Accurate forecasting of household energy load and generation is critical for energy management systems, especially in the context of the rapid development of smart grids and renewable energy. However, privacy concerns often arise when handling sensitive household energy data. Federated learning (FL), as a privacy-preserving distributed learning method, enables collaborative model training across households without exposing sensitive energy data. Nevertheless, traditional federated learning still faces challenges in meeting the personalized needs of households due to the differences in consumption patterns among households, which affects the forecasting accuracy. In this paper, we propose a novel personalized FL method that combines mixture of expert and conformal predictions to improve forecasting accuracy while quantifying prediction uncertainty. Our method utilizes personalized federated learning (PFL) to develop a personalized model for each household that captures its unique consumption behavior. The mixture of experts dynamically integrates global and local personalized models to enhance prediction and adaptability. In addition, uncertainty quantification is achieved through conformal prediction, providing reliable prediction interval. Experiments conducted on two real-world household energy datasets demonstrate that our method outperforms existing approaches in terms of prediction accuracy and uncertainty assessment.

Embodied intelligence and related disciplines have identified several mechanisms that help embodied agents learn how to solve complex problems. Reinforcement learning (RL) is one of the most promising computational approaches toward enhancement of the learning-based problem-solving abilities of such agents. Given the recent rapid evolution of artificial intelligence, RL has become a keystone technology, accelerating scientific discoveries and also finding applications in many other domains. In RL, an agent collects data when interacting with the environment, which optimizes a policy ensuring a higher return. Further improvement requires more exploration of the action space. However, not all actions in that space are safe and acceptable. The exploration of an agent must be constrained. In this work, a novel mirror descent safe policy optimization (MDSPO) algorithm is proposed to ensure the safety of an RL agent. The algorithm leverages mirror descent optimization to maximize the return while satisfying the safety constraint. A novel optimization objective is formulated, and an innovative three-stage optimization strategy is employed-comprising gradient descent without the cost constraint, projection onto the nonparametric policy space with the cost constraint, and projection onto the parametric policy space. Compared to previous methods, MDSPO is a simple and easy to implement first-order approach, which does not impose a hard constraint on the trust region. Theoretical analysis of the MDSPO reveals a lower bound on return improvement and an upper bound on constraint violation at the time of each policy update. The numerical results obtained from two sets of different constrained locomotive experiments demonstrate that MDSPO improves the average return by about 12% and better satisfies the cost constraints than other state-of-the-art methods do. In a real-world obstacle avoidance experiment using an unmanned surface vessel, MDSPO both finds the optimal path and guarantees agent safety.

This paper is concerned with the distributed coordination problem for the nonlinear multi-agent system (MAS) over a general digraph, where each agent is a multi-input multi-output system. The existing solutions are limited to the system without inputs coupling and with known, global Lipschitz, or linearly growing nonlinearities. To remove these requirements, we propose an integrated sub-optimal and control strategy for the more general nonlinear MAS. It consists of a fully distributed adaptive gradient optimization algorithm and a set of model-free prescribed performance controllers. Our approach ensures that the outputs of the MAS converge to the arbitrarily small neighborhoods of the optimal outputs; in particular, the reference-tracking performance is allowed to be freely predefined. Besides, the proposed control strategy is notably simple compared to the existing approaches, which typically employ function approximation, parameter identification, or derivative calculation. Finally, the simulation results illustrate the effectiveness and superiority of the proposed approach.

Energy trading in industrial parks has great potential for reducing carbon emissions and lowering energy bills. This article proposes a safe multiagent deep reinforcement learning algorithm for optimizing the energy trading strategy in industrial parks to achieve less reliance on the main grid and save energy costs. Specifically, an industrial park that contains multiple industrial users with both thermal and electrical load requirements is considered, in which the different users can trade energy with each other and with the main grid based on their own strategies. Unlike the existing studies, the time-phased energy trading problem is transformed into a constrained partially observable Markov game, which models the industrial users and objectives of the buyers and sellers. Finally, a novel multiagent primal-dual proximal policy optimization algorithm that guarantees safety is developed to achieve the optimal trading strategies between the main grid and multiple users. Numerical simulations with real-world data demonstrate that the proposed algorithm allows higher total revenue for sellers and lower total costs for buyers in the park, limits each user's bid or offer to a relatively safe range, and increases the amount of electricity traded locally, while reducing trading with the grid.

