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With the growing reliance of modern supercomputers on accelerator-based architecture such a graphics processing units (GPUs), the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development GPU accelerated, distributed memory algorithms for many modern electronic structure methods, the primary focus of GPU development for Gaussian basis atomic orbital methods has been for shared memory systems with only a handful of examples pursing massive parallelism. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact exchange matrices for hybrid Kohn–Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer. [ABSTRACT FROM AUTHOR]

This paper investigates the mean-square bounded consensus issue in a two-layer multi-agent network under deception attacks. The two-layer network is composed of the leader and follower layers with a switching topology. Employing an impulsive control method, the mean-square bounded consensus for the leader layer and the node-to-node mean-square bounded consensus of the two-layer network are analyzed. Based on the knowledge of graph theory, Lyapunov stability theory, and linear matrix inequalities, sufficient conditions for the mean-square bounded consensus of multi-agent systems in the two-layer network are derived. Finally, the practicability and efficacy of the theoretical outcomes are corroborated via the provided numerical simulations. [ABSTRACT FROM AUTHOR]

Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem and also a special hidden subgroup problem: Given a function f : { 0 , 1 } n → { 0 , 1 } m , it is promised that there exists a hidden subgroup S ≤ Z 2 n of rank k such that for any x , y ∈ { 0 , 1 } n , f (x) = f (y) iff x ⊕ y ∈ S . The goal of generalized Simon's problem is to find the hidden subgroup S. In this paper, we present two key contributions. Firstly, we characterize the structure of the generalized Simon's problem in distributed scenario and introduce a corresponding distributed quantum algorithm. Secondly, we refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique. Our algorithm offers exponential speedup compared to the distributed classical algorithm. When contrasted with the quantum algorithm for the generalized Simon's problem, our algorithm's oracle requires fewer qubits, thus making it easier to be physically implemented. Particularly, the exact distributed quantum algorithm we develop for the generalized Simon's problem outperforms the best previously proposed distributed quantum algorithm for Simon's problem in terms of generalizability and exactness. [ABSTRACT FROM AUTHOR]

This study investigates distributed convex optimisation that accounts for the inequality constraints over unbalanced directed graphs. In distributed optimisation, agents exchange information on a network to obtain an optimal solution when they only know their own cost function. We propose a distributed primal-dual subgradient method based on a row stochastic weight matrix that is associated with a communication network. In the proposed method, the normalised left eigenvector of the weight matrix is estimated by a consensus algorithm. Then, the subgradient of the Lagrange function is scaled by the estimated values of the left eigenvector to compensate for the imbalance of the information flow in the network. We show that the pair of estimations for the primal and dual problems converge to an optimal primal-dual solution. We also show the relation between the convergence rate of the proposed algorithm and the step-size rule. A numerical example confirms the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper models a class of hierarchical cyber-physical systems and studies its consensus problem. The model has a pyramid structure, reflecting many realistic natural or human systems. By analysing the spectrum of the coupling matrix, it is shown that all nodes in the physical layer can reach consensus based on the proposed distributed protocols without interlayer delays. Then, the result is extended to the case with interlayer delays. A necessary and sufficient condition for consensus seeking is derived from the frequency domain perspective, which describes a permissible range of the delay. Finally, the application of the proposed model in the power-sharing problem is simulated to demonstrate the effectiveness and significance of the developed results. [ABSTRACT FROM AUTHOR]

This article studies the distributed containment control of a second‐order discrete‐time multi‐agent system with convex constraints on positions, nonconvex constraints on velocities, bounded disturbances on static points and switching topologies. A distributed control algorithm with disturbance information and local information is proposed. It is proved that when the static points with disturbances and the joint graph have a directed spanning forest among each time interval, all agents are gradually driven to the neighborhood of a convex hull spanned by the static points, and an upper bound of the neighborhood is obtained. The most innovative point is to utilize a rigorous mathematical theory to deal with convex constraint error rather than a geometric explanation. Meanwhile, another control algorithm with static point information and local information is proposed to converge all agents to the convex hull in the absence of external disturbances. Additionally, a numerical example is conducted to illustrate this theory. [ABSTRACT FROM AUTHOR]

This article studies the practical fixed‐time average consensus problem of general linear multi‐agent systems under switching topologies. First, a distributed fixed‐time consensus control protocol based on dynamic event‐triggered mechanism is designed by using the local information exchange between neighboring agents. The protocol introduces an internal dynamic variable and the triggering condition changes in real time based on the dynamic variable obtained online, which can significantly reduce the number of triggering events and effectively decrease the energy consumption of the multi‐agent system. Then, the sufficient conditions for the multi‐agent system to solve the practical fixed‐time average consensus problem are given, and it is proved that there is no Zeno behavior in the system. Furthermore, a self‐triggered control scheme is proposed such that the neighboring agents communicate with each other only when one of them is triggered. In other words, this scheme does not require continuous communication between neighboring agents and thus reduces communication cost of the system. Finally, the simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques. [ABSTRACT FROM AUTHOR]

