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Fast solution to the free return orbit's reachable domain of the manned lunar mission by deep neural network
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作者 YANG Luyi LI Haiyang +1 位作者 ZHANG Jin ZHU Yuehe 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第2期495-508,共14页
It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly eval... It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly evaluated and calculated via the classification and regression neural networks. An efficient databasegeneration method is developed for obtaining eight types of free return orbits and then the RD is defined by the orbit’s inclination and right ascension of ascending node(RAAN) at the perilune. A classify neural network and a regression network are trained respectively. The former is built for classifying the type of the RD, and the latter is built for calculating the inclination and RAAN of the RD. The simulation results show that two neural networks are well trained. The classification model has an accuracy of more than 99% and the mean square error of the regression model is less than 0.01°on the test set. Moreover, a serial strategy is proposed to combine the two surrogate models and a recognition tool is built to evaluate whether a lunar site could be reached. The proposed deep learning method shows the superiority in computation efficiency compared with the traditional double two-body model. 展开更多
关键词 manned lunar mission free return orbit reachable domain(RD) deep neural network computation efficiency
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Reachable set estimation for discrete-time Markovian jump neural networks with unified uncertain transition probability
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作者 Yufeng Tian Wengang Ao Peng Shi 《Journal of Automation and Intelligence》 2023年第3期167-174,共8页
This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism... This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches. 展开更多
关键词 Markovian jump neural networks Unified uncertain transition probabilities reachable set estimation Double-boundary approach Vector wirtinger-based summation inequality
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Error reachable set based stabilization of switched linear systems with bounded peak disturbances
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作者 Xinxin Shang Songlin Zhuang +1 位作者 Tianyu Tan Yang Shi 《Journal of Automation and Intelligence》 2023年第2期87-98,共12页
This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clock... This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results. 展开更多
关键词 Bounded peak disturbances Persistent dwell-time reachable set minimization Stability and stabilization Switched systems
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Last train timetable optimization for metro network to maximize the passenger accessibility over the end-of-service period
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作者 Fang Wen Yun Bai +2 位作者 Xin Zhang Yao Chen Ninghai Li 《Railway Sciences》 2023年第2期273-288,共16页
Purpose-This study aims to improve the passenger accessibility of passenger demands in the end-ofoperation period.Design/methodology/approach-A mixed integer nonlinear programming model for last train timetable optim... Purpose-This study aims to improve the passenger accessibility of passenger demands in the end-ofoperation period.Design/methodology/approach-A mixed integer nonlinear programming model for last train timetable optimization of the metro was proposed considering the constraints such as the maximum headway,the minimum headway and the latest end-of-operation time.The objective of the model is to maximize the number of reachable passengers in the end-of-operation period.A solution method based on a preset train service is proposed,which significantly reduces the variables of deciding train services in the original model and reformulates it into a mixed integer linear programming model.Findings-The results of the case study of Wuhan Metro show that the solution method can obtain highquality solutions in a shorter time;and the shorter the time interval of passenger flow data,the more obvious the advantage of solution speed;after optimization,the number of passengers reaching the destination among the passengers who need to take the last train during the end-of-operation period can be increased by 10%.Originality/value-Existing research results only consider the passengers who take the last train.Compared with previous research,considering the overall passenger demand during the end-of-operation period can make more passengers arrive at their destination.Appropriately delaying the end-of-operation time can increase the proportion of passengers who can reach the destination in the metro network,but due to the decrease in passenger demand,postponing the end-of-operation time has a bottleneck in increasing the proportion of passengers who can reach the destination. 展开更多
关键词 Urban rail transit Last train of metro Timetable optimization End-of-operation period Passenger demand OD reachability
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Reachability-Based Confidence-Aware Probabilistic Collision Detection in Highway Driving
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作者 Xinwei Wang Zirui Li +1 位作者 Javier Alonso-Mora Meng Wang 《Engineering》 SCIE EI CAS CSCD 2024年第2期90-107,共18页
