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Bayesian Game for Distributed Weighted K-Path Vertex Cover of Dynamic Networks 动态网络分布加权k路径顶点覆盖的贝叶斯博弈
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-16 DOI: 10.1109/JSYST.2025.3565659
Long Qi;Xiang Li
The weighted $k$-path vertex cover (WVCP$_{k}$) problem is a main branch of covering problems on dynamic networks with many numerous instances in real-world complex systems. A pivotal challenge in distributed systems for network covering optimization is designing decentralized schemes for autonomous decision-making agents. This article focuses on the distributed optimization of the WVCP$_{k}$ problem, where individual vertices, acting as rational agents, make decisions independently based on incomplete information. We formulate a Bayesian game model to capture the interactions among agents, who face the uncertainty to the statuses of their $k$-path neighbors and rely on communications to enhance their individual beliefs on the actual cover state. Our analysis delves into the Bayesian Nash equilibrium and the ex-post Pareto optimal cover state (POCS) within this framework. In addition, a Bayesian game-based perturbation parallel algorithm (BGPPA) is developed and shown to converge to the ex-post POCS set, even when agents are restricted to using only estimated expected utility. A series of numerical simulations indicate that the BGPPA delivers superior performance with rapid convergence across various networks.
加权$k$路径顶点覆盖(WVCP$_{k}$)问题是现实世界复杂系统中具有许多实例的动态网络覆盖问题的一个主要分支。分布式系统中网络覆盖优化的一个关键挑战是为自主决策代理设计分散的方案。本文主要关注WVCP$_{k}$问题的分布式优化,其中单个顶点作为理性代理,基于不完全信息独立做出决策。我们建立了一个贝叶斯博弈模型来捕捉agent之间的相互作用,agent面对其$k$路径邻居状态的不确定性,并依靠通信来增强他们对实际覆盖状态的个人信念。我们的分析深入到贝叶斯纳什均衡和前后帕累托最优覆盖状态(POCS)在这个框架内。此外,开发了一种基于贝叶斯博弈的扰动并行算法(BGPPA),并证明即使智能体仅限于使用估计的期望效用,该算法也收敛于事后POCS集。一系列的数值模拟表明,BGPPA具有优异的性能,可以快速收敛于各种网络。
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引用次数: 0
FIPO: A Lightweight and Customized Software-Defined Programmable Packet Scheduling Primitive FIPO:一种轻量级的自定义软件定义可编程包调度原语
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-16 DOI: 10.1109/JSYST.2025.3567017
Shang Liu;Shuai Gao;Jia Chen;Jing Chen;Wentao Cui;Shangbing Qiao;Hongke Zhang
The current Internet struggles to meet the deterministic transmission requirements in terms of end-to-end delay. Time-sensitive networking (TSN) provides a solution by offering deterministic forwarding services for critical flows, ensuring strict latency requirements. However, the costs and complexity of hardware associated with TSN increases the barriers for researchers to build prototype for validating newly proposed queue scheduling algorithms. To address this dilemma, software-based simulation platforms are widely used for reduction of simulation expenses. However, these platforms cannot flexibly simulate various queue scheduling algorithms. Although existing programmable packet scheduling methods can adapt to TSN queue scheduling algorithms for common hardware base, they cannot be directly applied to software-based TSN simulation platforms. In response, we propose a novel lightweight software-defined packet scheduling primitive—first-in-pick-out (FIPO), based on the programmable switch behavior-model-version-2 (BMV2). FIPO is capable of expressing customized queue scheduling algorithms to support current TSN algorithms and can be flexibly extended to future algorithms. Particularly, FIPO consists only of multipriority queues and eligible time comparator to implement TSN queue scheduling with minimal computational and management overhead. We also propose a fine-grained logical queue-based flow queue mechanism to enhance FIPO. Finally, a lightweight prototype system for the FIPO is established, incorporating four customized deterministic scheduling algorithms. Extensive experimental results show that FIPO can quickly implement customized queue scheduling algorithms and simulate network conditions that closely resemble real environments. It also demonstrates increased implementation flexibility, achieving millisecond-level configuration times with only a moderate increase in CPU utilization (less than 10%).
