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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., Comment: This manuscript has been submitted to IEEE

Defense hardening can effectively enhance the resilience of distribution networks against extreme weather disasters. Currently, most existing hardening strategies focus on reducing load shedding. However, for electricity-hydrogen distribution networks (EHDNs), the leakage risk of hydrogen should be controlled to avoid severe incidents such as explosions. To this end, this paper proposes an optimal hardening strategy for EHDNs under extreme weather, aiming to minimize load shedding while limiting the leakage risk of hydrogen pipelines. Specifically, modified failure uncertainty models for power lines and hydrogen pipelines are developed. These models characterize not only the effect of hardening, referred to as decision-dependent uncertainties (DDUs), but also the influence of disaster intensity correlations on failure probability distributions. Subsequently, a hardening decision framework is established, based on the two-stage distributionally robust optimization incorporating a hydrogen leakage chance constraint (HLCC). To enhance the computational efficiency of HLCC under discrete DDUs, an efficient second-order-cone transformation is introduced. Moreover, to address the intractable inverse of the second-order moment under DDUs, lifted variables are adopted to refine the main-cross moments. These reformulate the hardening problem as a two-stage mixed-integer second-order-cone programming, and finally solved by the column-and-constraint generation algorithm. Case studies demonstrate the effectiveness and superiority of the proposed method.

This paper studies the tracking problem of target with the partially unknown motion model by an active agent with bearing-only measurements using Gaussian process learning. To address this problem, a learning-planning-control framework is proposed. First, to learn and predict the target motion under mild assumptions, a Gaussian-process-based scheme is proposed, and a probabilistic uniform prediction error bound can be rigorously proved. Second, by analyzing the data dependence of the posterior covariance, we obtain an optimal relative trajectory to achieve efficient sampling. Third, to realize efficient learning, a controller to track the planned path is proposed based on the learned target motion, which can provide guaranteed tracking performance. Theoretical analysis is conducted to prove the the given probabilistic error bounds. Numerical examples and comparison with other typical methods verify the feasibility and superior performance of our proposed framework.

High renewable energy penetration into power distribution systems causes a substantial risk of exceeding voltage security limits, which needs to be accurately assessed and properly managed. However, the existing methods usually rely on the joint probability models of power generation and loads provided by probabilistic prediction to quantify the voltage risks, where inaccurate prediction results could lead to over or under estimated risks. This paper proposes an uncertain voltage component (UVC) prediction method for assessing and managing voltage risks. First, we define the UVC to evaluate voltage variations caused by the uncertainties associated with power generation and loads. Second, we propose a Gaussian mixture model-based probabilistic UVC prediction method to depict the non-Gaussian distribution of voltage variations. Then, we derive the voltage risk indices, including value-at-risk (VaR) and conditional value-at-risk (CVaR), based on the probabilistic UVC prediction model. Third, we investigate the mechanism of UVC-based voltage risk management and establish the voltage risk management problems, which are reformulated into linear programming or mixed-integer linear programming for convenient solutions. The proposed method is tested on power distribution systems with actual photovoltaic power and load data and compared with those considering probabilistic prediction of nodal power injections. Numerical results show that the proposed method is computationally efficient in assessing voltage risks and outperforms existing methods in managing voltage risks. The deviation of voltage risks obtained by the proposed method is only 15% of that by the methods based on probabilistic prediction of nodal power injections.

Hydrogen-enriched compressed natural gas (HCNG) is a promising way to utilize surplus renewable energy through hydrogen electrolysis and blending it into natural gas. However, the optimal hydrogen volume fraction (HVF) of HCNG varies following the daily fluctuations of renewable energy. Besides, facing the rapid volatility of renewable energy, ensuring rapid and reliable real-time adjustments is challenging for electricity-HCNG (E-HCNG) coupling networks. To this end, this paper proposes a flexible operation framework for electricity-HCNG (E-HCNG) networks against the fluctuations and volatility of renewable energy. Based on operations with variable HVF, the framework developed an E-HCNG system-level affine policy, which allows real-time re-dispatch of operations according to the volatility. Meanwhile, to guarantee the operational reliability of the affine policy, a distributionally robust joint chance constraint (DRJCC) is introduced, which limits the violation probability of operational constraints under the uncertainties of renewable energy volatility. Furthermore, in the solving process, to mitigate the over-conservation in DRJCC decomposition, an improved risk allocation method is proposed, utilizing the correlations among violations under the affine policy. Moreover, to tackle the non-convexities arising from the variable HVF, customized approximations for HCNG flow formulations are developed. The problem is finally reformulated into a mix-integer second-order cone programming problem. The effectiveness of the proposed method is validated both in small-scale and large-scale experiments.