Risk assessment is a crucial component of collision warning and avoidance systems for intelligent vehicles.Reachability-based formal approaches have been developed to ensure driving safety to accurately detect potenti... Risk assessment is a crucial component of collision warning and avoidance systems for intelligent vehicles.Reachability-based formal approaches have been developed to ensure driving safety to accurately detect potential vehicle collisions.However,they suffer from over-conservatism,potentially resulting in false–positive risk events in complicated real-world applications.In this paper,we combine two reachability analysis techniques,a backward reachable set(BRS)and a stochastic forward reachable set(FRS),and propose an integrated probabilistic collision–detection framework for highway driving.Within this framework,we can first use a BRS to formally check whether a two-vehicle interaction is safe;otherwise,a prediction-based stochastic FRS is employed to estimate the collision probability at each future time step.Thus,the framework can not only identify non-risky events with guaranteed safety but also provide accurate collision risk estimation in safety-critical events.To construct the stochastic FRS,we develop a neural network-based acceleration model for surrounding vehicles and further incorporate a confidence-aware dynamic belief to improve the prediction accuracy.Extensive experiments were conducted to validate the performance of the acceleration prediction model based on naturalistic highway driving data.The efficiency and effectiveness of the framework with infused confidence beliefs were tested in both naturalistic and simulated highway scenarios.The proposed risk assessment framework is promising for real-world applications. 展开更多
关键词 Probabilistic collision detection Confidence awareness Probabilistic acceleration prediction Reachability analysis Risk assessment
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Detecting Data-flow Errors Based on Petri Nets With Data Operations 被引量:4
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作者 Dongming Xiang Guanjun Liu +1 位作者 Chungang Yan Changjun Jiang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第1期251-260,共10页
In order to guarantee the correctness of business processes, not only control-flow errors but also data-flow errors should be considered. The control-flow errors mainly focus on deadlock, livelock, soundness, and so o... In order to guarantee the correctness of business processes, not only control-flow errors but also data-flow errors should be considered. The control-flow errors mainly focus on deadlock, livelock, soundness, and so on. However, there are not too many methods for detecting data-flow errors. This paper defines Petri nets with data operations(PN-DO) that can model the operations on data such as read, write and delete. Based on PN-DO, we define some data-flow errors in this paper. We construct a reachability graph with data operations for each PN-DO, and then propose a method to reduce the reachability graph. Based on the reduced reachability graph, data-flow errors can be detected rapidly. A case study is given to illustrate the effectiveness of our methods. 展开更多
关键词 Business process modeling data-flow errors Petri nets reachability graph
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An Algorithm to Construct Concurrent Reachability Graph of Petri Nets 被引量:3
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作者 张金泉 倪丽娜 蒋昌俊 《Journal of Donghua University(English Edition)》 EI CAS 2004年第3期180-184,共5页
Reachability graph is a very important tool to analyze the dynamic properties of Petri nets, but the concurrent relation of transitions in Petri nets cannot be represented by reachability graph. Petri net is a concurr... Reachability graph is a very important tool to analyze the dynamic properties of Petri nets, but the concurrent relation of transitions in Petri nets cannot be represented by reachability graph. Petri net is a concurrent system, while reachability graph is a serial one. However, concurrency is a kind of property which is not only very significant but also difficult to be analyzed and controlled. This paper presents the concepts of concurrent reachable marking and concurrent reachable graph in order to represent and analyze the concurrent system. The algorithm constructing concurrent reachable marking set and concurrent reachability graph is also shown so that we can study the response problems among services in a network computing environment and analyze the throughput of the system. The Dining Philosophers Problem, which is a classic problem of describing the management of concurrent resources, is given as an example to illustrate the significance of concurrent reachability graph. 展开更多
关键词 Petri nets concurrent system Concurrent reachable Marking concurrent reachable marking set Concurrent Reachability Graph
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Bitcoin Network Measurement and a New Approach to Infer the Topology 被引量:2
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作者 Ruiguang Li Jiawei Zhu +3 位作者 Dawei Xu Fudong Wu Jiaqi Gao Liehuang Zhu 《China Communications》 SCIE CSCD 2022年第10期169-179,共11页
Bitcoin has made an increasing impact on the world's economy and financial order,which attracted extensive attention of researchers and regulators from all over the world.Most previous studies had focused more on ... Bitcoin has made an increasing impact on the world's economy and financial order,which attracted extensive attention of researchers and regulators from all over the world.Most previous studies had focused more on the transaction layer,but less on the network layer.In this paper,we developed BNS(Bitcoin Network Sniffer),which could find and connect nodes in the Bitcoin network,and made a measurement in detail.We collected nearly 4.1 million nodes in 1.5 hours and identified 9,515 reachable nodes.We counted the reachable nodes'properties such as:service type,port number,client version and geographic distribution.In addition,we analyzed the stability of the reachable nodes in depth and found nearly 60%kept stable during 15 days.Finally,we proposed a new approach to infer the Bitcoin network topology by analyzing the Neighbor Addresses of Adjacent Nodes and their timestamps,which had an accuracy over 80%. 展开更多
