Microservice architecture decomposes industrial applications into multiple services deployed on cloud servers to deliver timely user services. However, existing approaches often overlook deployment optimization from the user's perspective, particularly in minimizing cloud server leasing costs. Moreover, it remains challenging to determine the optimal number of instances and resource utilization for microservices under dynamic and large-scale conditions. To address these challenges, we propose a Column Generation (CG) deployment strategy that introduces soft demand constraints with adaptive penalty terms, enabling flexible trade-offs between cost and service satisfaction. To further improve convergence stability, a doubledual stabilization mechanism is incorporated into the master problem, effectively suppressing dual oscillations during iterative optimization. We also extend the framework to a Distributed Column Generation (DCG) scheme to enhance computational scalability across multiple server types. Experimental results based on real-world server pricing demonstrate that the proposed method achieves a tight optimality gap relative to the theoretical lower bound, reducing the total cost of ownership (TCO) by $\mathbf{1 1. 3 5 \%}$ compared to baseline methods, while achieving decision times only 20.47 % of those required by the comparison approaches.

In microservice architecture, each industrial application is decomposed into multiple microservices and deployed on cloud servers to provide timely services to users. However, existing methods rarely optimize service deployment strategies from the user's perspective to reduce the leasing costs of cloud servers. Furthermore, accurately estimating the required number of instances and resource utilization for microservices remains challenging, and decision-making in large-scale scenarios also faces significant timeliness constraints. To solve this problem, this article proposes a Column Generation deployment strategy, which decomposes the microservice deployment problem into a master problem for scheme selection and subproblems for scheme generation and proves the gap between its convergent solution and the optimal solution. A Distributed Column Generation strategy is further introduced to enable efficient problem-solving. Experimental results based on real-world server pricing demonstrate that the proposed method exhibits a high degree of consistency with the theoretically optimal solution. Compared to the baseline methods, it reduces the average total cost of ownership (TCO) for users by 11.3%, while the decision-making time is only 21.5% of that of the comparative methods. At the same time we used our approach to make deployment decisions for real industrial microservices and deployed them on real cloud servers. Compared to the baseline approach, it reduces TCO by 4%, but decision-making is 97% faster.

This paper addresses the problem of learning-based optimal control for safety-critical systems, where optimal stabilization, safety guarantees, and real-time implementability must be achieved simultaneously. First, to bridge optimal stabilization and hard safety constraints, we construct a primal—dual value function. This is enabled by a closed—form Lagrange multiplier induced by a Lyapunov-compensated control barrier function (LCBF), which embeds an explicit safety-filter structure and provides an analytic safety—stabilization trade-off in the optimal controller. Second, to enable efficient real-time execution, we develop a self-triggered (ST) mechanism based on dual stability—safety margins, which adaptively schedules controller updates and substantially reduces computation while preserving certified safety and stability. Third, to approximate the resulting LCBF-constrained optimal controller implemented via the ST mechanism, we propose an online safety-embedded critic learning framework with concurrent learning, which evaluates Bellman errors under the safety-certified controller to enable safe exploration toward a performance-driven policy. Simulation results verify that the proposed framework delivers safety assurance, reliable control performance, and reduced computational load.

In this paper, we propose a distributed feedback controller to steer a multi-agent dynamical system to the generalized Nash equilibrium (GNE) for an aggregative game with only a monotone pseudo-gradient. First, a monotone aggregative game among the agents is formulated, which considers operational constraints in both the transient process and the steady state. Then, a distributed controller based on primal-dual gradient dynamics is designed for each agent to steer the system to track the GNE of the predefined game autonomously. The controller relaxes the requirement of the strictly/strongly monotone pseudo-gradient. At the same time, the hard limits of the control input are satisfied both at equilibrium and during the transient process. We further prove that the closed-loop system is asymptotically stable and its equilibrium attains the GNE. Finally, a practical example of frequency control on IEEE 68-bus system verifies the effectiveness of the proposed method. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This letter presents AutoHPFL, an autonomous algorithm-design framework that coordinates large language model (LLM) agents to explore and refine Physics-data-hybrid-driven power flow linearization (HPFL) methods. Rather than relying on manually crafted feature mappings, AutoHPFL autonomously searches the design space of linearization strategies through structured exploration, where agents iteratively refine candidates via tree-informed reflection on real-environment execution feedback, coordinated through novelty-aware Monte Carlo Tree Search (MCTS) to systematically identify high-performing methods beyond manual feature engineering. Experiments on IEEE 118-bus, 300-bus and 33-bus test systems demonstrate up to 35.9% error reduction over representative baselines. Moreover, the generated candidates exhibit interpretable design patterns, such as physics-guided feature construction and topology-aware local modeling, indicating the potential of LLM-agent search for autonomous power system algorithm design.