当前的互联网在端到端延迟方面难以满足确定性传输要求。TSN (Time-sensitive networking)通过为关键流提供确定性的转发服务,保证严格的延迟要求,提供了一种解决方案。然而,与TSN相关的硬件成本和复杂性增加了研究人员构建验证新提出的队列调度算法的原型的障碍。为了解决这一困境,基于软件的仿真平台被广泛使用,以减少仿真费用。然而,这些平台不能灵活地模拟各种队列调度算法。现有的可编程分组调度方法虽然可以适应通用硬件基础上的TSN队列调度算法,但不能直接应用于基于软件的TSN仿真平台。作为回应,我们提出了一种基于可编程交换机行为模型版本2 (BMV2)的新型轻量级软件定义数据包调度基本先入先取(FIPO)。FIPO能够表达自定义队列调度算法,以支持当前的TSN算法,并可以灵活地扩展到未来的算法。特别是,FIPO仅由多优先级队列和合适的时间比较器组成,以最小的计算和管理开销实现TSN队列调度。我们还提出了一种基于细粒度逻辑队列的流队列机制来增强FIPO。最后,结合四种自定义确定性调度算法,建立了FIPO的轻量级原型系统。大量的实验结果表明,FIPO可以快速实现自定义队列调度算法,并模拟与真实环境非常相似的网络条件。它还展示了更高的实现灵活性,实现了毫秒级的配置时间,而CPU利用率仅略有增加(不到10%)。
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引用次数: 0
A Profit-Oriented Attack by Virtual Power Plants for Economic Risk Transfer: Profitability Analysis and Defense Strategy 面向经济风险转移的虚拟电厂盈利攻击:盈利能力分析与防御策略
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-16 DOI: 10.1109/JSYST.2025.3566018
Luyu Wang;Jiping Wu;Zhetong Ding;Kaifeng Zhang;Biplab Sikdar
Virtual power plants (VPP) may face the risk of economic losses arising from the deviation between day-ahead schedule and real-time energy delivery. This article introduces a novel profit-oriented attack by some greedy VPP (G-VPP) for the first time, which aims to transfer its risk of economic losses to other normal VPPs (N-VPPs) and obtain a risk-free profit. Particularly, the G-VPP launches the load-altering attack (LAA) on N-VPPs to fail their real-time (RT) generation schedule via modifying the generation instructions of the managed resources. The optimal LAA strategy considering stealthiness is proposed to avoid priori detection and the optimal bidding strategy using CVaR is proposed to quantify bidding risk and maximize profit. To defend against such profit-oriented attacks, this article constitutes the first attack traceability research. A defense scheme with attack detection and attacker identification is proposed, which is executed by VPPs and the independent system operator (ISO). VPPs employ an attack detection algorithm based on complex features, and if any, report it to the ISO. The ISO constructs a knowledge graph of electricity market transactions and embeds a rules-based identification algorithm to identify suspected attackers. Simulation results show the effectiveness of the defense scheme and Neo4j is used to visualize.