关键词 Bitcoin network reachable nodes node properties node stability network topology
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Hybrid Petri Nets for Modeling and Analysis of Microgrid Systems 被引量:2
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作者 Xiaoyu Lu MengChu Zhou +1 位作者 Ahmed Chiheb Ammari Jingchu Ji 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2016年第4期349-356,共8页
Hybrid Petri nets(HPNs) are widely used to describe and analyze various industrial hybrid systems that have both discrete-event and continuous discrete-time behaviors. Recently,many researchers attempt to utilize them... Hybrid Petri nets(HPNs) are widely used to describe and analyze various industrial hybrid systems that have both discrete-event and continuous discrete-time behaviors. Recently,many researchers attempt to utilize them to characterize power and energy systems. This work proposes to adopt an HPN to model and analyze a microgrid that consists of green energy sources. A reachability graph for such a model is generated and used to analyze the system properties. 展开更多
关键词 Hybrid Petri nets(HPNs) MICROGRID reachability graph system simulation
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A Network Security Risk Assessment Method Based on a B_NAG Model 被引量:2
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作者 Hui Wang Chuanhan Zhu +3 位作者 Zihao Shen Dengwei Lin Kun Liu MengYao Zhao 《Computer Systems Science & Engineering》 SCIE EI 2021年第7期103-117,共15页
Computer networks face a variety of cyberattacks.Most network attacks are contagious and destructive,and these types of attacks can be harmful to society and computer network security.Security evaluation is an effecti... Computer networks face a variety of cyberattacks.Most network attacks are contagious and destructive,and these types of attacks can be harmful to society and computer network security.Security evaluation is an effective method to solve network security problems.For accurate assessment of the vulnerabilities of computer networks,this paper proposes a network security risk assessment method based on a Bayesian network attack graph(B_NAG)model.First,a new resource attack graph(RAG)and the algorithm E-Loop,which is applied to eliminate loops in the B_NAG,are proposed.Second,to distinguish the confusing relationships between nodes of the attack graph in the conversion process,a related algorithm is proposed to generate the B_NAG model.Finally,to analyze the reachability of paths in B_NAG,the measuring indexs such as node attack complexity and node state transition are defined,and an iterative algorithm for obtaining the probability of reaching the target node is presented.On this basis,the posterior probability of related nodes can be calculated.A simulation environment is set up to evaluate the effectiveness of the B_NAG model.The experimental results indicate that the B_NAG model is realistic and effective in evaluating vulnerabilities of computer networks and can accurately highlight the degree of vulnerability in a chaotic relationship. 展开更多
关键词 network attack graph Bayesian network state transition REACHABILITY risk assessment
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A Mutual Authentication and Cross Verification Protocol for Securing Internet-of-Drones (IoD)
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作者 Saeed Ullah Jan Irshad Ahmed Abbasi Fahad Algarni 《Computers, Materials & Continua》 SCIE EI 2022年第9期5845-5869,共25页
With the rapid miniaturization in sensor technology,Internet-ofDrones(IoD)has delighted researchers towards information transmission security among drones with the control station server(CSS).In IoD,the drone is diffe... With the rapid miniaturization in sensor technology,Internet-ofDrones(IoD)has delighted researchers towards information transmission security among drones with the control station server(CSS).In IoD,the drone is different in shapes,sizes,characteristics,and configurations.It can be classified on the purpose of its deployment,either in the civilian or military domain.Drone’s manufacturing,equipment installation,power supply,multi-rotor system,and embedded sensors are not issues for researchers.The main thing is to utilize a drone for a complex and sensitive task using an infrastructureless/self-organization/resource-less network type called Flying Ad Hoc Network(FANET).Monitoring data transmission traffic,emergency and rescue operations,border surveillance,search and physical phenomenon sensing,and so on can be achieved by developing a robust mutual authentication and cross-verification scheme for IoD deployment civilian drones.Although several protocols are available in the literature,they are either design issues or suffering from other vulnerabilities;still,no one claims with conviction about foolproof security mechanisms.Therefore,in this paper,the researchers highlighted the major deficits in prior protocols of the domain,i.e.,these protocols are either vulnerable to forgery,side channel,stolen-verifier attacks,or raised the outdated data transmission flaw.In order to overcome these loopholes and provide a solution to the existing vulnerabilities,this paper proposed an improved and robust public key infrastructure(PKI)based authentication scheme for the IoD environment.The proposed protocol’s security analysis section has been conducted formally using BAN(Burrows-Abadi-Needham)logic,ProVerif2.03 simulation,and informally using discussion/pragmatic illustration.While the performance analysis section of the paper has been assessed by considering storage,computation,and communication cost.Upon comparing the proposed protocol with prior works,it has been demonstrated that it is efficient and effective and recommended for practical implementation in the IoD environment. 展开更多