Environment sensing and fusion via onboard sensors are envisioned to be widely applied in future autonomous driving networks. This paper considers a vehicular system with multiple self-driving vehicles that is assisted by multi-access edge computing (MEC), where image data collected by the sensors is offloaded from cellular vehicles to the MEC server using vehicle-to-infrastructure (V2I) links. Sensory data can also be shared among surrounding vehicles via vehicle-to-vehicle (V2V) communication links. To improve spectrum utilization, the V2V links may reuse the same frequency spectrum as the V2I links, which may cause severe interference. To tackle this issue, we leverage reconfigurable intelligent computational surfaces (RICSs) to jointly enable V2I reflective links and mitigate interference appearing at the V2V links. Considering the limitations of traditional algorithms in addressing this problem, such as the assumption of quasi-static channel state information, which restricts their ability to adapt to dynamic environmental changes and leads to poor performance under frequently varying channel conditions, in this paper, we formulate the problem at hand as a Markov game. Our novel formulation is applied to time-varying channels subject to multi-user interference and introduces a collaborative learning mechanism among users. The considered optimization problem is solved via a driving safety-enabled multi-agent deep reinforcement learning (DS-MADRL) approach that capitalizes on the RICS presence. Our extensive numerical investigations showcase that the proposed reinforcement learning approach achieves faster convergence and significant enhancements in both data rate and driving safety, as compared to various state-of-the-art benchmarks.

Under stringent uncertainty, alkaline water electrolyzers must achieve precise tracking of current references to maximize the utilization of renewable power while ensuring the safety of the hydrogen production process. To address challenges such as model inaccuracies, renewable generation fluctuations, and insufficient system robustness, this paper develops an electrolyzer control framework based on Active Disturbance Rejection Control (ADRC). To meet safety requirements and overcome the challenges of high-dimensional and strongly coupled ADRC parameters, a Safe Reinforcement Learning enhanced ADRC method (ADRC-SRL) is further proposed. The proposed method simultaneously optimizes all ADRC parameters during the learning process while explicitly incorporating the electrolyzer’s safety constraints, thereby achieving unified improvements in control accuracy, safety, and robustness. Transfer learning evaluations are conducted to verify the adaptability of the proposed method to electrolyzers with different geometries and aging states. Numerical simulation results demonstrate that ADRC-SRL significantly outperforms conventional methods in terms of control precision and safety performance. Hardware-in-loop experiments further confirm its effectiveness under membrane stress constraint, contributing to the mitigation of mechanical fatigue and the extension of electrolyzer service life.

High-precision simulation of electrical systems is essential for system monitoring and optimization. However, existing modeling methods rely on predefined structures and large labeled datasets, making it difficult to jointly infer structural discrepancies and parameter variations under incomplete observations. To address this challenge, we propose the Simulation Optimization Agent (SOA), an LLM-driven bilevel optimization framework for electrical system simulation modeling. SOA formulates simulation modeling as variational inference over a probabilistic model space, enabling tractable exploration of structural and parametric discrepancies using simulation feedback. In the upper level, LLMs propose candidate structural and parametric corrections, which are processed by a Takagi–Sugeno fuzzy inference system (TSFIS) to convert uncertain symbolic suggestions into stable structural and parametric adjustments. In the lower level, a mechanism–process–format (MPF) reward post-trains the LLM policy using simulation feedback and physical constraints, reducing reliance on labeled data while mitigating cognitive biases. Experiments on photovoltaic systems and analog circuits show that SOA achieves up to 93.9% simulation accuracy and evolution efficiency close to 90%, outperforming existing approaches.

Coordinated operation of alkaline water electrolysis (AWE) systems with multiple electrolyzers under fluctuating renewable power input is challenging due to varying power availability and dynamic safety constraints. Moreover, the conventional separation between optimization and control may result in inconsistent decisions across timescales. To address these issues, this paper proposes a two-layer coordinated operation method integrating feedback optimization (FO) with a projection-based safety layer. The FO layer generates real-time reference inputs to improve renewable energy utilization, while the safety layer corrects these inputs to ensure compliance with operational and safety constraints. To explicitly address the safety constraints arising from the inertial dynamics of AWE systems, discrete-time control barrier function theory is incorporated into the safety layer, thereby enhancing safety assurance and online computational tractability. Theoretical analysis establishes the feasibility and effectiveness of the proposed method. Case studies based on annual wind generation data show that the proposed method achieves high energy utilization, maintains safe operation, and demonstrates online applicability, scalability, and robustness.

