The state estimation problem of linear time-invariant (LTI) systems is investigated in this article. Distributed observers are designed to estimate the complete states of LTI systems under time-varying delays. A class of edge-based switching event-triggered mechanisms (SETMs) are designed for distributed observers to continuously estimate the states of the target system by the discrete relative state information, reducing the consumption of communication/computation resources significantly. The positive lower bounds of intersampling times are guaranteed, which further avoids Zeno behaviors. A unified framework for the stability analysis of the estimation error system under the SETM is presented, and the sufficient conditions for the asymptotic state estimation of the distributed observer are derived. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method.

Load forecasting is critical to the task of energy management in power systems, for example, balancing supply and demand and minimizing energy transaction costs. There are many approaches used for load forecasting such as the support vector regression (SVR), the autoregressive integrated moving average (ARIMA), and neural networks, but most of these methods focus on single-step load forecasting, whereas multistep load forecasting can provide better insights for optimizing the energy resource allocation and assisting the decision-making process. In this work, a novel sequence-to-sequence (Seq2Seq)-based deep learning model based on a time series decomposition strategy for multistep load forecasting is proposed. The model consists of a series of basic blocks, each of which includes one encoder and two decoders; and all basic blocks are connected by residuals. In the inner of each basic block, the encoder is realized by temporal convolution network (TCN) for its benefit of parallel computing, and the decoder is implemented by long short-term memory (LSTM) neural network to predict and estimate time series. During the forecasting process, each basic block is forecasted individually. The final forecasted result is the aggregation of the predicted results in all basic blocks. Several cases within multiple real-world datasets are conducted to evaluate the performance of the proposed model. The results demonstrate that the proposed model achieves the best accuracy compared with several benchmark models.

Due to extreme external environments and changes in component health status, offshore wind turbines can generate out-of-distribution (OOD) data compared to normal operation. Traditional wind power forecasting (WPF) models are typically trained using historical data. Nevertheless, these models fail to maintain robustness with respect to OOD data. This paper introduces the matching based Transformer (MatTF) to mine shared knowledge from data across different distributions, thereby addressing the OOD problem. First, an algorithm for the detection of distribution boundaries is designed to partition the training data into subsets. Then, adaptive factors are added to the self-attention module in traditional transformer to solve the distribution matching problem. Finally, the effectiveness of the model is verified through case study comparing with other WPF models.

This article explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on the internal model are proposed for the case with perfect and imperfect information, respectively. Different from the existing algorithms based on gradient dynamics, by introducing the integral of the gradient of cost functions on the basis of the passivity theory, the rules are proposed to force the strategies of all agents to evolve to the Nash equilibrium, regardless of the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via the Lyapunov stability theory, passivity theory, and singular perturbation theory. Simulations are performed to illustrate the effectiveness of the proposed methods.

This article considers consensus of first-order/second-order hybrid multiagent systems (MASs) based on game modeling. In the first-order hybrid MAS (HMAS), a subset of agents select the Nash equilibrium of a multiplayer game as their states at each game time and the others update their states with first-order continuous-time (C-T) dynamics. By graph theory and matrix theory, we establish sufficient and necessary conditions for consensus of the first-order HMAS with two proposed protocols. The second-order HMAS is composed of agents whose states are determined by the Nash equilibrium of a multiplayer game and agents whose states are governed by second-order C-T dynamics. Similarly, sufficient and necessary conditions are given for consensus of the second-order HMAS with two proposed protocols. Several numerical simulations are provided to verify the effectiveness of our theoretical results.

This article proposes a resilient distributed Nash equilibrium (NE) seeking algorithm for noncooperative games with multiple double-integrator agents who suffer from false data injection (FDI) attacks. A malicious attacker injects false data into agents’ actuators and sensors so that agents’ strategies deviate from the NE of the game with the compromised control inputs and interactive information. First, the robustness of the seeking algorithm against the FDI attacks is analyzed. Then, to mitigate the effect of the attacks on agents’ strategies, the false data injected in the actuators and sensors are regarded as extended states which can be observed by extended state observers (ESOs). Thus, a resilient NE seeking algorithm is proposed based on ESOs. The resilient algorithm can drive the system to converge to the NE without requiring any information about the nature of the attacks. An explicit criterion is given to ensure the effectiveness of the designed algorithms. An example is given to illustrate the results.

In this article, a class of continuous-time noncooperative games in networks of double-integrator agents is explored. The existing methods require that agents communicate with their neighbors in real time. In this article, we propose two discrete-time communication schemes based on the designed continuous-time strategy-updating rule for the efficient use of communication resources. First, the property of the designed continuous-time rule is analyzed to ensure that all agents’ strategies can reach the Nash equilibrium (NE). Then, we propose, respectively, periodic and event-triggered communication schemes for the discrete-time interactions among agents. The rule in the periodic case is implemented synchronously. The rule in the event-triggered case is executed asynchronously without Zeno behaviors. All agents in both cases can reach the NE asymptotically by interacting with neighbors at discrete times. Simulations are performed in networks of Cournot competition to illustrate the effectiveness of the proposed methods.