虚拟电厂(VPP)可能会因日前计划与实时供能的偏差而面临经济损失的风险。本文首次提出了一种贪婪VPP (G-VPP)的新型利润导向攻击,其目的是将自身的经济损失风险转移给其他正常VPP (n -VPP),从而获得无风险的利润。特别是,G-VPP通过修改被管理资源的生成指令,对n - vpp发起负载改变攻击(load-alter attack, LAA),破坏n - vpp的实时生成计划。提出了考虑隐身性的最优LAA策略,避免了先验检测;提出了基于CVaR的最优竞价策略,量化了竞价风险,实现了利润最大化。为了防范这种以盈利为目的的攻击,本文首次对攻击的可追溯性进行了研究。提出了一种基于攻击检测和攻击者识别的防御方案,该方案由vpp和独立系统操作符(ISO)执行。vpp采用基于复杂特征的攻击检测算法,如果有攻击,则上报给ISO。ISO构建了一个电力市场交易的知识图谱,并嵌入了一个基于规则的识别算法来识别可疑的攻击者。仿真结果表明了该防御方案的有效性,并使用Neo4j进行了可视化。
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引用次数: 0
Consensus Control for Discrete-Time Stochastic Multiagent Systems Under a Multiple Description Coding Mechanism 多描述编码机制下离散时间随机多智能体系统的一致性控制
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-16 DOI: 10.1109/JSYST.2025.3567254
Licheng Wang;Zidong Wang;Wei Qian;Shuxin Du
This article addresses the consensus control problem for a specific class of discrete-time stochastic multiagent systems (MASs). When transmitting the local measurement output to the local controller and neighboring agents, a multiple description coding (MDC) scheme is introduced to reduce the communication burden and enhance data transmission reliability in a resource-constrained environment. The MDC scheme encodes each signal into two descriptions, which are then transmitted through separate channels, and decoding schemes are employed to address the different characteristics of the arrival of the two descriptions, ensuring the boundedness of the decoding error. The proposed consensus control scheme uses the relative decoded measurement errors between local agents and their neighbors. The aim is to design an output-feedback control scheme that ensures the error dynamics of the controlled MAS reach exponentially mean-square boundedness. Sufficient conditions are established for the existence of the controllers through stochastic analysis techniques, and the desired controller gains are parameterized using the feasibility of certain matrix inequalities. The effectiveness of the proposed coding-decoding-based consensus control scheme is verified through a numerical simulation.
本文研究一类特定的离散时间随机多智能体系统(MASs)的一致性控制问题。在将本地测量输出传输到本地控制器和相邻代理时,引入了多描述编码(multi - description coding, MDC)方案,以减少通信负担,提高资源受限环境下数据传输的可靠性。MDC方案将每个信号编码为两个描述,然后通过单独的信道传输,并采用解码方案来解决两个描述到达的不同特征,确保解码错误的有界性。所提出的共识控制方案利用了局部智能体与其相邻智能体之间的相对解码测量误差。目的是设计一种输出反馈控制方案,以确保被控MAS的误差动态达到指数均方有界。利用随机分析技术建立了控制器存在的充分条件,并利用若干矩阵不等式的可行性参数化了控制器的期望增益。通过数值仿真验证了所提出的基于编码-解码的一致性控制方案的有效性。
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引用次数: 0
Performance Analysis of STAR-RIS Aided Short-Packet NOMA Network Under Imperfect SIC and CSI 不完全SIC和CSI条件下STAR-RIS辅助短包NOMA网络性能分析
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-15 DOI: 10.1109/JSYST.2025.3562732
Shiv Kumar;Brijesh Kumbhani;Sam Darshi
Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) and nonorthogonal multiple access (NOMA) are promising solutions for next-generation wireless networks with massive connectivity, ultra-low latency, ultra-high reliability, and spectral efficiency. This article analyzes the performance of the downlink STAR-RIS-aided short-packet (SP)-NOMA (STAR-RIS-SP-NOMA) network under the constraint of imperfect successive interference cancellation (ipSIC) and imperfect channel state information (ipCSI) by using a Nakagami-$m$ fading environment. To characterize the system performance, first, we derive the statistical distribution of cascaded Nakagami-$m$ channels using the Laguerre polynomial series approximation. Second, the approximate closed-form expressions in terms of average block error rate (ABLER), system throughput, goodput, latency, and reliability are derived. Third, the asymptotic analysis is also done at a high signal-to-noise ratio to gain further insights. Finally, the Monte Carlo simulations are performed to verify the correctness of the theoretical results. Numerical results validate the superiority of STAR-RIS-SP-NOMA over STAR-RIS-SP-orthogonal multiple access (OMA) (STAR-RIS-SP-OMA) and the conventional cooperative communication scenarios, such as decode and forward relay-assisted half-duplex-SP-OMA and fixed-gain amplify and forward relay-assisted half-duplex-SP-OMA. We have compared the ABLER expression for all three STAR-RIS operating protocols. Also, the effect of various parameters, such as the ipCSI correlation factor, ipSIC factor, blocklength, information bits, and number of STAR-RIS elements on the system performance is examined.