With the development of artificial intelligence integrated next-generation communication networks, mobile users (MUs) are increasingly demanding the efficient processing of computation-intensive and latency-sensitive tasks. However, existing mobile computing networks struggle to support the rapidly growing computational needs of the MUs. Fortunately, space-air-ground integrated network (SAGIN) supported mobile edge computing (MEC) is regarded as an effective solution, offering the MUs multi-tier and efficient computing services. In this paper, we consider an SAGIN supported MEC system, where a low Earth orbit satellite and multiple unmanned aerial vehicles (UAVs) are dispatched to provide computing services for MUs. An energy efficiency maximization problem is formulated, with the joint optimization of the MU-UAV association, the UAV trajectory, the task offloading decision, the computing frequency, and the transmission power control. Since the problem is non-convex, we decompose it into four subproblems, and propose an alternating optimization based algorithm to solve it. Simulation results confirm that the proposed algorithm outperforms the benchmarks., Comment: This work has been submitted to the IEEE for possible publication

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., Comment: 5 pages, 6 figures, this work has been submitted to the IEEE for possible publication

Heterogeneous systems consisting of a multiloop wireless control system (WCS) and a mobile agent system (MAS) are ubiquitous in Industrial Internet of Things systems. Within these systems, positions of mobile agents may lead to shadow fading on the wireless channel that the WCS is controlled over and can significantly compromise its performance. This paper focuses on the infinite-horizon optimal control of MAS to ensure the performance of WCS while minimizing an average cost for the heterogeneous system subject to state and input constraints. Firstly, the state-dependent fading channel is modeled, which characterizes the interference among transmission links, and shows that the probability of a successful transmission for WCS depends on the state of MAS. A necessary and sufficient condition in terms of constrained set stabilization is then established to ensure the Lyapunov-like performance of WCS with expected decay rate. Secondly, using the semi-tensor product of matrices and constrained reachable sets, a criterion is presented to check the constrained set stabilization of MAS and to ensure the performance of WCS. In addition, a constrained optimal state transition graph is constructed to address state and input constraints, by resorting to which the feasibility analysis of the optimal control problem is presented. Finally, an algorithm is proposed for the construction of optimal input sequences by minimum-mean cycles for weighted graph. An illustrative example is provided to demonstrate effectiveness of the proposed method.

In this paper, we study the existence of equilibrium in a single-leader-multiple-follower game with decision-dependent chance constraints (DDCCs), where decision-dependent uncertainties (DDUs) exist in the constraints of followers. DDUs refer to the uncertainties impacted by the leader's strategy, while the leader cannot capture their exact probability distributions. To address such problems, we first use decision-dependent ambiguity sets under moment information and Cantelli's inequality to transform DDCCs into second-order cone constraints. This simplifies the game model by eliminating the probability distributions. We further prove that there exists at least one equilibrium point for this game by applying Kakutani's fixed-point theorem. Finally, a numerical example is provided to show the impact of DDUs on the equilibrium of such game models.

Intelligent reflecting surface (IRS) and rate-splitting multiple access (RSMA) technologies are at the forefront of enhancing spectrum and energy efficiency in the next generation multi-antenna communication systems. This paper explores a RSMA system with multiple IRSs, and proposes two purpose-driven scheduling schemes, i.e., the exhaustive IRS-aided (EIA) and opportunistic IRS-aided (OIA) schemes. The aim is to optimize the system weighted energy efficiency (EE) under the above two schemes, respectively. Specifically, the Dinkelbach, branch and bound, successive convex approximation, and the semidefinite relaxation methods are exploited within the alternating optimization framework to obtain effective solutions to the considered problems. The numerical findings indicate that the EIA scheme exhibits better performance compared to the OIA scheme in diverse scenarios when considering the weighted EE, and the proposed algorithm demonstrates superior performance in comparison to the baseline algorithms.