关键词 Cryptography authentication CONFIDENTIALITY REACHABILITY ZSP
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Applying a semantic information Petri Net modeling method to AUV systems design
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作者 冯晓宁 王朔 +1 位作者 王卓 刘群 《Journal of Marine Science and Application》 2008年第4期273-277,共5页
This paper informally introduces colored object-oriented Petri Nets(COOPN) with the application of the AUV system.According to the characteristic of the AUV system's running environment,the object-oriented method ... This paper informally introduces colored object-oriented Petri Nets(COOPN) with the application of the AUV system.According to the characteristic of the AUV system's running environment,the object-oriented method is used in this paper not only to dispart system modules but also construct the refined running model of AUV system,then the colored Petri Net method is used to establish hierarchically detailed model in order to get the performance analyzing information of the system.After analyzing the model implementation,the errors of architecture designing and function realization can be found.If the errors can be modified on time,the experiment time in the pool can be reduced and the cost can be saved. 展开更多
关键词 autonomous underwater vehicle (AUV) colored Petri net modeling language (CPNML) substitution transition reachable tree
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Extended and improved slicing technologies for Petri nets
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作者 于汪洋 Yan Chungang +1 位作者 Ding Zhijun Fang Xianwen 《High Technology Letters》 EI CAS 2013年第1期98-104,共7页
Petri net is an important tool to model and analyze concurrent systems,but Petri net models are frequently large and complex,and difficult to understand and modify.Slicing is a technique to remove unnecessary parts wi... Petri net is an important tool to model and analyze concurrent systems,but Petri net models are frequently large and complex,and difficult to understand and modify.Slicing is a technique to remove unnecessary parts with respect to a criterion for analyzing programs,and has been widely used in specification level for model reduction,but researches on slicing of Petri nets are still limited.According to the idea of program slicing,this paper extends slicing technologies of Petri nets to four kinds of slices,including backward static slice,backward dynamic slice,forward static slice and forward dynamic slice.Based on the structure properties,the algorithms of obtaining two kinds of static slice are constructed.Then,a new method of slicing backward dynamic slice is proposed based on local reachability graph which can locally reflect the dynamic properties of Petri nets.At last,forward dynamic slice can be obtained through the reachability marking graph under a special marking.The algorithms can be used to reduce the size of Petri net,which can provide the basic technical support for simplifying the complexity of formal verification and analysis. 展开更多
关键词 Petri nets SLICE model reduction local reachability graph
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The No-Ellipsoidal Bound of Reachable Sets for Neutral Markovian Jump Systems with Disturbances
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作者 Changchun Shen Shouwei Zhou Hongyong Deng 《Journal of Applied Mathematics and Physics》 2020年第5期799-813,共15页
This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration... This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results. 展开更多
关键词 reachable Set No-Ellipsoidal BOUND LINEAR NEUTRAL System LYAPUNOV-KRASOVSKII LINEAR Matrix INEQUALITIES
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Computing Reachable Sets as Capture-Viability Kernels in Reverse Time
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作者 Noel Bonneuil 《Applied Mathematics》 2012年第11期1593-1597,共5页
The set SF(x0;T) of states y reachable from a given state x0 at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x0 at T... The set SF(x0;T) of states y reachable from a given state x0 at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x0 at T in reverse time of the target {x0} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted;for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example. 展开更多
关键词 Set-Valued Analysis reachable Set
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Optimization control of systemic condition of satellite prototype based on hybrid system
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作者 安实 龙江 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第4期552-557,共6页
This article proposes an optimization control model of the systemic condition of satellite prototype based on the hybrid system. A dynamic programming algorithm is also proposed because the problem is NPhard. An empir... This article proposes an optimization control model of the systemic condition of satellite prototype based on the hybrid system. A dynamic programming algorithm is also proposed because the problem is NPhard. An empirical study validates the model and the algorithm,and proves that the pointed important management resources can be recognized and allocated optimally and correctly. 展开更多