同时传输和反射可重构智能表面(STAR-RIS)和非正交多址(NOMA)是下一代无线网络具有大规模连接、超低延迟、超高可靠性和频谱效率的解决方案。本文利用Nakagami-$m$衰落环境,分析了下行链路star - ris辅助短包(SP)- noma (STAR-RIS-SP-NOMA)网络在不完全连续干扰抵消(ipSIC)和不完全信道状态信息(ipCSI)约束下的性能。为了描述系统的性能,首先,我们使用拉格尔多项式级数近似推导了级联Nakagami-$m$信道的统计分布。其次,导出了平均块错误率(ABLER)、系统吞吐量、goodput、延迟和可靠性的近似封闭表达式。第三,渐近分析也在高信噪比下进行,以获得进一步的见解。最后,通过蒙特卡罗仿真验证了理论结果的正确性。数值结果验证了STAR-RIS-SP-NOMA优于star - ris - sp -正交多址(OMA) (STAR-RIS-SP-OMA)和传统的协同通信场景,如解码和转发中继辅助半双工sp -OMA和固定增益放大和转发中继辅助半双工sp -OMA。我们比较了所有三种STAR-RIS操作方案的ABLER表达。此外,还研究了各种参数对系统性能的影响,如ipCSI相关因子、ipSIC因子、块长度、信息位和STAR-RIS元素数量。
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引用次数: 0
Distributed Design of Joint Transmit and Receive Beamforming for MIMO Radar Networks Using Game Theory 基于博弈论的MIMO雷达网络联合收发波束形成分布式设计
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-13 DOI: 10.1109/JSYST.2025.3565289
Jiale Wu;Chenguang Shi;Jianjiang Zhou;Jinhai Huang
This article investigates the problem of joint transmit and receive beamforming for a colocated multiple-input multiple-output radar network with multiple targets and signal-dependent interferences. At first, a distributed beamforming design scheme is developed using noncooperative game theory. The basis of this scheme is to minimize the maximum transmit power of antennas for each radar while adhering to the constraint of signal-to-interference-plus-noise ratio for the targets. By transforming the formulated optimization problem into a convex problem, the Lagrangian duality theory is utilized to decompose the original problem into two sub-problems. Then, a subgradient projection method and an equivalent receive beamforming optimization method are developed to tackle the two sub-problems, yielding the optimal transmit beamformers for the radars. After obtaining the transmit and receive beamformers iteratively, the game relationship among radars is then formulated as a power control game, and the paper proves the existence and uniqueness of the Nash equilibrium. Furthermore, a centralized beamforming design problem is explored for comparative analysis, where the beamformers of all radars are jointly optimized to suppress power fluctuations among transmit antennas. Simulation results are provided to validate the effectiveness of the proposed schemes.
本文研究了具有多目标和信号相关干扰的多输入多输出雷达网络的联合发射和接收波束形成问题。首先,利用非合作博弈理论,提出了一种分布式波束形成设计方案。该方案的基础是在满足目标信噪比约束的前提下,使各雷达天线的最大发射功率最小。通过将公式化的优化问题转化为一个凸问题,利用拉格朗日对偶理论将原问题分解为两个子问题。针对这两个子问题,分别提出了亚梯度投影法和等效接收波束形成优化方法,得到了雷达的最优发射波束形成方案。在迭代得到发射和接收波束形成器后,将雷达间的博弈关系表示为功率控制博弈,并证明了纳什均衡的存在唯一性。在此基础上,探讨了集中波束形成设计问题,对所有雷达的波束形成进行联合优化,以抑制发射天线之间的功率波动。仿真结果验证了所提方案的有效性。
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引用次数: 0
Systems of Systems Governance Frameworks: A Thorough Scoping Review and Synthesis Towards Enhancing Healthcare Delivery 系统治理框架的系统:全面的范围审查和综合,以加强医疗保健服务
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-12 DOI: 10.1109/JSYST.2025.3545815
Mohamed Mogahed;Mo Mansouri
The healthcare delivery system exhibits inherent complexities stemming from its composition of multiple autonomous constituent systems with intricate interdependencies, characterized by dynamic and often decentralized operations. In this context, systems of systems (SoS) governance emerges as a promising paradigm to address these multifaceted challenges and optimize system-wide performance. This article conducts a comprehensive scoping review of SoS governance frameworks, focusing on their applicability to healthcare systems. Through a rigorous review process, 45 studies were selected from three major databases, yielding 37 distinct governance frameworks. The review analyzes publication trends, research objectives, applied frameworks, domains of application, and methodologies, providing a multifaceted understanding of the SoS governance landscape. The study highlights one framework that aligns closely with our proposed construct for healthcare system governance, and the alignment is discussed. In addition, technical components and variations across frameworks are identified and discussed, revealing the complexity and diversity of approaches in SoS governance.