A charge and discharge management scheme is proposed. The stored electric energy in distributed storage devices will converge to the consistent. The consistency of the stored electric energy of the devices helps to maintain the maximum load capacity and maximum consumption capacity of distributed storage devices. The charging and discharging process is constructed as a time-varying optimization problem, and the proposed algorithm can respond to the time-varying parameters of the distributed storage devices in real time. The time-varying neurodynamic algorithms can obtain time-varying optimal solution trajectories to give the optimal charging and discharging strategy in real time. In addition, the proposed approach in this paper focuses on the privacy protection of device data. Each device can calculate the power of discharging or charging by communicating with the partially connected nodes. Numerical simulations of the proposed scheme in the paper are given to verify the effectiveness of the scheme. Numerical simulations show that our scheme can make the electric energy stored in each storage device converge and maintain the maximum load capacity or maximum consumption capacity of the whole distributed storage device. [ABSTRACT FROM AUTHOR]

Plug-in hybrid electric vehicles (PHEVs) are becoming increasingly widespread due to their environmental benefits. However, PHEV penetration can overload distribution systems and increase operational costs. It is a major challenge to find an economically optimal solution under the condition of flattening load demand for systems. To this end, we formulate this problem as a two-layer optimization problem, and propose a hierarchical algorithm to solve it. For the upper layer, we flatten the load demand curve by using the water-filling principle. For the lower layer, we minimize the total cost for all consumers through a consensus-like iterative method in a distributed manner. Technical constraints caused by consumer demand and power limitations are both taken into account. In addition, a moving horizon approach is used to handle the random arrival of PHEVs and the inaccuracy of the forecast base demand. This paper focuses on distributed solutions under a time-varying switching topology so that all PHEV chargers conduct local computation and merely communicate with their neighbors, which is substantially different from the existing works. The advantages of our algorithm include a reduction in computational burden and high adaptability, which clearly has its own significance for the future smart grid. Finally, we demonstrate the advantages of the proposed algorithm in both theory and simulation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a distributed online optimization method on multiagent communication networks. We consider a distributed prime-dual subgradient algorithm for an online convex optimization problem with time-varying coupled constraints. Each agent updates the estimations for the primal and dual optimizers by a consensus-based online algorithm. In the proposed algorithm, the gradient direction is scaled by estimating the left eigenvector of a weight matrix associated with the directed communication network. The scaling procedure enables agents in the network to estimate the time-varying optimal solutions by counterbalancing the unbalanced communication flows. The performance of the proposed algorithm is examined by a dynamic regret and a fit, which evaluate the cumulative error against the time-varying optimal cost function and the constraint function, respectively. We provide a sufficient condition under which both the dynamic regret and the fit are sublinear. A numerical example of an online economic dispatch problem confirms the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The growing integration of distributed energy resources underscores the critical importance of having precise insights into the dynamics of an electrical power system (EPS). Consequently, an estimator must align with the EPS dynamics to enhance the overall reliability, safety, and system stability. This alignment ensures that operators can make informed decisions during system operations. An initial step in gaining insight into the system's state involves examining its state vector, which is represented by voltage phasors. These results are derived through the application of a distributed state-estimation process in large-scale systems. This study delved into the effectiveness of Bayesian filters, with a particular emphasis on the extended Kalman filter (EKF) algorithm in the context of distributed state estimation. To analyze the outcomes, the nodal partitioning process was incorporated within the distributed state-estimation framework. The synergy between the EKF algorithm and the partitioning method was evaluated using the IEEE118 test system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of asynchronous estimation in the presence of packet losses for the randomly sampling nonlinear system. Packet losses occur at the control input and at the measurement side. Firstly, the synchronization of the asynchronous sampling system is realized by weighting the state of the adjacent state update points. Secondly, the projection theorem is used to estimate the system state at the sampling time. Due to modeling errors and unmodeled dynamics, obtaining an accurate dynamic model is challenging. Therefore, observation inference based on interpolation techniques is proposed to solve the asynchronous estimation problem. Furthermore, the algorithm is extended to multi-sensor systems to obtain a distributed fusion estimator. Finally, simulation experiments are conducted to validate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the fully distributed containment problem is investigated for a class of second-order nonlinear multi-agent systems (MASs) with disturbance and uncertain control coefficient. In the dynamics of the multi-agent systems, the nonlinear term of the multi-agent systems is Lipshitz, the leaders are subject to bounded inputs, and the disturbances are also bounded. But, the Lipshitz constant, the upper bounds of the disturbances and the leaders' control inputs are unknown; thus, they cannot be used for the design of feedback control. To overcome the difficulty from such unknown bounds and uncertain coefficient, a new fully distributed adaptive protocol is proposed by combining the Lyapunov analysis and adaptive control technique, which based only on relative states of neighboring agents without using any global information, such that the states of the followers converge to the convex hull formed by the states of the leaders. Compared with the existing works, one main contribution is that only one adaptive gain is adopted in the fully distributed adaptive protocol to deal with containment problem of second-order nonlinear MASs, where four unknown parameters are involved. Two simulation examples are given to show the performance of the proposed protocol. [ABSTRACT FROM AUTHOR]