Deep learning has become increasingly important in fault diagnosis, but it relies on a large amount of high-quality labeled data. Collecting data from distributed machines can expand the dataset, but it usually leads to privacy concerns. Moreover, since the operating conditions are complex in real-world applications, the collected training data and the test data often have different distributions. Therefore, a well-trained model on the training data may not be suitable for test data due to the domain shift. To preserve privacy and to mitigate the domain shift, in existing federated transfer learning fault diagnosis methods, distributed machines exchange model parameters and features rather than raw data with the central server. However, such methods suffer from a single point of failure and high communication burden. To address these issues, we propose a fully decentralized federated transfer learning fault diagnosis method. More specifically, the proposed method obtains a pretrained model among source nodes with labeled training data where each source node exchanges model parameters with its neighboring source nodes. Moreover, a novel transfer learning strategy is proposed, which aligns features of test data at the target node with features of training data at its connected source nodes to mitigate misclassifications resulting from the domain shift. The effectiveness of the proposed method is verified by various experiments on two public bearing datasets.

This paper considers the distributed nonconvex optimization problem, where the goal is to minimize the average of local nonconvex cost functions through local information exchange. Firstly, we propose a distributed optimization algorithm that integrates the gradient tracking method with a dynamic event-triggered communication scheme, thereby reducing communication overhead. Secondly, we demonstrate that the algorithm linearly converges to the global optimum under the Polyak-Łojasiewicz condition, which indicates that every stationary point is a global minimizer. The numerical experiment is presented to validate the theoretical results and confirm the algorithm's effectiveness.

This paper delves into a class of distributed nonconvex optimization control (DNOC) problems for multiagent systems (MASs), aiming to attain consensus among agents while minimizing the collective sum of local cost functions, referred to as the global cost function, through local information exchange. To accomplish this objective, it is introduced a novel distributed predefined-time optimal (DPTO) control algorithm. We prove that the proposed DPTO control algorithm guides the system states towards convergence to the global optimal solution within a user-defined time frame, provided that the global cost function satisfies the Polyak-Lojasiewicz condition, which is less stringent than the standard strong convexity condition. Finally, theoretical findings are substantiated through simulation studies.

This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak-Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.

As environmental pollution becomes increasingly serious and industrial energy consumption continuously rises, an intelligent and efficient industrial energy management policy is urgently needed to reduce costs and maximize the benefits of industrial energy systems. However, modern industrial energy systems are characterized by hybrid industrial equipment actions, diverse objectives, and highly intermittent and stochastically distributed renewable energy sources. Therefore, efficient operation and control are difficult. This article presents a novel, model-free energy management policy using a hybrid action deep reinforcement learning algorithm for energy scheduling of industrial equipments operating in various modes. Specifically, the interaction process between the industrial energy management center and each equipment is modeled as a Markov decision process that minimizes the daily operating cost of the energy system and maximizes the revenue of the production equipment. Then, a double parameterized deep Q-networks that does not require an explicit environmental model is developed to learn the hybrid action signals using actor and critic networks, in which the double Q value mechanism avoids value overestimation and improves the algorithm efficiency. In addition, the policy gradient of the proposed algorithm is derived and its convergence proof is discussed. Finally, numerical studies are conducted using real-world data to evaluate algorithm performance and verify its effectiveness.

State of health (SOH) estimation of lithium-ion batteries (LIBs) is of critical importance for battery management systems (BMSs) of electronic devices. An accurate SOH estimation is still a challenging problem limited by diverse usage conditions between training and testing LIBs. To tackle this problem, this article proposes a transfer learning-based method for personalized SOH estimation of a new battery. More specifically, a convolutional neural network (CNN) combined with an improved domain adaptation method is used to construct an SOH estimation model, where the CNN is used to automatically extract features from raw charging voltage trajectories, while the domain adaptation method named maximum mean discrepancy (MMD) is adopted to reduce the distribution difference between training and testing battery data. This article extends MMD from classification tasks to regression tasks, which can therefore be used for SOH estimation. Three different datasets with different charging policies, discharging policies, and ambient temperatures are used to validate the effectiveness and generalizability of the proposed method. The superiority of the proposed SOH estimation method is demonstrated through the comparison with direct model training using state-of-the-art machine learning methods and several other domain adaptation approaches. The results show that the proposed transfer learning-based method has wide generalizability as well as a positive precision improvement.