医疗保健服务系统表现出固有的复杂性,源于其组成的多个自主成分系统具有复杂的相互依赖关系,其特点是动态和分散的操作。在这种情况下,系统的系统(SoS)治理作为一种有前途的范例出现,以解决这些多方面的挑战并优化系统范围的性能。本文对SoS治理框架进行了全面的范围审查,重点关注其对医疗保健系统的适用性。通过严格的审查过程,从三个主要数据库中选择了45项研究,产生了37个不同的治理框架。该综述分析了出版趋势、研究目标、应用框架、应用领域和方法,提供了对SoS治理前景的多方面理解。该研究强调了一个与我们提出的医疗保健系统治理结构密切一致的框架,并讨论了这种一致性。此外,还识别和讨论了跨框架的技术组件和变化,揭示了SoS治理方法的复杂性和多样性。
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引用次数: 0
Robust Interval Type-2 Fuzzy Predictive Automatic Generation Control of Multiarea Interconnected Power Systems 多区域互联电力系统鲁棒区间2型模糊预测自动发电控制
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-11 DOI: 10.1109/JSYST.2025.3544320
Reza M. Kia;Mahsan Tavakoli-Kakhki
This research investigates a supervisory interval type-2 fuzzy predictive control (SIT2FPC) technique to propose a novel control method for the automatic generation control (AGC) problem in interconnected power systems. The proposed control method comprises two main components: the interval type-2 fuzzy control (IT2FC) technique, employing a proportional integral derivative approach, and a supervisory predictive controller. IT2FC sets are considered for a multiarea interconnected power network, followed by the implementation of a supervisory predictive control method for the entire system. It is demonstrated that the SIT2FPC method effectively addresses the challenges within the overall system. By incorporating a predictive controller as a robust supervisory control technique, the proposed method can effectively handle unexpected problems that may arise within the IT2FC units. In order to evaluate the efficiency and validity of the proposed robust SIT2FPC technique, it is applied to address the AGC problem in a four-area interconnected power grid. Also, the IEEE 39-bus power system is considered as a case study to validate the proposed AGC method. The outcomes of six different simulation scenarios clearly illustrate the effectiveness of the proposed robust control method.