This paper presents a carbon-energy coupling management framework for an industrial park, where the carbon flow model accompanying multi-energy flows is adopted to track and suppress carbon emissions on the user side. To deal with the quadratic constraint of gas flows, a bound tightening algorithm for constraints relaxation is adopted. The synergies among the carbon capture, energy storage, power-to-gas further consume renewable energy and reduce carbon emissions. Aiming at carbon emissions disparities and supply-demand imbalances, this paper proposes a carbon trading ladder reward and punishment mechanism and an energy trading and scheduling method based on Lyapunov optimization and matching game to maximize the long-term benefits of each industrial cluster without knowing the prior information of random variables. Case studies show that our proposed trading method can reduce overall costs and carbon emissions while relieving energy pressure, which is important for Environmental, Social and Governance (ESG).

Low-light image enhancement is a crucial visual task, and many unsupervised methods tend to overlook the degradation of visible information in low-light scenes, which adversely affects the fusion of complementary information and hinders the generation of satisfactory results. To address this, our study introduces "Enlighten-Your-Voice", a multimodal enhancement framework that innovatively enriches user interaction through voice and textual commands. This approach does not merely signify a technical leap but also represents a paradigm shift in user engagement. Our model is equipped with a Dual Collaborative Attention Module (DCAM) that meticulously caters to distinct content and color discrepancies, thereby facilitating nuanced enhancements. Complementarily, we introduce a Semantic Feature Fusion (SFM) plug-and-play module that synergizes semantic context with low-light enhancement operations, sharpening the algorithm's efficacy. Crucially, "Enlighten-Your-Voice" showcases remarkable generalization in unsupervised zero-shot scenarios. The source code can be accessed from https://github.com/zhangbaijin/Enlighten-Your-Voice, Comment: It needs revised

Time-Sensitive Networking (TSN) is a promising industrial Internet of Things technology. Clock synchronization provides unified time reference, which is critical to the deterministic communication of TSN. However, changes in internal network status and external work environments of devices both degrade practical synchronization performance. This paper proposes a temperature-resilient architecture considering delay asymmetry (TACD) to enhance the timing accuracy under the impacts of internal delay and external thermal changes. In TACD, an anti-delay-asymmetry method is developed, which employs a partial variational Bayesian algorithm to promote adaptability to non-stationary delay variation. An optimized skew estimator is further proposed, fusing the temperature skew model for ambiance perception with the traditional linear clock model to compensate for nonlinear error caused by temperature changes. Theoretical derivation of skew estimation lower bound proves the promotion of optimal accuracy after the fusion of clock models. Evaluations based on measured delay data demonstrate accuracy advantages regardless of internal or external influences., Comment: Submitted to IEEE Transactions on Cybernetics on 2023-Sep-28. 11 pages incl. references, 15 figures

Industrial Time-Sensitive Networking (TSN) provides deterministic mechanisms for real-time and reliable flow transmission. Increasing attention has been paid to efficient scheduling for time-sensitive flows with stringent requirements such as ultra-low latency and jitter. In TSN, the fine-grained traffic shaping protocol, cyclic queuing and forwarding (CQF), eliminates uncertain delay and frame loss by cyclic traffic forwarding and queuing. However, it inevitably causes high scheduling complexity. Moreover, complexity is quite sensitive to flow attributes and network scale. The problem stems in part from the lack of an attribute mining mechanism in existing frame-based scheduling. For time-critical industrial networks with large-scale complex flows, a so-called hyper-flow graph based scheduling scheme is proposed to improve the scheduling scalability in terms of schedulability, scheduling efficiency and latency & jitter. The hyper-flow graph is built by aggregating similar flow sets as hyper-flow nodes and designing a hierarchical scheduling framework. The flow attribute-sensitive scheduling information is embedded into the condensed maximal cliques, and reverse maps them precisely to congestion flow portions for re-scheduling. Its parallel scheduling reduces network scale induced complexity. Further, this scheme is designed in its entirety as a comprehensive scheduling algorithm GH^2. It improves the three criteria of scalability along a Pareto front. Extensive simulation studies demonstrate its superiority. Notably, GH^2 is verified its scheduling stability with a runtime of less than 100 ms for 1000 flows and near 1/430 of the SOTA FITS method for 2000 flows.

