IET Control Theory and Applications最新文献

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Iterative-recursive estimation of parameters of regression models with resistance to outliers on practical examples 在实际案例中对回归模型参数进行迭代递归估计,以抵御异常值的影响
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-12 DOI: 10.1049/cth2.12628
Janusz Kozłowski, Zdzisław Kowalczuk
{"title":"Iterative-recursive estimation of parameters of regression models with resistance to outliers on practical examples","authors":"Janusz Kozłowski,&nbsp;Zdzisław Kowalczuk","doi":"10.1049/cth2.12628","DOIUrl":"10.1049/cth2.12628","url":null,"abstract":"<p>Here, identification of processes and systems in the sense of the least sum of absolute values is taken into consideration. The respective absolute value estimators are recognised as exceptionally insensitive to large measurement faults or other defects in the processed data, whereas the classical least squares procedure appears to be completely impractical for processing the data contaminated with such parasitic distortions. Since the absolute value quality index cannot be minimised analytically, an iterative solution is used to find optimal estimates of the parameters of the underlying regression model. In addition, an approximate recursive estimator is proposed and implemented for on-line evaluation of system parameters. The convergence (basic property) of the iterative estimator is show to be proven and some aspects related to the absolute value criterion are explained. This allows for the formulation of practical conclusions and indication of directions for further research. In addition, the effectiveness of the described iterative-recursive estimation procedures is practically verified by appropriate numerical experiments.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 9","pages":"1099-1113"},"PeriodicalIF":2.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12628","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140711265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partial information target defense game in the presence of a line segment obstacle 存在线段障碍物时的部分信息目标防御博弈
IF 2.2 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-12 DOI: 10.1049/cth2.12664
Jingwen Xu, Qiyong He, Min Meng, Xiuxian Li, Jiaqi Yan
{"title":"Partial information target defense game in the presence of a line segment obstacle","authors":"Jingwen Xu,&nbsp;Qiyong He,&nbsp;Min Meng,&nbsp;Xiuxian Li,&nbsp;Jiaqi Yan","doi":"10.1049/cth2.12664","DOIUrl":"10.1049/cth2.12664","url":null,"abstract":"<p>A two-player planar target defense game where the intruder attempts to breach the circular region guarded by the defender in the presence of a fixed line segment obstacle is addressed. Based on prior research, the entire game was divided into three phases to address the partial information problem. Additionally, the impact of obstacles on the game outcome is thoroughly analyzed. In contrast to the scenario without obstacles, this paper presents redesigned strategies for both defender and intruder, accompanied by quantitative results illustrating the influence on the winning probability. Finally, illustrative examples are given to demonstrate the effect of the obstacle.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 10","pages":"1289-1300"},"PeriodicalIF":2.2,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12664","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved input-to-state stability criteria for time-varying switched singular systems 改进时变开关奇异系统的输入到状态稳定性准则
IF 2.2 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-11 DOI: 10.1049/cth2.12669
Junjie Lu, Yongqi Li, Shijie Wang, Zhikun She
{"title":"Improved input-to-state stability criteria for time-varying switched singular systems","authors":"Junjie Lu,&nbsp;Yongqi Li,&nbsp;Shijie Wang,&nbsp;Zhikun She","doi":"10.1049/cth2.12669","DOIUrl":"10.1049/cth2.12669","url":null,"abstract":"<p>This paper is dedicated to proposing improved input-to-state stability (ISS) criteria for a class of continuous-time time-varying switched singular systems (CTSSS) under slow/fast/slow-fast switching signals. Specifically, for a CTSSS with time-varying singular matrices, the authors start with an improved sufficient condition for verifying its ISS under slow switching signals based on the average dwell time method and a relaxed multiple Lyapunov function. Then, considering several or all subsystems may destroy the overall ISS, relaxed sufficient conditions are presented to ensure the ISS of the CTSSS under fast switching signals and slow-fast switching signals, respectively. Note that the improvement of the proposed ISS criteria is embodied in the derivative of the required multiple Lyapunov functions along with the state trajectories of CTSSS can be positive or negative. Finally, three numerical examples are provided to illustrate the feasibility of the obtained results.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 10","pages":"1338-1356"},"PeriodicalIF":2.2,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140712410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A model-based failure times identification for a system governed by a 2D parabolic partial differential equation 基于模型的二维抛物线偏微分方程系统失效时间识别
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-11 DOI: 10.1049/cth2.12652
Mohamed Salim Bidou, Laetitia Perez, Sylvain Verron, Laurent Autrique