本文研究了一种监督区间2型模糊预测控制(SIT2FPC)技术,为解决互联电力系统中的自动发电控制(AGC)问题提供了一种新的控制方法。所提出的控制方法包括两个主要部分:采用比例积分导数方法的区间2型模糊控制(IT2FC)技术和监督预测控制器。考虑了多区域互联电网的IT2FC机组,然后对整个系统实施监督预测控制方法。结果表明,SIT2FPC方法有效地解决了整个系统中的挑战。通过将预测控制器作为鲁棒监督控制技术,所提出的方法可以有效地处理IT2FC单元中可能出现的意外问题。为了评估所提出的鲁棒SIT2FPC技术的效率和有效性,将其应用于解决四区互联电网的AGC问题。最后,以IEEE 39总线电力系统为例,验证了所提出的AGC方法。六个不同仿真场景的结果清楚地说明了所提出的鲁棒控制方法的有效性。
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引用次数: 0
Distributed Containment Control for Discrete-Time Nonlinear Multiagent Systems Over Dynamic Topology With System Uncertainties 具有不确定性的动态拓扑上离散非线性多智能体系统的分布式包容控制
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-09 DOI: 10.1109/JSYST.2025.3554233
Changkun Du;Nannan Li;Zhen Li;Samson Shenglong Yu;Chee Peng Lim
This article explores the distributed containment control problem under dynamic directed topologies in discrete-time nonlinear multiagent systems (MASs) subject to parameter uncertainties that are nonlinearly coupled with the agents' states. Specifically, a parameter estimation algorithm is first adopted to deal with the parametric uncertainty. Then, based on the estimated parameters, a distributed adaptive containment control protocol is proposed in a distributed fashion for nonlinear and uncertain MASs over dynamic digraphs. To tackle the challenges caused by the dynamic topology, the evolution of the dynamic topology of MASs is transformed into time-varying Markov chains. By analyzing the characteristics of time-varying Markov chains, the properties of some key matrices related to the dynamic topology are derived, which benefits the convergence analysis of containment control. By applying the proposed control protocol, the reference signals can be tracked by the leaders, while the followers' states are driven into the convex hull formed by leaders. Finally, simulation results and performance analysis are discussed to demonstrate the effectiveness of developed methods.
本文研究了离散时间非线性多智能体系统(MASs)中参数不确定性与智能体状态非线性耦合的动态有向拓扑下的分布式包容控制问题。具体来说,首先采用参数估计算法来处理参数的不确定性。在此基础上,针对动态有向图上的非线性不确定质量,提出了一种分布式自适应控制协议。为了解决动态拓扑带来的挑战,将质量的动态拓扑演化转化为时变马尔可夫链。通过分析时变马尔可夫链的特征,得到了与动态拓扑相关的一些关键矩阵的性质,有利于遏制控制的收敛性分析。通过应用所提出的控制协议,参考信号可以被领导者跟踪,而追随者的状态被驱动到领导者形成的凸包中。最后,通过仿真结果和性能分析验证了所开发方法的有效性。
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引用次数: 0
Probability-Constrained Multisensor Distributed Fusion Filtering for Cyber-Physical Systems 面向信息物理系统的概率约束多传感器分布式融合滤波
IF 4 3区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-03-09 DOI: 10.1109/JSYST.2025.3563693
Yun Chen;Qian Zhang;Xueyang Meng;Yunfei Guo
This article makes one of the first few attempts to investigate the multisensor distributed fusion filtering problem for a special type of time-varying nonlinear stochastic cyber-physical systems (CPSs) via encoding–decoding strategy (EDS) within the finite-horizon probability constraint framework. The random EDS is employed to orchestrate the data transmissions between sensors and remote local filters to enhance the resource-utilization efficiency and data security. A novel probability-constrained distributed fusion filtering (DFF) scheme is established such that the prescribed probabilistic ellipsoidal constraints and stochastic $H_{infty }$ disturbance attenuation index are satisfied for the resultant local and fusion filtering errors. Sufficient conditions are firstly presented to guarantee the existence of desired local filters by iteratively solving a sequence of matrix inequalities. Subsequently, the derived multisensor distributed fusion filter is designed by means of a certain optimization problem to maximize the ellipsoidal set constraint probability of the fused filtering error. Finally, a numerical example demonstrates the validity of the proposed distributed fusion filtering approach.
本文首次尝试在有限视界概率约束框架下,利用编解码策略研究一类特殊时变非线性随机网络物理系统的多传感器分布式融合滤波问题。利用随机能谱来编排传感器与远程本地滤波器之间的数据传输,提高了资源利用效率和数据安全性。建立了一种新的概率约束分布式融合滤波(DFF)方案,该方案使局部滤波和融合滤波误差满足规定的概率椭球约束和随机$H_{infty }$干扰衰减指标。首先通过迭代求解一系列矩阵不等式,给出了期望局部滤波器存在的充分条件。然后,通过求解一定的优化问题,以最大化融合滤波误差的椭球集约束概率为目标,设计了衍生的多传感器分布式融合滤波器。最后,通过一个算例验证了分布式融合滤波方法的有效性。
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引用次数: 0
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