In the early commercialization stage of hydrogen fuel cell vehicles (HFCVs), reasonable hydrogen supply infrastructure (HSI) planning decisions is a premise for promoting the popularization of HFCVs. However, there is a strong causality between HFCVs and hydrogen refueling stations (HRSs): the planning decisions of HRSs could affect the hydrogen refueling demand of HFCVs, and the growth of demand would in turn stimulate the further investment in HRSs, which is also known as the ``chicken and egg'' conundrum. Meanwhile, the hydrogen demand is uncertain with insufficient prior knowledge, and thus there is a decision-dependent uncertainty (DDU) in the planning issue. This poses great challenges to solving the optimization problem. To this end, this work establishes a multi-network HSI planning model coordinating hydrogen, power, and transportation networks. Then, to reflect the causal relationship between HFCVs and HRSs effectively without sufficient historical data, a distributionally robust optimization framework with decision-dependent uncertainty is developed. The uncertainty of hydrogen demand is modeled as a Wasserstein ambiguity set with a decision-dependent empirical probability distribution. Subsequently, to reduce the computational complexity caused by the introduction of a large number of scenarios and high-dimensional nonlinear constraints, we developed an improved distribution shaping method and techniques of scenario and variable reduction to derive the solvable form with less computing burden. Finally, the simulation results demonstrate that this method can reduce costs by at least 10.4% compared with traditional methods and will be more effective in large-scale HSI planning issues. Further, we put forward effective suggestions for the policymakers and investors to formulate relevant policies and decisions.

Preserving the topology from being inferred by external adversaries has become a paramount security issue for network systems (NSs), and adding random noises to the nodal states provides a promising way. Nevertheless, recent works have revealed that the topology cannot be preserved under i.i.d. noises in the asymptotic sense. How to effectively characterize the non-asymptotic preservation performance still remains an open issue. Inspired by the deviation quantification of concentration inequalities, this paper proposes a novel metric named trace-based variance-expectation ratio. This metric effectively captures the decaying rate of the topology inference error, where a slower rate indicates better non-asymptotic preservation performance. We prove that the inference error will always decay to zero asymptotically, as long as the added noises are non-increasing and independent (milder than the i.i.d. condition). Then, the optimal noise design that produces the slowest decaying rate for the error is obtained. More importantly, we amend the noise design by introducing one-lag time dependence, achieving the zero state deviation and the non-zero topology inference error in the asymptotic sense simultaneously. Extensions to a general class of noises with multi-lag time dependence are provided. Comprehensive simulations verify the theoretical findings., Comment: 17 pages

With the rapid development of smart manufacturing, edge computing-oriented microservice platforms are emerging as an important part of production control. In the containerized deployment of microservices, layer sharing can reduce the huge bandwidth consumption caused by image pulling, and chain sharing can reduce communication overhead caused by communication between microservices. The two sharing methods use the characteristics of each microservice to share resources during deployment. However, due to the limited resources of edge servers, it is difficult to meet the optimization goals of the two methods at the same time. Therefore, it is of critical importance to realize the improvement of service response efficiency by balancing the two sharing methods. This paper studies the optimal microservice deployment strategy that can balance layer sharing and chain sharing of microservices. We build a problem that minimizes microservice image pull delay and communication overhead and transform the problem into a linearly constrained integer quadratic programming problem through model reconstruction. A deployment strategy is obtained through the successive convex approximation (SCA) method. Experimental results show that the proposed deployment strategy can balance the two resource sharing methods. When the two sharing methods are equally considered, the average image pull delay can be reduced to 65% of the baseline, and the average communication overhead can be reduced to 30% of the baseline.