This article considers the semiglobal cooperative suboptimal output regulation problem of heterogeneous multi-agent systems with unknown agent dynamics in the presence of input saturation. To solve the problem, we develop distributed suboptimal control strategies from two perspectives, namely, model-based and data-driven. For the model-based case, we design a suboptimal control strategy by using the low-gain technique and output regulation theory. Moreover, when the agents' dynamics are unknown, we design a data-driven algorithm to solve the problem. We show that proposed control strategies ensure each agent's output gradually follows the reference signal and achieves interference suppression while guaranteeing closed-loop stability. The theoretical results are illustrated by a numerical simulation example.

This article is concerned with the fast and accurate trajectory tracking control problem for a sort of underactuated surface vehicle under model uncertainties and environmental disturbances. A novel neural networks (NNs)-based prescribed performance control strategy is proposed to solve the problem. In the control design, a new type of performance function is constructed which provides a way to predefine the settling time and accuracy, straightforward. Then, a pair of barrier functions are employed to combat not only the position error but also the virtual control input. This evades the possible singularity or discontinuity of the control solution. Next, an initialization technique is exploited, removing the requirement for the initial condition of the control system. Finally, two NNs are employed to deal with the unknown ship nonlinearities. The performance analysis not only demonstrates the effectiveness of the proposed approach but also reveals its robustness against disturbances and unknown reference trajectory derivatives. There is, thus, no need to acquire such knowledge or employ specialized tools to handle disturbances. The theoretical findings are illustrated by a simulation study.

This article focuses on solving the synchronization problem of neural networks (NNs) in the presence of denial-of-service (DoS) attacks and communication delays. Specifically, an attack detection algorithm constructed based upon the acknowledgment (ACK) signal is provided to detect the sleeping and active intervals of DoS attacks. To reduce information transmission during the synchronization-seeking process, a new kind of Lyapunov function-based resilient event-triggered mechanism (ETM) is designed to modulate the information transmission between the master and slave systems. Then, an event-based impulsive controller is designed to achieve synchronization in the master–slave systems with event-triggered communication and communication delay between the event generator and the controller, where the impulsive control instants are produced by the resilient ETM rather than prescribed. Furthermore, a resilient sampled-data-based ETM and an event-based controller consisting of hybrid state feedback and impulsive controllers are developed. Under the proposed ETMs and controllers, some sufficient yet efficient criteria are derived to guarantee the master–slave synchronization of NNs. The influence of the attack parameters and triggering parameters on the synchronization performance is also discussed. Finally, two numerical examples and an application in image encryption and decryption based on the master–slave chaotic systems are given to demonstrate the effectiveness of the theoretical results.

This article studies bipartite consensus of multiagent systems (MASs) with input saturation and denial-of-service (DoS) attacks over weighted directed networks. First, a distributed control protocol is proposed by using low-gain technology to address the input saturation constraint. Then, an estimator is introduced to design a dynamic event-triggered communication protocol, which avoids continuous communication between agents. In addition, sufficient conditions for realizing bipartite security consensus are obtained under insecure communication networks with DoS attacks. Moreover, the dual-channel concept is considered to further save resources. An event-triggered controller protocol and a dynamic event-triggered communication protocol are designed in the communication channel and the controller–actuator channel, respectively. By considering an exponential threshold, the event-triggered controller protocol can operate stably when the control signal is minute. Thus, a novel dynamic event-triggered communication protocol is obtained to implement bipartite security consensus and exclude Zeno behavior. Finally, a practical example is presented to show the effectiveness of our design method.

With the increasing penetration of renewable energy and flexible loads in smart grids, a more complicated power system with high uncertainty is gradually formed, which brings about great challenges to smart grid operations. Traditional optimization methods usually require accurate mathematical models and parameters and cannot deal well with the growing complexity and uncertainty. Fortunately, the widespread popularity of advanced meters makes it possible for smart grid to collect massive data, which offers opportunities for data-driven artificial intelligence methods to address the optimal operation and control issues. Therein, deep reinforcement learning (DRL) has attracted extensive attention for its excellent performance in operation problems with high uncertainty. To this end, this article presents a comprehensive literature survey on DRL and its applications in smart grid operations. First, a detailed overview of DRL, from fundamental concepts to advanced models, is conducted in this article. Afterward, we review various DRL techniques as well as their extensions developed to cope with emerging issues in the smart grid, including optimal dispatch, operational control, electricity market, and other emerging areas. In addition, an application-oriented survey of DRL in smart grid is presented to identify difficulties for future research. Finally, essential challenges, potential solutions, and future research directions concerning the DRL applications in smart grid are also discussed.