Summary: This study investigates the issue of containment control (CC) of multi‐agent systems (MASs) that are heterogeneous, nonlinear, and fractional‐order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time‐varying state delays, and distributed time‐varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type‐2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self‐information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov‐Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional‐order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: The identification of switched systems amounts to a mixed integer nonlinear optimization problem, where the continuous variables are associated to the model parameterizations of the different modes, and the discrete ones are related to the switching signal (each data sample is assigned to a mode, and switching occurs when the mode assignment changes over time). In the batch form of the identification problem, the combinatorial complexity increases exponentially with the size of the training set, which makes the precise identification of the switching signal the most challenging task in the identification problem. To tackle this complexity we propose a distributed optimization approach, based on the solution of multiple instances of a much simpler problem, where switching can occur only at specific time instants (different for each subproblem), and an information sharing mechanism that preserves likely switching times to improve the local solutions. We employ an adapted version of a previously developed randomized algorithm to solve the individual subproblems. Another important feature of the proposed method is an a posteriori heuristic correction method, that is applied to further refine the switching locations based on the estimated local models before the information sharing phase. The performance of the proposed algorithm is analyzed and compared with other methods on synthetic datasets. [ABSTRACT FROM AUTHOR]

Frequently, unit disk graphs (UDGs) are used as abstractions of wireless networks. In the paper, we study the problem of finding an extended minimum connected dominating set (E-MCDS) in a wireless network with cooperative communication (CC), which was proposed in Wu et al. (IEEE Trans Parallel Distrib Syst 17(8):851–864, 2006) and is NP-hard. We propose a two-phase centralized algorithm to construct an extended connected dominating set (ECDS) for a given UDG with CC. First, we construct a 2-hop extended dominating set (EDS) in the UDG. Then, we add some new nodes into the 2-hop EDS to make it connected. To obtain the performance ratio of this two-phase centralized algorithm, we first give an upper bound on the size of the 2-hop EDS. Using this upper bound, we prove that the size of the ECDS found by the centralized algorithm is no greater than 27.192 opt - 3 or 160 ECDS opt - 3 , where opt and ECDS opt are the sizes of the minimum connected dominating set and the E-MCDS, respectively, in the UDG. Finally, a 160-approximate distributed algorithm based on the two-phase centralized algorithm is proposed, and its message and time complexities are analyzed, both of which are O (n 3) . Simulation results show that our work outperforms competing methods on average. [ABSTRACT FROM AUTHOR]

Distributed algorithms are receiving renewed attention across multiple disciplines due to the dramatically increasing demand of big data processing. We consider a class of consensus optimization problems over a static network system of multiple agents, where each of local cost functions is a sum of a smooth function and a non-Lipschitz regularization term. This kind of problems is widely found in scientific and engineering areas such as machine learning and data analysis. Inspired by Bian and Chen (SIAM J. Opt. 23(3), 1718–1741 2017), we propose a decentralized smoothing quadratic regularization algorithm (abbreviated as D-SQRA) for solving the composite consensus problem with non-Lipschitz singularities. To some extent, D-SQRA can be seen as an extension in the decentralized setup of the smoothing quadratic regularization algorithm (SQRA) proposed in (SIAM J. Opt. 23(3), 1718–1741 2017). Our main contribution is to show that D-SQRA can inherit the theoretical properties of its centralized counterpart, i.e., SQRA, in both sides of convergence and worst-case iteration complexity to achieve an ϵ scaled stationary point. We also present some numerical examples on sparse sensing problems based on synthetic and real datasets to corroborate the effectiveness of the proposed decentralized algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time consensus control for a class of multi-agent systems subject to unknown bounded disturbances under undirected topology. Firstly, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid the non-differential problem. Secondly, a distributed fixed-time control protocol is designed, which can realise the fixed-time convergence and improve the system convergence rate independent of the system's initial state. Thirdly, the dynamic event-triggered mechanism is proposed, such that the triggering frequency of events is reduced and communication energy consumption can be saved. The stability analysis is presented by employing the Lyapunov theory and the Zeno phenomenon is excluded. Finally, the simulation examples are presented to show the effectiveness and advantages of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problem of strong stabilisation for a class of distributed semilinear systems by means of a nonlinear feedback control. The systems under consideration evolve in a Hilbert space and present periodic time-varying state delay. We first give a proof for the existence and uniqueness of the solution for the considered systems. Then, under a null controllability condition, we establish the stabilisation result and provide an explicit optimal decay rate estimate. The particular case of such systems for which the linear part generates a differentiable semigroup is also investigated. Some illustrating applications to hyperbolic and parabolic equations are displayed. Finally, a conclusion and some perspectives are given. [ABSTRACT FROM AUTHOR]