This article studies lag group consensus problems of multiagent systems with directed information transformations. Agents in the network are divided into finite groups, and modeled by high-order systems. Distributed consensus protocols with constant lags are presented to realize the lag group consensus: the states of the agents in a group approach to a consensus value asymptotically, while there exist given ratios between the final values of different groups. Necessary and sufficient criteria for the lag group consensus are obtained by the Laplace transformation. Finally, theoretical results are proved to be effective by several simulation results.

This paper addresses the consensus problem of linear multiagent systems via nonlinear couplings. First, we show that the multiagent system can achieve consensus via nonlinear couplings provided the coupling strength surpasses a threshold, which depends on the smallest nonzero eigenvalue of the interaction graph Laplacian. Second, an adaptive coupling protocol is proposed to adjust the coupling strength without any usage of global information. Some numerical simulations are given to illustrate the effectiveness of the proposed protocols.

In this article, we are concerned with the synchronization problem of Kuramoto oscillators under the sampled-data updating law. This article is motivated by the needs of synchronization of Kuramoto oscillators in the presence of periodic and asynchronous coupling updates. Based on the periodical sampled-data method, a sufficient condition ensuring synchronization under periodic updates is derived. In order to relax the requirement of having all data updated simultaneously, an event-triggered law is designed to implement asynchronous coupling updates. Our synchronization analysis does not rely on any linearization technique around equilibrium points. Instead, we employ the Lyapunov stability theory and nonsmooth analysis technique to deduce the synchronization conditions and estimate the region of attraction. The effectiveness of the proposed sampled-data coupling is illustrated by numerical simulations.

In this article, we consider the distributed synchronization problem of dynamic networked systems with adaptive nonlinear couplings. Based on how the information is collected, the interactions between subsystems are characterized by nonlinear relative state couplings and nonlinear absolute state couplings. In both cases, we show that the considered nonlinear interactions can be used to simulate the couplings with disturbed relative or absolute states. In order to implement the nonlinear couplings in a fully distributed fashion, adaptive control laws are proposed for the adjustment of coupling strengths between connected subsystems. It is shown that the connected network topology is sufficient to ensure the synchronization of dynamic networked systems with the proposed adaptive nonlinear coupling methods. Different from many existing works, the σ -modification technique is used to suppress the increase of the coupling strengths with an additional benefit of preventing the coupling strengths from increasing. Simulation examples are given to assess the performance of the proposed adaptive nonlinear couplings.

In this paper, we propose an event-triggered rendezvous control method for multiple two-wheeled mobile robots (2WMRs) subject to time-varying communication delays. By checking the integral-type event-triggering conditions asynchronously and periodically, each 2WMR determines whether or not to sample and broadcast its states. When the information used in an agent's controller is updated, the 2WMR calculates its x (or y ) control input, and then a Rotate&Compensate&Run Rendezvous Scheme is provided for 2WMRs to update their states. We present a sufficient condition for 2WMRs to asymptotically reach rendezvous, and the convergence analysis is conducted using the Lyapunov functional approach. Experiments are further presented to validate the effectiveness of the proposed control method.

This paper investigates the containment control problem of multiagent systems with double integrator dynamics under directed topologies. A model-based edge-event-triggered control protocol is proposed, in which the control input to each agent only contains edge information and its own velocity information. Continuous detection is avoided by the establishment of a predictive model and each controller is only updated at its own event time instants. The theoretical results show that, under our control protocol, the containment control problem can be solved and the Zeno behavior is excluded. The effectiveness is further illustrated by simulation results.

This paper focuses on the average consensus of double-integrator networked systems based on the asynchronous periodic edge-event triggered control. The asynchronous property lies in the edge event-detecting procedure. For different edges, their event detections are performed at different times and the corresponding events occur independently of each other. When an event is activated, the two adjacent agents connected by the corresponding link sample their relative state information and update their controllers. The application of incidence matrix facilitates the transformation of control objects from the agent-based to the edge-based. Practically, due to the constraints of network bandwidth and communication distance, agents usually cannot receive the instantaneous information of some others, which has an impact on the system performance. Hence, it is necessary to investigate the presence of communication time delays. For double-integrator multiagent systems with and without communication time delays, the average state consensus can be asynchronously achieved by designing appropriate parameters under the proposed event-detecting rules. The presented results specify the relationship among the maximum allowable time delays, interaction topologies, and event-detecting periods. Furthermore, the proposed protocols have the advantages of reduced communication costs and controller-updating costs. Simulation examples are given to illustrate the proposed theoretical results.

The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.

This paper studies the delay robustness of a class of synchronous hybrid event- and time-driven consensus protocols in undirected networks. These protocols can ensure the system performance at reduced data-sampling rates. We consider three types of time delays in feedbacks, including one common time delay, multiple time-invariant delays, and multiple time-varying delays; and by sampled-data control techniques, we characterize the maximum allowable time delay and the event-detecting period for solving the average consensus problem in terms of the algebraic structure of interaction topologies. Simulations are given to show the effectiveness of theoretical results.

This paper considers an anisotropic swarm model with an attraction/repulsion function. We study its aggregation properties and show that the swarm members aggregate and eventually form a cohesive cluster of finite size around their weighted center in a finite time. Numerical simulations demonstrate that all agents eventually enter and remain in a bounded region around the weighted center. The swarm may eventually stop moving or exhibit complex spiral motion due to asymmetry of the coupling structure. The model in this paper is more general than isotropic swarms and our results provide further insight into the effect of the interaction pattern on individual motion in a swarm system