This article investigates the distributed fuzzy adaptive containment control problem of stochastic nonlinear multiagent systems under a directed communication topology suffering denial-of-service (DoS) attacks. First, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It$\hat{o}$stochastic nonlinearity terms approximated through fuzzy logic systems. Second, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through the backstepping control approach despite suffering DoS cyberattacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

This paper proposes a distributed cooperative control strategy for cyber-physical microgrids in a distributed sparse network with communication delays by using predictive control theory, which enables each distributed generator (DG) unit to achieve voltage restoration. In the proposed control strategy, we first design a primary droop-free model predictive controller to make the output voltage track its nominal set points timely, with the neighbor-based error information a secondary distributed coordinated predictive controller is then proposed to actively compensate the general communication delays for cyber-physical microgrids caused by low-bandwidth communication networks. Sufficient conditions, in terms of communication network connectivity and control gains for the system stability are derived by using the tools of special matrix theory and algebraic graph theory. The proposed control protocols are fully distributed and can be implemented through a sparse communication network and thus, satisfy the plug-and-play feature of the future smart grid. The effectiveness of the control strategy in compensating communication delays is also verified by real-time simulation experiments in OPAL-RT on a test microgrid.

This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to measure constraint violations, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. A novel algorithm is first proposed and it achieves an $\mathcal{O}(T^{\max\{c,1-c\}})$ bound for static regret and an $\mathcal{O}(T^{(1-c)/2})$ bound for cumulative constraint violation, where $c\in(0,1)$ is a user-defined trade-off parameter, and thus has improved performance compared with existing results. Both static regret and cumulative constraint violation bounds are reduced to $\mathcal{O}(\log(T))$ when the loss functions are strongly convex, which also improves existing results. %In order to bound the regret with respect to any comparator sequence, In order to achieve the optimal regret with respect to any comparator sequence, another algorithm is then proposed and it achieves the optimal $\mathcal{O}(\sqrt{T(1+P_T)})$ regret and an $\mathcal{O}(\sqrt{T})$ cumulative constraint violation, where $P_T$ is the path-length of the comparator sequence. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

This Special Section presents the latest developments on intelligent modeling, neural networks, deep learning, and adaptive estimation, and their applications in industrial applications. Through a rigorous peer-review process, eleven articles have been accepted, which are summarized below.

The electricity demand of the fused magnesia smelting process (FMSP) is defined as the average electric power consumption over a fixed period of time, which is used to monitor the electricity cost in the FMSP. In this article, we develop a dynamic model of the electricity demand based on the closed-loop control system of the smelting current in the FMSP. The electricity demand prediction model combines an identifiable linear model with an unknown nonlinear dynamic system, which takes advantage of system identification. To predict the unknown nonlinear dynamic system, an adaptive deep learning prediction approach is proposed based on a multilayer long short-term memory. The real data in the FMSP is used to verify the effectiveness of the proposed electricity demand forecasting method.

In this paper, we study consensus in distributed sensor networks (DSN) with communication time delays. In particular, we focus on the DSN with multi-layer multi-group (MLMG) communication structures and show that consensus can be achieved even in the presence of arbitrarily large but bounded time-varying communication delays. Moreover, we explicitly characterize the final consensus value for the case where communication time delays are fixed.

Driven by smart grid technologies, distributed energy resources (DERs) have been rapidly developing in recent years for improving reliability and efficiency of distribution systems. Emerging DERs require effective and efficient coordination in order to reap their potential benefits. In this paper, we consider an optimal DER coordination problem over multiple time periods subject to constraints at both system and device levels. Fully distributed algorithms are proposed to dynamically and automatically coordinate distributed generators with multiple/single storages. With the proposed algorithms, the coordination agent at each DER maintains only a set of variables and updates them through information exchange with a few neighbors. We show that the proposed algorithms with properly chosen parameters solve the DER coordination problem as long as the underlying communication network is connected. The simulation results are used to illustrate and validate the proposed method.

In this paper, we consider the recovery of piecewise sparse signals from incomplete noisy measurements via a greedy algorithm. Here piecewise sparse means that the signal can be approximated in certain domain with known number of nonzero entries in each piece/segment. This paper makes a two-fold contribution to this problem: 1) formulating a piecewise sparse model in the framework of compressed sensing and providing the theoretical analysis of corresponding sensing matrices; 2) developing a greedy algorithm called piecewise orthogonal matching pursuit (POMP) for the recovery of piecewise sparse signals. Experimental simulations verify the effectiveness of the proposed algorithms.