Transitioning to low-carbon energy is key for reaching carbon neutrality and modernizing our energy systems, but it presents significant cost-related challenges for energy businesses. To foster optimal outcomes, this paper develops a game model including power generators, high-energy businesses, and consumers in the carbon trading framework. The model explores how different entities evolve their low-carbon strategies under social learning influence to optimize utility. Stability analysis of strategy and simulation experiments reveal the following findings: (1) Greater carbon quotas reduce power generators' low-carbon transition willingness while high-energy-consuming enterprises and consumers remain unchanged. (2) Higher prices for low-carbon products offered by high-energy-consuming enterprises boost low-carbon transition motivation across all parties. (3) Increased green premiums enhance revenue for all parties but are constrained by policy and carbon pricing. (4) Both direct and indirect increases in carbon emissions negatively impact the revenue and utility for all stakeholders. (5) Increasing social learning effect fosters a shift towards low-carbon strategies, accelerating the attainment of game equilibrium, and enhancing market stability and sustainability. This research provides decision support for carbon trading policy design and low-carbon transition of energy enterprises. [ABSTRACT FROM AUTHOR]

The emergence of microgrids arises from the growing integration of Renewable Energy Resources (RES) and Energy Storage Systems (ESSs) into Distribution Networks (DNs). Effective integration, coordination, and control of Multiple Microgrids (MMGs) whereas navigating the complexities of energy transition within this context poses a significant challenge. The dynamic operation of MMGs is a challenge faced by the traditional distributed hierarchical control techniques. The application of Artificial Intelligence (AI) techniques is a promising way to improve the control and dynamic operation of MMGs in future smart DNs. In this paper, an innovative hybrid optimization technique that originates from Cheetah Optimization (CHO) and Particle Swarm Optimization (PSO) techniques is proposed, known as HYCHOPSO. Extensive benchmark testing validates HYCHOPSO's superiority over CHO and PSO in terms of convergence performance. The objective for this hybridization stems from the complementary strengths of CHO and PSO. CHO demonstrates rapid convergence in local search spaces, while PSO excels in global exploration. By combining these techniques, the aim is to leverage their respective advantages and enhance the algorithm's overall performance in addressing complex optimization problems. The contribution of this paper offering a unique approach to addressing optimization challenges in microgrid systems. Through a comprehensive comparative study, HYCHOPSO is evaluated against various metaheuristic optimization approaches, demonstrating superior performance, particularly in optimizing the design parameters of Proportional-Integral (PI) controllers for hierarchical control systems within microgrids. This contribution expands the repertoire of available optimization methodologies and offers practical solutions to critical challenges in microgrid optimization, enhancing the efficiency, reliability, and sustainability of microgrid operations. HYCHOPSO achieves its optimal score within fewer than 50 iterations, unlike CHO, GWO, PSO, Hybrid-GWO-PSO, and SSIA-PSO, which stabilize after around 200 iterations. Across various benchmark functions, HYCHOPSO consistently demonstrates the lowest mean values, attains scores closer to the optimal values of the benchmark functions, underscoring its robust convergence capabilities.the proposed HYCHOPSO algorithm, paired with a PI controller for distributed hierarchical control, minimizes errors and enhances system reliability during dynamic MMG operations. Using HYCHOPSO framework, an accurate power sharing, voltage/frequency stability, seamless grid-to-island transition, and smooth resynchronization are achieved. This enhances the real application's reliability, flexibility, scalability and robustness. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the optimization problem of multi-agent systems (MAS) under undirected graph. To reduce the communication frequency among agents, a zero-gradient-sum (ZGS) algorithm based on dynamic event-triggered (DET) mechanism is investigated. The event-triggered condition of each agent only uses its own state information and the neighbor's state information at the previous triggering instants, without requiring continuous state information from the neighbor. In addition, the designed algorithm allows for the sampling period to be arbitrarily large. The Lyapunov method is utilized to derive the sufficient conditions that incorporate time delay and parameters. As the event is only checked at the periodic moment, zeno behavior can be directly excluded. Finally, numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The increasing penetration rate of distributed resources in the distribution network has brought about significant volatility and uncertainty problems. Demand response (DR) can flexibly change the energy consumption method of the user to balance supply and demand. This paper first considers the spatial distribution characteristics of DR resources to schedule DR resources to construct a distributed resource cloud-edge collaborative scheduling framework. Based on this, the distribution network scheduling requirements are combined with the multi-time scale characteristics of DR. A three-stage cloud-edge collaborative optimization scheduling strategy for distributed resources in the distribution network is proposed, which allocates the multi-time scale scheduling tasks of DR resources to the cloud and edge. Secondly, taking the cloud and edge as the optimization platform, a three-stage optimization decision-making model of the distribution network is established. In the day-ahead stage, the global optimization decision is made by combining cloud-centralized optimization with edge-independent optimization. In the intraday stage, edge-rolling optimization is carried out. In the real-time stage, the edge-distributed calculation is based on the consensus algorithm. Finally, the effectiveness and economy of the proposed model and strategy are verified by an example analysis. [ABSTRACT FROM AUTHOR]