At the early commercialization stage of hydrogen fuel cell vehicle (HFCV), there is a ubiquitous interaction relationship between the sales of HFCVs and the deployment of hydrogen refueling stations (HRSs), which poses difficulties in the investment planning of HRSs. This work introduces a new hydrogen supply infrastructure (HSI) expansion planning method that takes into account indirect network effects. First, to characterize the effects of HRS planning decisions on HFCVs, we propose a traffic flow redistribution model and a hydrogen demand differentiated calculation method. Second, to characterize the effects of HFCV parc on HRS planning decisions, we propose a decision-dependent ambiguity set in which the endogenous and exogenous factors affecting uncertainty are portrayed. Combining the concept of out-of-sample disappointment, we identify a meta-optimization problem and further derive a tighter upper bound on the out-of-sample risk by applying the probability scaling theory and measure concentration theory. On this basis, we present a novel approach to quantify the actual investment risk. Then, we establish a decision-dependent distributionally robust optimization (DRO) problem considering potential investment attitudes, to resolve the contradiction that lower decision conservatism and lower out-of-sample disappointment cannot be achieved simultaneously. To solve this optimization problem, we propose a logic-based iterative solution method. It can effectively avoid uncontrolled infrastructure planning due to positive effects between vehicles and stations. Simulation results show that the proposed method can reduce the out-of-sample costs by 5.2% and 4.1% relatively while lowering the investment cost.

This paper proposes a multi-objective control framework for wake-affected wind farms to manage the trade-off between power maximization and fatigue load minimization. The conflicting objectives are formulated using Nash bargaining theory, providing a fair, Pareto-efficient solution without heuristic weight tuning. A Warm-started Proximal Alternating Direction Method of Multipliers (W-PADMM) algorithm is proposed to efficiently solve the bargaining problem, which embeds a learning-aided mechanism using a Long Short-Term Memory (LSTM) network to proactively guide the optimization. Case studies on both an illustrative 9-turbine system and a real offshore wind farm under seasonally varying wind conditions demonstrate that the proposed W-PADMM approach achieves an improved power-fatigue trade-off together with substantial computational acceleration.

Thermal management is critical to the safe and economic operation of electrolytic hydrogen production, yet its coupled electro-thermal behavior remains difficult to represent accurately in scheduling. Many mechanistic scheduling models rely on separated piecewise-linear approximations of energy conversion and temperature dynamics, which can introduce notable modeling error and are difficult to update under equipment aging. This article proposes a coordinated electricity–hydrogen–heat scheduling framework based on constraint learning for hydrogen-integrated microgrids. First, to capture coupled electro-thermal behavior in an optimization-ready form, a neural surrogate is trained to jointly represent stack heat generation and temperature dynamics. It is then reformulated exactly as mixed-integer linear constraints for direct embedding into the scheduling optimization problem. Second, to improve computational efficiency in multistack scheduling, a tight-bound propagation and adaptive cutting-plane strategy is developed. Third, to maintain model fidelity under equipment aging and environmental drift, a continual-learning mechanism based on elastic weight consolidation is introduced to update the surrogate without changing the optimization structure. Case studies show that, compared with a separated linearized mechanistic baseline, the proposed framework reduces the modeling errors in hydrogen-production efficiency and stack temperature dynamics, thereby improving scheduling fidelity and reducing the operating cost. The acceleration strategy preserves computational efficiency in multistack settings, while the updating mechanism maintains modeling and scheduling accuracy under progressive aging.

The scheme of online optimization as a feedback controller is widely used to steer the states of a physical system to the optimal solution of a predefined optimization problem. Such methods focus on the optimality in the steady state, without considering the performance during the transient process. In this article, we simultaneously consider the performance in both the steady state and the transient process of a linear time-invariant system with unknown disturbances. The performance of the transient process is illustrated by the concept of overtaking optimality. An overtaking optimal controller with known disturbances is first derived to achieve the transient overtaking optimality while guaranteeing steady-state performance. We propose a disturbance independent near-optimal controller, which can achieve optimal steady-state performance and approach the overtaking optimal performance in the transient process. The system performance gap between the proposed controller and the optimal counterpart proves to be inversely proportional to the control gains. A case study on a power system with four buses is used to validate the effectiveness of the proposed controller.

Intelligent reflecting surface (IRS)-assisted mobile edge computing (MEC) systems have shown notable improvements in efficiency, such as reduced latency, higher data rates, and better energy efficiency. However, the resource competition among users will lead to uneven allocation, increased latency, and lower throughput. Fortunately, the rate-splitting multiple access (RSMA) technique has emerged as a promising solution for managing interference and optimizing resource allocation in MEC systems. This paper studies an IRS-assisted MEC system with RSMA, aiming to jointly optimize the passive beamforming of the IRS, the active beamforming of the base station, the task offloading allocation, the transmit power of users, the ratios of public and private information allocation, and the decoding order of the RSMA to minimize the average delay from a novel uplink transmission perspective. Since the formulated problem is non-convex and the optimization variables are highly coupled, we propose a hierarchical deep reinforcement learning-based algorithm to optimize both continuous and discrete variables of the problem. Additionally, to better extract channel features, we design a novel network architecture within the policy and evaluation networks of the proposed algorithm, combining convolutional neural networks and densely connected convolutional network for feature extraction. Simulation results indicate that the proposed algorithm not only exhibits excellent convergence performance but also outperforms various benchmarks.