Widespread utilization of electric vehicles (EVs) incurs more uncertainties and impacts on the scheduling of the power-transportation coupled network. This paper investigates optimal power scheduling for a power-transportation coupled network in the day-ahead energy market considering multiple uncertainties related to photovoltaic (PV) generation and the traffic demand of vehicles. The crux of this problem is to model the coupling relation between the two networks in the day-ahead scheduling stage and consider the intra-day spatial uncertainties of the source and load. Meanwhile, the flexible load with a certain adjustment margin is introduced to ensure the balance of supply and demand of power nodes and consume the renewable energy better. Furthermore, we show the interactions between the power system and EV users from a potential game-theoretic perspective, where the uncertainties are characterized by an ambiguity set. In order to ensure the individual optimality of the two networks in a unified framework in day-ahead power scheduling, a two-stage distributionally robust centralized optimization model is established to carry out the equilibrium of power-transportation coupled network. On this basis, a combination of the duality theory and the Benders decomposition is developed to solve the distributionally robust optimization (DRO) model. Simulations demonstrate that the proposed approach can obtain individual optimal and less conservative strategies., Comment: arXiv admin note: substantial text overlap with arXiv:2110.14209

Traditionally, offline optimization of power systems is acceptable due to the largely predictable loads and reliable generation. The increasing penetration of fluctuating renewable generation and Internet-of-Things devices allowing for fine-grained controllability of loads have led to the diminishing applicability of offline optimization in the power systems domain, and have redirected attention to online optimization methods. However, online optimization is a broad topic that can be applied in and motivated by different settings, operated on different time scales, and built on different theoretical foundations. This paper reviews the various types of online optimization techniques used in the power systems domain and aims to make clear the distinction between the most common techniques used. In particular, we introduce and compare four distinct techniques used covering the breadth of online optimization techniques used in the power systems domain, i.e., optimization-guided dynamic control, feedback optimization for single-period problems, Lyapunov-based optimization, and online convex optimization techniques for multi-period problems. Lastly, we recommend some potential future directions for online optimization in the power systems domain.

With the proliferation of distributed generations, traditional passive consumers in distribution networks are evolving into "prosumers", which can both produce and consume energy. Energy trading with the main grid or between prosumers is inevitable if the energy surplus and shortage exist. To this end, this paper investigates the peer-to-peer (P2P) energy trading market, which is formulated as a generalized Nash game. We first prove the existence and uniqueness of the generalized Nash equilibrium (GNE). Then, an distributed online algorithm is proposed to track the GNE in the time-varying environment. Its regret is proved to be bounded by a sublinear function of learning time, which indicates that the online algorithm has an acceptable accuracy in practice. Finally, numerical results with six microgrids validate the performance of the algorithm.

Topology inference for networked dynamical systems (NDSs) has received considerable attention in recent years. The majority of pioneering works have dealt with inferring the topology from abundant observations of NDSs, so as to approximate the real one asymptotically. Leveraging the characteristic that NDSs will react to various disturbances and the disturbance's influence will consistently spread, this paper focuses on inferring the topology by a few active excitations. The key challenge is to distinguish different influences of system noises and excitations from the exhibited state deviations, where the influences will decay with time and the exciatation cannot be arbitrarily large. To practice, we propose a one-shot excitation based inference method to infer $h$-hop neighbors of a node. The excitation conditions for accurate one-hop neighbor inference are first derived with probability guarantees. Then, we extend the results to $h$-hop neighbor inference and multiple excitations cases, providing the explicit relationships between the inference accuracy and excitation magnitude. Specifically, the excitation based inference method is not only suitable for scenarios where abundant observations are unavailable, but also can be leveraged as auxiliary means to improve the accuracy of existing methods. Simulations are conducted to verify the analytical results., Comment: Accepted by IEEE CDC 2022

In this paper we consider estimating the system parameters and designing stable observer for unknown noisy linear time-invariant (LTI) systems. We propose a Support Vector Regression (SVR) based estimator to provide adjustable asymmetric error interval for estimations. This estimator is capable to trade-off bias-variance of the estimation error by tuning parameter $\gamma > 0$ in the loss function. This method enjoys the same sample complexity of $\mathcal{O}(1/\sqrt{N})$ as the Ordinary Least Square (OLS) based methods but achieves a $\mathcal{O}(1/(\gamma+1))$ smaller variance. Then, a stable observer gain design procedure based on the estimations is proposed. The observation performance bound based on the estimations is evaluated by the mean square observation error, which is shown to be adjustable by tuning the parameter $\gamma$, thus achieving higher scalability than the OLS methods. The advantages of the estimation error bias-variance trade-off for observer design are also demonstrated through matrix spectrum and observation performance optimality analysis. Extensive simulation validations are conducted to verify the computed estimation error and performance optimality with different $\gamma$ and noise settings. The variances of the estimation error and the fluctuations in performance are smaller with a properly-designed parameter $\gamma$ compared with the OLS methods., Comment: Submitted to AUTOMATICA