The new power generation systems, the increasing number of equipment connected to the power grid, and the introduction of technologies such as the smart grid, underline the importance and complexity of the Power Quality (PQ) evaluation. In this scenario, an Automatic PQ Events Classifier (APQEC) that detects, segments, and classifies the anomaly in the power signal is needed for the timely intervention and maintenance of the grid. Due to the extension and complexity of the network, the number of points to be monitored is large, making the cost of the infrastructure unreasonable. To reduce the cost, a new architecture for an APQEC is proposed. This architecture is composed of several Locally Distributed Nodes (LDNs) and a Central Classification Unit (CCU). The LDNs are in charge of the acquisition, the detection of PQ events, and the segmentation of the power signal. Instead, the CCU receives the information from the nodes to classify the PQ events. A low-computational capability characterizes low-cost LDNs. For this reason, a suitable PQ event detection and segmentation method with low resource requirements is proposed. It is based on the use of a sliding observation window that establishes a reasonable time interval, which is also useful for signal classification and the multi-sine fitting algorithm to decompose the input signal in harmonic components. These components can be compared with established threshold values to detect if a PQ event occurs. Only in this case, the signal is sent to the CCU for the classification; otherwise, it is discarded. Numerical tests are performed to set the sliding window size and observe the behavior of the proposed method with the main PQ events presented in the literature, even when the SNR varies. Experimental results confirm the effectiveness of the proposal, highlighting the correspondence with numerical results and the reduced execution time when compared to FFT-based methods. [ABSTRACT FROM AUTHOR]

In this paper, the distributed online optimisation problem is considered in an unknown dynamic environment. Compared with the existing results, an unknown dynamic environment causes the problem to be more challenging. An online optimisation algorithm is designed based on distributed mirror descent and distributed average tracking technology. The analysis of dynamic regret is presented and a bounded regret is obtained. Some simulations are given to verify the validity of the designed algorithm. [ABSTRACT FROM AUTHOR]

This article develops distributed optimal control policies via Q‐learning for multi‐agent systems (MASs) by solving dual games. According to game theory, first, the distributed consensus problem is formulated as a multi‐player non‐zero‐sum game, where each agent is viewed as a player focusing only on its local performance and the whole MAS achieves Nash equilibrium. Second, for each agent, the anti‐disturbance problem is formulated as a two‐player zero‐sum game, in which the control input and external disturbance are a pair of opponents. Specifically, (1) an offline data‐driven off‐policy for distributed tracking algorithm based on momentum policy gradient (MPG) is developed, which can effectively achieve consensus of MASs with guaranteed l2$$ {l}_2 $$‐bounded synchronization error. (2) An actor‐critic‐disturbance neural network is employed to implement the MPG algorithm and obtain optimal policies. Finally, numerical and practical simulation results are conducted to verify the effectiveness of the developed tracking policies via MPG algorithm. [ABSTRACT FROM AUTHOR]

This article focuses on the robust fault tolerant control (FTC) problem for a class of Lipschitz nonlinear multi‐agent systems(MASs) subject to sensor faults. Firstly, sensor faults are transformed into actuator faults via introducing a new intermediate auxiliary state variable, and a distributed adaptive fault estimation observer is designed to estimate the state information and the concerned faults by using the relative output estimation error. Then, the sufficient existence conditions for the observer to satisfy the robust performance index are given. Thirdly, based on the results of observer design, a new design method of dynamic output feedback controller is proposed to implement consensus of MASs and ensure the desired disturbance rejection performance. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a new distributed finite‐time optimization algorithm for agents under directed graphs. By employing the nonsmooth technique and graph theory, a distributed discontinuous algorithm for continuous‐time agents subject to strongly convex local cost functions is first designed with a finite‐time distributed estimator, where the gradients of the local cost functions are estimated in finite time. It is shown that for a strongly connected graph and arbitrary initial conditions, the proposed algorithms can achieve consensus, and the systems can converge to the optimal point in finite time. Then, a two‐step approach is proposed to achieve finite‐time optimization of high‐order agents with disturbances under directed graphs. Finally, the validity of the proposed finite‐time optimization algorithm is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we consider the nonfragile containment control problem of nonlinear multi‐agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer‐based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

There are a series of challenges in microgrid transactions, and blockchain technology holds the promise of addressing these challenges. However, with the increasing number of users in microgrid transactions, existing blockchain systems may struggle to meet the growing demands for transactions. Therefore, this paper proposes an efficient and secure blockchain consensus algorithm designed to meet the demands of large-scale microgrid electricity transactions. The algorithm begins by utilizing a Spectral clustering algorithm to partition the blockchain network into different lower-level consensus set based on the transaction characteristics of nodes. Subsequently, a dual-layer consensus process is employed to enhance the efficiency of consensus. Additionally, we have designed a secure consensus set leader election strategy to promptly identify leaders with excellent performance. Finally, we have introduced an authentication method that combines zero-knowledge proofs and key sharing to further mitigate the risk of malicious nodes participating in the consensus. Theoretical analysis indicates that our proposed consensus algorithm, incorporating multiple layers of security measures, effectively withstands blockchain attacks such as denial of service. Simulation experiment results demonstrate that our algorithm outperforms similar blockchain algorithms significantly in terms of communication overhead, consensus latency, and throughput. [ABSTRACT FROM AUTHOR]