The variability of renewable energy sources (RESs) and load demand variations may lead to power alternations in converter control actions, potentially compromising stability and reliability and posing operational security risks, particularly in islanded microgrids. To address these challenges, this research introduces an innovative optimal control approach structured around a reformulated version of the Bolza problem. A variational control methodology is employed to ensure regularity, with boundary conditions derived to optimize power tracking and frequency control at nodes. Additionally, a solution dimension reduction technique leveraging the augmented Bolza problem is proposed to efficiently approximate the optimal control solution. The effectiveness of the proposed control methodology is validated through MATLAB/Simulink simulations by comparing the novel augmented Bolza-based control approach with conventional methods from the literature, namely Model Predictive Control (MPC) and Pontryagin's Minimum Principle (PMP). A real-time hardware-in-the-loop experimental test is conducted to validate the superiority of the proposed methodology.

Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may exhibit myopic behavior and local trapping when the safeguarding action conflicts with the nominal optimal control. This paper develops a safety-aware infinite-horizon optimal control framework by embedding a barrier-Lyapunov function (BLF)-based safeguarding action into the system dynamics and introducing a barrier-regulating auxiliary variable, thereby reformulating the original constrained problem as an unconstrained one on an extended state space. To mitigate local trapping, we introduce an adaptive alignment-conditioned tangential excitation orthogonal to the safety direction, with activation adaptively modulated by the degree of directional alignment between the nominal and safeguarding controllers, and incorporate it as an admissible ℒ2 disturbance in an H∞ formulation. For high-relative-degree systems under disturbances, we further augment the recursive high-order safe-set construction with barrier compensation terms to obtain a high-order BLF and formulate an adversarial disturbance attenuation problem, which is approximately solved via safe-exploration-enhanced online critic learning. Simulations demonstrate reduced local trapping, improved safety–performance trade-offs, and safe operation under disturbances.

Autonomous Underwater Vehicles (AUVs) have shown great potential for cooperative detection and reconnaissance. However, collaborative AUV communications introduce risks of exposure. In adversarial environments, achieving efficient collaboration while ensuring covert operations becomes a key challenge for underwater cooperative missions. In this paper, we propose a novel dual time-scale Hierarchical Multi-Agent Proximal Policy Optimization (H-MAPPO) framework. The high-level component determines the individuals participating in the task based on a central AUV, while the low-level component reduces exposure probabilities through power and trajectory control by the participating AUVs. Simulation results show that the proposed framework achieves rapid convergence, outperforms benchmark algorithms in terms of performance, and maximizes long-term cooperative efficiency while ensuring covert operations.

Unmanned aerial vehicles (UAVs) assisted Internet of things (IoT) systems have become an important part of future wireless communications. To achieve higher communication rate, the joint design of UAV trajectory and resource allocation is crucial. This letter considers a scenario where a multi-antenna UAV is dispatched to simultaneously collect data from multiple ground IoT nodes (GNs) within a time interval. To improve the sum data collection (SDC) volume, i.e., the total data volume transmitted by the GNs, the UAV trajectory, the UAV receive beamforming, the scheduling of the GNs, and the transmit power of the GNs are jointly optimized. Since the problem is non-convex and the optimization variables are highly coupled, it is hard to solve using traditional optimization methods. To find a near-optimal solution, a double-loop structured optimization-driven deep reinforcement learning (DRL) algorithm and a fully DRL-based algorithm are proposed to solve the problem effectively. Simulation results verify that the proposed algorithms outperform two benchmarks with significant improvement in SDC volumes.

AI-driven digitalization is intensifying data center (DC) energy use and emissions, while variable demands and renewables exacerbate supply-demand and carbon allocation-emission imbalances. These challenges are further compounded by existing strategies that often overlook carbon-energy coupling and lack real-time, incentive-compatible coordination across DCs and energy resources. To address these challenges and satisfy online demands, a tiered carbon trading and capture coordination model is proposed, along with a multi-energy market framework integrating energy storage, an electrolyzer and a combined cooling and power unit, to maximize overall benefits and fully absorb renewable energy. Then, an improved stochastic optimization constructs virtual queues and introduces an auxiliary variable to ensure charge/discharge benefits and system stability while decarbonizing DCs without requiring priori information of system random processes. To avoid privacy leakage, a distributed energy clearing method is applied to facilitate low-complexity trading among DCs. Through case studies, the proposed method can reduce carbon emissions and approach the optimal costs while mitigating battery degradation.