Recent years have witnessed the fast advance of security research for networked dynamical system (NDS). Considering the latest inference attacks that enable stealthy and precise attacks into NDSs with observation-based learning, this article focuses on a new security aspect, i.e., how to protect control mechanism secrets from inference attacks, including state information, interaction structure and control laws. We call this security property as control mechanism secrecy, which provides protection of the vulnerabilities in the control process and fills the defense gap that traditional cyber security cannot handle. Since the knowledge of control mechanism defines the capabilities to implement attacks, ensuring control mechanism secrecy needs to go beyond the conventional data privacy to cover both transmissible data and intrinsic models in NDSs. The prime goal of this article is to summarize recent results of both inference attacks on control mechanism secrets and countermeasures. We first introduce the basic inference attack methods on the state and structure of NDSs, respectively, along with their inference performance bounds. Then, the corresponding countermeasures and performance metrics are given to illustrate how to preserve the control mechanism secrecy. Necessary conditions are derived to guide the secrecy design. Finally, thorough discussions on the control laws and open issues are presented, beckoning future investigation on reliable countermeasure design and tradeoffs between the secrecy and control performance.

The interaction topology is critical for efficient cooperation of mobile robotic networks (MRNs). We focus on the local topology inference problem of MRNs under formation control, where an inference robot with limited observation range can manoeuvre among the formation robots. This problem faces new challenges brought by the highly coupled influence of unobservable formation robots, inaccessible formation inputs, and unknown interaction range. The novel idea here is to advocate a range-shrink strategy to perfectly avoid the influence of unobservable robots while filtering the input. To that end, we develop consecutive algorithms to determine a feasible constant robot subset from the changing robot set within the observation range, and estimate the formation input and the interaction range. Then, an ordinary least squares based local topology estimator is designed with the previously inferred information. Resorting to the concentration measure, we prove the convergence rate and accuracy of the proposed estimator, taking the estimation errors of previous steps into account. Extensions on nonidentical observation slots and more complicated scenarios are also analyzed. Comprehensive simulation tests and method comparisons corroborate the theoretical findings.

This paper considers privacy-concerned distributed constraint-coupled resource allocation problems over an undirected network, where each agent holds a private cost function and obtains the solution via only local communication. With privacy concerns, we mask the exchanged information with independent Laplace noise against a potential attacker with potential access to all network communications. We propose a differentially private distributed mismatch tracking algorithm (diff-DMAC) to achieve cost-optimal distribution of resources while preserving privacy. Adopting constant stepsizes, the linear convergence property of diff-DMAC in mean square is established under the standard assumptions of Lipschitz gradients and strong convexity. Moreover, it is theoretically proven that the proposed algorithm is {\epsilon}-differentially private.And we also show the trade-off between convergence accuracy and privacy level. Finally, a numerical example is provided for verification.

Contemporary industrial parks are challenged by the growing concerns about high cost and low efficiency of energy supply. Moreover, in the case of uncertain supply/demand, how to mobilize delay-tolerant elastic loads and compensate real-time inelastic loads to match multi-energy generation/storage and minimize energy cost is a key issue. Since energy management is hardly to be implemented offline without knowing statistical information of random variables, this paper presents a systematic online energy cost minimization framework to fulfill the complementary utilization of multi-energy with time-varying generation, demand and price. Specifically to achieve charging/discharging constraints due to storage and short-term energy balancing, a fast distributed algorithm based on stochastic gradient with two-timescale implementation is proposed to ensure online implementation. To reduce the peak loads, an incentive mechanism is implemented by estimating users' willingness to shift. Analytical results on parameter setting are also given to guarantee feasibility and optimality of the proposed design. Numerical results show that when the bid-ask spread of electricity is small enough, the proposed algorithm can achieve the close-to-optimal cost asymptotically., Comment: Accepted by Applied Energy