In the era of digital intelligence, this paper studies the task allocation algorithm of distributed large data stream group computing, and reasonably allocates the task of group computing to meet the needs of massive computing and analysis of distributed large data stream. According to the idea of swarm intelligence perception and crowdsourcing platform, the task allocation model of distributed large data stream group computing is constructed to realize the task allocation of group computing. A distributed large data stream group computing task model and a user model are constructed, user attributes are initialized by using the accuracy of the answers submitted by users, the possibility that users can participate in the group computing task is predicted by a logistic regression algorithm, so that user candidate sequences participating in the computing task can be obtained, and the accuracy of the user's real topics and corresponding topics can be grasped by capturing the candidate users' real topics and evaluating the accuracy algorithm. Select the users who meet the subject area, update the candidate user sequence, and filter the users again on the basis of fully considering the factors such as information gain, user integrity and cost, so as to get the final user sequence and complete the task allocation of group computing. Experiments show that this method can solve the problem of distributed large data flow group computing task allocation, achieve high accuracy, reduce the cost, and effectively improve the information gain. [ABSTRACT FROM AUTHOR]

This paper focuses on distributed consensus optimization problems with coupled constraints over time-varying multi-agent networks, where the global objective is the finite sum of all agents' private local objective functions, and decision variables of agents are subject to coupled equality and inequality constraints and a compact convex subset. Each agent exchanges information with its neighbors and processes local data. They cooperate to agree on a consensual decision vector that is an optimal solution to the considered optimization problems. We integrate ideas behind dynamic average consensus and primal-dual methods to develop a distributed algorithm and establish its sublinear convergence rate. In numerical simulations, to illustrate the effectiveness of the proposed algorithm, we compare it with some related methods by the Neyman–Pearson classification problem. [ABSTRACT FROM AUTHOR]

The question of how to simultaneously perform frequency regulation and integrated economic scheduling for microgrids with low-inertia islanding operation under communication constraints is a difficult problem that needs to be solved for many current applications. To this end, this paper establishes a microgrid scheduling control model containing a virtual synchronous generator (VSG) with multiple types of power sources and proposes a distributed optimization algorithm that integrates frequency regulation and comprehensive economic scheduling to simultaneously realize frequency regulation and economic scheduling in a microgrid. Firstly, a distributed economic dispatch problem is proposed based on a comprehensive consideration of the costs and benefits of various types of power VSGs, as well as the overall inertia and standby capacity requirements of the microgrid, which minimizes the integrated costs incurred by the participation of each type of VSG in the frequency regulation and improves the stable operation of the microgrid in terms of frequency under perturbation. Then, the optimal scheduling problem is solved by reconstructing the optimization problem based on considering the dynamic characteristics of microgrid inverters and using event-triggered communication to sense and compensate for the supply-demand imbalance online. The proposed method can avoid inter-layer coordination across time scales, improve the inertia, frequency regulation capability, and economy of the system, and enhance its robustness to short-term communication failures. Finally, simulation results are used to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The AIoT, with its artificial intelligence capabilities, can further enhance Device‐to‐Device (D2D) communication. Based on Non‐Orthogonal Multiple Access (NOMA), D2D technology can effectively alleviate wireless spectrum resource pressure and improve the capacity of heterogeneous cellular networks. However, it also introduces significant system interference issues. In this paper, a resource allocation algorithm is proposed for the NOMA‐D2D heterogeneous cellular network, based on a multi‐agent deep reinforcement learning framework. Firstly, the algorithm allocates appropriate channels to D2D clusters. Then, the power allocation factors and D2D transmit power are jointly optimized to suppress the interference and improve the system performance. Simulation results show that both the channel allocation efficiency and the power control performance of the system can be significantly improved. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus control problem of Euler–Lagrange systems which can be used to describe the motion of various mechanical systems such as manipulators and quadcopters. We focus on consensus control strategies, which are important for achieving coordinated behavior in multi-agent systems. The paper considers the key challenges posed by random communication delays and packet losses that are increasingly common in networked control systems. In addition, it is assumed that each system receives information from neighboring agents intermittently. Addressing these challenges is critical to ensure the reliability and efficiency of such systems in real-world applications. Communication delay is time-varying and can be very large, but should be smaller than some bounded constant. To decrease the frequency of control input updates, we implement an event-triggered scheme that regulates the controller's updates for each agent. Specifically, it does not update control inputs at traditional fixed intervals, but responds to predefined conditions and introduces a dynamic consensus item to handle information irregularities caused by communication delays and intermittent information exchange. The consensus can be achieved if the communication graph of agents contains a spanning tree with the desired velocity as the root node. That is, all Euler–Lagrange systems need to obtain the desired velocity, directly or indirectly (via neighbors), to reach consensus. We establish that the Zeno behavior can be avoided, ensuring a positive minimum duration between successive event-triggered instances. Finally, we provide simulation results to show the performance of our proposed algorithm. [ABSTRACT FROM AUTHOR]