{"title":"A model-based failure times identification for a system governed by a 2D parabolic partial differential equation","authors":"Mohamed Salim Bidou,&nbsp;Laetitia Perez,&nbsp;Sylvain Verron,&nbsp;Laurent Autrique","doi":"10.1049/cth2.12652","DOIUrl":"10.1049/cth2.12652","url":null,"abstract":"<p>This research focuses on the identification of failure times in thermal systems governed by partial differential equations, a task known for its complexity. A new model-based diagnostic approach is presented that aims to accurately identify failing heat sources and accurately determine their failure times, which is crucial when multiple heat sources fail and there is a delay in detection by distant sensors. To validate the effectiveness of the approach, a comparative analysis is carried out with an established method based on a Bayesian filter, the Kalman filter. The aim is to provide a comprehensive analysis, highlighting the advantages and potential limitations of the methodology. In addition, a Monte Carlo simulation is implemented to assess the impact of sensor measurements on the performance of this new approach.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 9","pages":"1163-1175"},"PeriodicalIF":2.6,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12652","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140713197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Intention inference-based interacting multiple model estimator in photoelectric tracking 光电跟踪中基于意向推理的交互式多模型估计器
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12657
Minxing Sun, Huabo Liu, Qianwen Duan, Junzhe Wang, Yao Mao, Qiliang Bao
{"title":"Intention inference-based interacting multiple model estimator in photoelectric tracking","authors":"Minxing Sun,&nbsp;Huabo Liu,&nbsp;Qianwen Duan,&nbsp;Junzhe Wang,&nbsp;Yao Mao,&nbsp;Qiliang Bao","doi":"10.1049/cth2.12657","DOIUrl":"10.1049/cth2.12657","url":null,"abstract":"<p>Aiming to improve the estimation and prediction accuracy of a target's position, this paper proposes a state estimation method for photoelectric tracking systems, based on the evaluation of the tracked target's motion intention. Traditional photoelectric tracking systems utilize external physical quantities such as the position, velocity, and acceleration of the target as the estimated states. While this method can output good results for pre-modelled target positions, it struggles to maintain the accuracy when facing manoeuvering targets or complex motion patterns targets. Here, the relevant parameters of the tracked target's motion intention are directly estimated innovatively, like estimating the circling point position rather than the circular flying target's position and velocity. This approach enables recognizing the target's motion intention and leads to precise estimation, which specifically consists of an interacting multiple model approach, multiple unscented Kalman estimators, and a robust estimator. The effectiveness and stability of this estimator are validated through software simulations and experiments on a dual-reflection mirror platform.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 9","pages":"1210-1222"},"PeriodicalIF":2.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12657","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140720723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal operation region prediction for networked control robotic manipulators subject to time-varying delays and disturbances 受时变延迟和干扰影响的网络控制机器人机械手的最小运行区域预测
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12650
Van Thanh Huynh, Chee Peng Lim, Zoran Najdovski, Dinh Cong Huong, Hieu Trinh
{"title":"Minimal operation region prediction for networked control robotic manipulators subject to time-varying delays and disturbances","authors":"Van Thanh Huynh,&nbsp;Chee Peng Lim,&nbsp;Zoran Najdovski,&nbsp;Dinh Cong Huong,&nbsp;Hieu Trinh","doi":"10.1049/cth2.12650","DOIUrl":"10.1049/cth2.12650","url":null,"abstract":"<p>Due to the disturbances and varying latency, a teleoperated robotic manipulator might not comply with the master control commands. Although prior studies on minimising the impact of network latency and disturbances on teleoperated robots were conducted, there has been very little research on the prediction of minimal operation regions of robotic arms, especially in the worst-case scenarios when the disturbances and time delays still prevail even after impact minimisation. This study investigates the problem and proposes a novel solution to predicting minimal operation regions of networked control robotic manipulators. The proposed method can be used to forecast safe operation regions in which the manipulators will certainly enter and exclude regions that the robots will never penetrate. Leveraging on a Lyanonov Krasovskii criterion, the method performs region prediction by establishing minimal reachable bounding sets of the nonlinear, perturbed robotic arm's state vectors guided via a time-varying delay-dominant network. Though predominantly nonlinear, the entire prediction process is formulated as a tractable Linear Matrix Inequality (LMI) optimisation problem, which can be solved efficiently and effectively. Efficacy of the proposed method is validated with simulations where a simulated robotic arm is distorted with time-varying delays and disturbances.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 8","pages":"1085-1097"},"PeriodicalIF":2.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12650","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140721539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiple adaptive factors based interacting multiple model estimator 基于交互式多重模型估算器的多重自适应因子
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12645
Minxing Sun, Qianwen Duan, Wanrun Xia, Qiliang Bao, Yao Mao
{"title":"Multiple adaptive factors based interacting multiple model estimator","authors":"Minxing Sun,&nbsp;Qianwen Duan,&nbsp;Wanrun Xia,&nbsp;Qiliang Bao,&nbsp;Yao Mao","doi":"10.1049/cth2.12645","DOIUrl":"10.1049/cth2.12645","url":null,"abstract":"<p>In the field of optoelectronic tracking, precisely modeling the motion equations of the tracked target is often challenging, and in some cases, they may even be entirely unknown. This necessitates the use of a robust state estimator for accurate state estimation. Additionally, atmospheric turbulence, variations in illumination, and intricate observation backgrounds may introduce a significant increase in observation noise for the tracked target. To address these challenges, one approach is to introduce adaptive factors, such as the Mahalanobis method, into the robust state estimator to enhance estimation accuracy. However, further exploration has revealed that adaptive factors designed using different methods offer unique advantages in scenarios with varying levels of noise amplification. In this paper, different adaptive factors are further combined using an interacting multiple model approach, allowing the designed state estimator to exhibit stronger adaptability to noise amplification. The stability and effectiveness of this algorithm are validated through program simulations, double reflection mirror experiment, and drone trace prediction, demonstrating its applicability and reliability in diverse scenarios.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 8","pages":"1059-1069"},"PeriodicalIF":2.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12645","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140727645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Robust T-S fuzzy-model-based nonfragile sampled-data control for cyber-physical systems with stochastic delay and cyber-attacks 针对具有随机延迟和网络攻击的网络物理系统的基于 T-S 模糊模型的鲁棒性非脆弱采样数据控制
