed into an affine one with uncertainties. Two filters with extended states in each follower are designed with the idea of extended state observer to reconstruct the states of the transformed MAS. Then, uncertainties of the MAS are compensated with the help of the estimations of the extended states. Moreover, the derivative of the virtual control signal in the backstepping technique is replaced by a tracking differentiator (TD), overcoming the so-called “explosion of complexity” problem. By means of Lyapunov theory, the containment errors of the followers are proven to converge to a small neighborhood around the origin via an appropriate choice of parameters. Simulation examples are provided to demonstrate the proposed control strategy.

An observer-based containment control issue is addressed for a class of uncertain nonlinear multiagent systems with a directed topology via the active disturbance rejection control and backstepping techniques. A kind of nonlinear extended state observers (ESOs) based on fractional power functions is developed, and the estimations of extended states are utilized to compensate uncertain dynamics in real time. Compared with linear ESOs, the advantages of the ESOs in this paper lie in peaking reduction and better tolerance of measurement noise for the closed-loop system. Moreover, tracking differentiators are employed to avoid the explosion of complexity caused by repeated differentiations of nonlinear functions. It is proven that the containment errors of the followers converge to small neighborhoods of the origin and they are adjustable by suitable choice of parameters. Finally, two simulation examples, both practical and numerical ones, are shown to demonstrate the effectiveness of the proposed control approach.

Accurate forecasting of wind speed is vital in renewable power system management. However, wind speed series is an extremely complex system with outliers. Considering the dilemma, we propose a robust extreme learning machine algorithm where a huber loss works as the optimized function for extreme learning machine training. And a decomposition-ensemble method is developed in modelling wind speed. In our hybrid system, the proposed robust extreme learning machine is employed to model high-frequent sub-signals, while least square extreme learning machine is used to model low-frequent sub-signals. Validated by forecasting a 5-minutely wind speed in China, our proposed forecasting framework can provide more accurate predictions.

This paper addresses an adaptive event-triggered consensus control problem for a class of second-order nonlinear multiagent systems (MASs) in an undirected communication topology. A novel adaptive distributed event-triggered consensus control scheme is presented for the MAS with unknown functions based on the definition of an auxiliary state, and the coefficient of the triggered function can be regulated adaptively with dependence on the auxiliary state error to ensure not only the control performance but also the efficiency of the network interactions. Furthermore, two self-triggered algorithms are developed for two cases, known functions and unknown ones, by the current state and information at the previous event time instant instead of the requirement for continuous monitoring auxiliary state errors. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and the Zeno behavior is ruled out. Finally, two simulation examples, both real-time and numerical ones, are provided to verify the theoretical claims.

In this paper, we address the issue of the prescribed performance control of a class of pure-feedback nonlinear systems with uncertainties and input saturation. The active disturbance rejection control is adopted at each step of the backstepping technology. In detail, the extended state observer is employed to estimate unknown functions to compensate for uncertain items. The tracking differentiator is used to take place of the derivative of the virtual control signals, which overcomes the repeated differentiations of nonlinear functions. The control input limitation is handled with the auxiliary system, and predefined tracking performance functions are utilized to improve the tracking accuracy and speed. By means of the input-to-state stability and Lyapunov stability theory, the tracking error is proven to converge to arbitrarily small neighborhood of the origin. Two simulation examples are provided to demonstrate the effectiveness of the presented results.

In this paper, we are concerned with the fault-tolerant control (FTC) issue for a class of large-scale uncertain multi-input and multioutput nonlinear systems. The features of such class of systems are that virtual control variables are in nonaffine pure-feedback form and actuator failures consist of both lock-in-place and loss of effectiveness. We develop an adaptive observer to reconstruct unavailable state information for this class of systems taking advantage of the universal approximation property of neural networks (NNs). And then, an observer-based decentralized adaptive FTC strategy is designed recursively by combining backstepping methods with NNs, FTC theory as well as the dynamic surface control (DSC) technique. The superiorities of this proposed strategy are that it is only dependent on output information of the system and there is no requirement for accurate parameters of the system. It is also hardly inevitable that repeat differentiation calculations of virtual functions with the help of DSC technology. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals remain uniformly ultimately bounded and tracking errors converge to a small neighborhood around the origin by suitable choice of design parameters. Finally, simulation results, both practical and numerical examples, are illustrated to verify the feasibility of the theoretical claims.