In most wireless networks, users/peers are connected to backbone networks using access links. The access link capacity is divided into upload and download capacity, and these capacities are used for upload and download of data, respectively. A peer can modify this division of link capacity between upload and download. A peer will allocate its entire link capacity for download to maximize utility. But incentive mechanism forces them to allocate some portion of capacity for upload. This paper investigates how to optimally divide link capacity so that peers receive maximum utility in a P2P network. We model this scenario as a game and determine capacity partitioning of peers during the Nash equilibrium NE. We also prove the social optimality of NE. As this portioning maximizes individual as well as social benefit, so NE is an optimal state of capacity partition. Using simulation, we verify that NE is an optimal state. BitTorrent network and a distributed algorithm for dividing access capacities are simulated, and partition providing maximum utility is compared with NE. This work provides a generalized expression and the mathematical proof for capacity partitioning at which peers receive maximum utility. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a distributed joint parameter and state variables estimation algorithm for large‐scale state‐space interconnected systems. In this distributed estimation scheme, each interconnected sub‐system is described by a linear discrete‐time state space mathematical model. Each sub‐system is supposed to be controlled by an intelligent controller that can communicate with its interconnected neighbors and exchange information, such as state variables. The proposed approach comprises two recursive estimation algorithms, a parameter estimation algorithm considering the state space model and a distributed Kalman filter for state variables estimation. It is a fully distributed cooperative approach that allows to reduce complexity and saves computational and communication resources. Theoretical analysis and numerical examples are provided to prove the feasibility and effectiveness of this joint estimation algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with a two-dimensional fractional optimal control problem whose governing equations are distributed order fractional differential equations in the Caputo sense. A generalized fractional-order Legendre wavelet method has been used to solve the two-dimensional distributed-order fractional optimal control problem. An exact formula for the Riemann–Liouville integration of generalized fractional-order Legendre wavelet has been derived by using regularized beta functions. This formula and the two-dimensional Gauss–Legendre integration formula have been used to solve the two-dimensional distributed order fractional optimal control problem. Moreover, an L 2-error estimate in the approximation of an unknown function with a generalized fractional-order Legendre wavelet has been derived and the estimated order has been verified for a given function. Furthermore, convergence analysis for the proposed method has been presented. In the last, two test problems have been considered to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the flocking behavior of a locally interacting multi‐agent system with a unit speed constraint. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimation on perturbations of a linearized system, we obtain a sufficient condition imposed only on initial data and model parameters to guarantee flocking and further show that the system achieves a consensus at an exponential rate. [ABSTRACT FROM AUTHOR]

Longitudinal data, measurements taken from the same subjects over time, appear routinely in many scientific fields, such as biomedical science, public health, ecology and environmental sciences. With the rapid development of information technology, modern longitudinal data are becoming massive in volume and high dimensional, hence often require distributed analysis in real-world applications. Standard divide-and-conquer techniques do not apply directly to longitudinal big data due to within-subject dependence. In this paper, we focus on developing a distributed algorithm to support quantile regression (QR) analysis of longitudinal big data, which currently remains an open and challenging issue. We employ weighted quantile regression (WQR) to accommodate the correlation in longitudinal big data, and parallelize the WQR estimation process with a two-stage algorithm to support distributed computing. Based on weights estimated in the first stage by the Newton–Raphson algorithm, the second stage solves the WQR problem using the multi-block alternating direction method of multipliers (ADMM). Simulation studies show that, compared to traditional non-distributed algorithms, our proposed method has favorable estimation accuracy and is computationally more efficient in both non-distributed and distributed environments. Further, we also analyze an air quality data set to illustrate the practical performance of this method. [ABSTRACT FROM AUTHOR]

Multicategory classification problems are frequently encountered in practice. Considering that the massive data sets are increasingly common and often stored locally, we first provide a distributed estimation in the multicategory angle-based classification framework and obtain its excess risk under general conditions. Further, under varied robustness settings, we develop two robust distributed algorithms to provide robust estimations of the multicategory classification. The first robust distributed algorithm takes advantage of median-of-means (MOM) and is designed by the MOM-based gradient estimation. The second robust distributed algorithm is implemented by constructing the weighted-based gradient estimation. The theoretical guarantees of our algorithms are established via the non-asymptotic error bounds of the iterative estimations. Some numerical simulations demonstrate that our methods can effectively reduce the impact of outliers. [ABSTRACT FROM AUTHOR]

This paper develops a distributed consensus control protocol that guarantees consensus tracking and global optimality with respect to a positive quadratic performance index for identical general linear multi-agent systems on an undirected graph. By using the previewable future reference signal, the consensus tracking control problem is converted into a preview control based optimal problem. The inverse optimality theory is introduced to overcome the difficulty of designing a distributed optimal controller, which is caused by the fact that the communication topology always interplays with the system dynamics and subsequently the global information is usually required in a conventional optimal controller design. First, a distributed optimal controller for tracking a reference signal with stable mode is designed. Then, an internal model based distributed optimal controller is further designed to track a time-varying reference signal. The structured quadratic performance indexes are derived for both cases, respectively, and based on which, two distributed optimal tracking control protocols are implemented to guarantee the asymptotic stability of the augmented systems only using local information. Simulation results show that an appropriate preview length can effectively improve the tracking performance. [ABSTRACT FROM AUTHOR]