IF 2.2 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12651
Srinivasan Arunagirinathan, Tae H. Lee
{"title":"Robust T-S fuzzy-model-based nonfragile sampled-data control for cyber-physical systems with stochastic delay and cyber-attacks","authors":"Srinivasan Arunagirinathan,&nbsp;Tae H. Lee","doi":"10.1049/cth2.12651","DOIUrl":"10.1049/cth2.12651","url":null,"abstract":"<p>This work addresses the nonfragile sampled-data control (SDC) of the Takagi-Sugeno (T-S) fuzzy model for cyber-physical systems (CPSs) subject to cyber-attacks (CAs). The sets of random variables satisfying the Bernoulli distribution are utilized to depict the probability of the data transmitted by the network being subjected to stochastic delay and CAs. Then, the information for the entire sampling interval <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>t</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <annotation>$t_k$</annotation>\u0000 </semantics></math> to <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>t</mi>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$t_{k+1}$</annotation>\u0000 </semantics></math> with a relation of the augmented state vectors is considered for designing the SDC of the T-S fuzzy systems (TSFSs). In this regard, the fractional delayed state looped functional (LF) approach is presented to handle the formulated Lyapunov-Krasovskii functional. Based on the LF method, new criteria are acquired to design SDC such that the proposed CPS is asymptotically stable in terms of linear matrix inequalities. It is worth noting that the proposed control strategy for the TSFSs guarantees stable performance while dealing with the attacks in the numerical section. Also, for the various attacking strengths of periodic and non-periodic nature, the TSFSs have been simulated to show the efficiency of the proposed control method. Additionally, three numerical models have been performed to validate the less conservatism and superiority of the derived results over the existing ones.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 16","pages":"2019-2037"},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12651","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140721483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies 基于交换拓扑结构的不完全信息的网络演化博弈建模与优化
IF 2.6 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12643
Yalin Gui, Lixin Gao, Zhitao Li
{"title":"Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies","authors":"Yalin Gui,&nbsp;Lixin Gao,&nbsp;Zhitao Li","doi":"10.1049/cth2.12643","DOIUrl":"10.1049/cth2.12643","url":null,"abstract":"<p>In the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever-shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi-tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 8","pages":"1045-1058"},"PeriodicalIF":2.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12643","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140726275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Practical fixed-time composite-learning control for full-state constraint strict-feedback non-linear systems: A dynamic regressor extension and mixing based approach 全状态约束严格反馈非线性系统的实用固定时间复合学习控制:基于动态回归器扩展和混合的方法
IF 2.2 4区 计算机科学
IET Control Theory and Applications Pub Date : 2024-04-09 DOI: 10.1049/cth2.12662
Man Cui, Zhonghua Wu
{"title":"Practical fixed-time composite-learning control for full-state constraint strict-feedback non-linear systems: A dynamic regressor extension and mixing based approach","authors":"Man Cui,&nbsp;Zhonghua Wu","doi":"10.1049/cth2.12662","DOIUrl":"10.1049/cth2.12662","url":null,"abstract":"<p>A practical fixed-time composite learning control scheme, by combining dynamic regressor extension and mixing (DREM) parameter identification algorithm and adaptive dynamic surface control (DSC) technique, is proposed for a class of strict-feedback non-linear systems subjected to linear-in-parameters uncertainties and full-state constraint. To address the problem of state constraint, a non-linear transformation function is introduced to convert the originally constrained non-linear system into an unconstrained one. Meanwhile, the hyperbolic tangent function is employed to avoid singularity issues that often appeared in the traditional fixed-time (FXT) control designs. In order to relax the requirement of persistency of excitation condition, a modified FXT-DREM parameter identification approach with an interval excitation condition is constructed by introducing a three-layer transformation technique derived from the classical DREM algorithm. Then, the modified FXT-DREM parameter identification algorithm is seamlessly integrated into the adaptive DSC framework, resulting in a composite-learning control scheme. By employing Lyapunov stability analysis, the fixed-time convergence of both the parameter estimation error and the trajectory tracking error is proved. Finally, the effectiveness of the proposed design is demonstrated through simulation test.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 10","pages":"1262-1274"},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12662","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140723789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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