The trajectory optimization of multiple quadcopters for Mars exploration has been a challenging task due to a difficult nonconvex space formed by multiple quadcopters in the flight, the complex dynamics model, and complicated obstacle environments. We propose a distributed optimization algorithm (DiPenOpt) using direct collocation methods to solve the optimization in the nonconvex space. The DiPenOpt algorithm contains a penalty function method to transfer the nonconvex space into a convex one and an iterative optimization strategy employing initial value selection methods to enhance the algorithm's convergence rate. We design a position-tracking controller to ensure that the quadcopters can effectively follow trajectories generated by the DiPenOpt, regardless of initial position deviations and uncertainties. We compare the results of the DiPenOpt with other algorithms and find that DiPenOpt has a faster solution speed and shows superior robustness for trajectory optimization of multiple quadcopters in large and complex environments. The simulation results show that the position-tracking controller can ensure error convergence and stabilize the flight path when the quadcopter has an initial error. Practical Applications: When exploring Mars with multiple quadcopters, ensuring they move efficiently and safely is critical. Think of it like trying to coordinate several quadcopters in a maze-like environment, where every quadcopter needs its own clear path. Our research introduces a new way (DiPenOpt) to help these quadcopters find their best paths, even in complicated surroundings. Our method makes challenging path-finding problems simpler, and we have added tools to make sure quadcopters stick to their paths, even if they start off a little off-course or have uncertain disturbances. Compared to other methods, DiPenOpt is faster and better suited for situations where there are many quadcopters and obstacles. In simple terms, if we were to send a team of quadcopters to explore Mars, our method would make it easier for them to navigate and provide more reliable results, which is crucial for successful space missions. [ABSTRACT FROM AUTHOR]

Summary: In the era of big data, massive amounts of data hold great value. However, much data exists as isolated islands, and the maximum value of the data cannot be fully utilized. Federated learning allows each client to train local data and then share the training model parameters securely, which can address the isolated data island problem and exploit data value while ensuring data privacy and security. Accordingly, in order to securely complete the electric power load forecasting using existing data, this paper constructs a federated learning‐based privacy‐preserving scheme to support electricity load forecasting in edge computing scenarios. To address the problems of the data‐isolated islands and data privacy in electric power systems, this paper proposes a decentralized distributed solution based on the federated learning technique. Our scheme achieves electricity load forecasting for power systems through the federated learning‐based framework and uses edge computing architecture to improve real‐time data capability and reduce network latency. For the hierarchical scheduling structure in power systems, we divide the system into a cloud‐side‐device three‐layer architecture, which achieves structural coordination and balance, and each layer collects information according to the scheduling control tasks, promoting scheduling effectiveness. Finally, different privacy protection methods are used on the cloud‐edge and edge‐device sides to significantly enhance data security. Moreover, We have conducted extensive experimental simulations for our proposed scheme. The experimental results show that the relative error of electricity load forecasting is around 1.580%. Meanwhile, our scheme achieves high accuracy and low memory usage. The security analysis proves the feasibility and security of our scheme. [ABSTRACT FROM AUTHOR]

A distributed control scheme based on historical information is designed to solve the problem of stable control of multi‐agent systems under denial of service (DoS) attacks in this article. It achieves the control objective of bipartite output containment control, that is, the output states of the followers smoothly enter the target area. The control scheme updates the states of followers through historical information in the control protocol when agents are subjected to DoS attacks. A distributed state observer with a storage module is designed to efficiently estimate the state of followers and store the observed information as history information. The historical information of control protocol calls is not necessarily the real state information in the existence of DoS attacks. Consequently, a closed‐loop feedback state compensator is designed. Then, the state compensator is converted from the time domain to the frequency domain for stability analysis using the Nyquist criterion. It is obtained that an upper bound on the amount of historical information can achieve the bipartite output trajectories containment of the controlled system. The output trajectories of the followers converge into two dynamic convex hulls, one of which is surrounded by multiple leaders, and the other is a convex hull with opposite signs of the leaders. Finally, a numerical simulation is used to verify the proposed control scheme, and the operability of the scheme is further demonstrated in a physical experiment. [ABSTRACT FROM AUTHOR]

This study addresses the problem of distributed optimization in control of heterogeneous linear multi‐agent systems. Instead of assuming a perfect communication medium as in many existing approaches, two important issues arising from communication networks are considered. First, the existence of communication delays is assumed when each agent receives information from its neighbors. Second, since communication networks are generally unreliable, it is assumed that each agent interacts with other agents through random digraphs. Finally, delay‐dependent sufficient conditions are derived in the form of linear matrix inequalities (LMIs) to prove convergence to optimal solutions. Numerical simulation results are analyzed to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]