关键词 systemic condition dynamic programming reachable net satellite prototype
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Position, Singularity and Workspace Analysis of 3-PSR-O Spatial Parallel Manipulator 被引量:10
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作者 SHAO Jiejie CHEN Wenyu FU Xin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2015年第3期437-450,共14页
Although the parallel mechanisms have the advantages of high accuracy, velocity, stiffness, and payload capacity, the shortcomings of the space utilization and workspace limit the applications in the confined space. A... Although the parallel mechanisms have the advantages of high accuracy, velocity, stiffness, and payload capacity, the shortcomings of the space utilization and workspace limit the applications in the confined space. A novel 3 degrees of freedom spatial parallel manipulator 3-PSR-O(prismatic-spherical-revolute) is proposed, which possesses a compact architecture and extended workspace while maintaining the inherent advantages of the parallel mechanisms. The direct-inverse position, singularity and workspace are investigated. The mapping method is adopted in the position analysis, and the closed form solution is derived in the form of a six order equation. The singularity analysis of the mechanism is also carried out based on the geometrical constraints, including six singularity boundaries. A feature boundary, which is independent of the prismatic joints' stroke limit, is obtained by integrating the six singularity boundaries. According to the formation of the reachable workspace, a concept of basic workspace is also introduced and presented in the analytical way. By demarcating the basic workspace along the central height with the feature boundary, the reachable workspace can be derived and analyzed more efficiently. Finally, a comparative study on the space utilization between the 3-PSP parallel mechanism and the new mechanism is also presented. The area of feature boundary of the new mechanism is about 140% of the 3-PSP parallel mechanism, while its installation radius is only 1/2 of the 3-PSP parallel mechanism. The proposed parallel mechanism shows great space utilization, and is ideally suited for applications in confined space occasions such as immersion lithography, nano-imprint etc. 展开更多
关键词 spatial-planar parallel mechanism direct-inverse position analysis reachable workspace basic workspace feature boundary
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Reachability analysis of switched linear discrete singular systems 被引量:2
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作者 Bin MENG Jifeng ZHAN 《控制理论与应用(英文版)》 EI 2006年第1期11-17,共7页
This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based o... This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems. 展开更多
关键词 Switched system Linear discrete singular system REACHABILITY Switching sequence
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Approximate Reachability and Bisimulation Equivalences for Transition Systems 被引量:1
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作者 王超 吴尽昭 +1 位作者 谭红艳 付军 《Transactions of Tianjin University》 EI CAS 2016年第1期19-23,共5页
Using Baire metric, this paper proposes a generalized framework of transition system approximation by developing the notions of approximate reachability and approximate bisimulation equivalences. The proposed framewor... Using Baire metric, this paper proposes a generalized framework of transition system approximation by developing the notions of approximate reachability and approximate bisimulation equivalences. The proposed framework captures the traditional exact equivalence as a special case. Approximate reachability equivalence is coarser than approximate bisimulation equivalence, just like the hierarchy of the exact ones. Both approximate equivalences satisfy the transitive property, consequently, they can be used in transition system approximation. 展开更多
关键词 approximate equivalence REACHABILITY BISIMULATION transition system
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Safety Assessment for Autonomous Aerial Refueling Based on Reachability Analysis 被引量:1
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作者 REN Jinrui MA Haibiao +1 位作者 QUAN Quan HANG Bin 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2021年第2期216-224,共9页
Autonomous aerial refueling(AAR)has demonstrated significant benefits to aviation by extending the aircraft range and endurance.It is of significance to assess system safety for autonomous aerial refueling.In this pap... Autonomous aerial refueling(AAR)has demonstrated significant benefits to aviation by extending the aircraft range and endurance.It is of significance to assess system safety for autonomous aerial refueling.In this paper,the reachability analysis method is adopted to assess system safety.Due to system uncertainties,the aerial refueling system can be considered as a stochastic system.Thus,probabilistic reachability is considered.Since there is a close relationship between reachability probability and collision probability,the collision probability of the AAR system is analyzed by using reachability analysis techniques.Then,the collision probability is accessed by using the Monte-Carlo experiment method.Finally,simulations demonstrate the effectiveness of the proposed safety assessment method. 展开更多
关键词 aerial refueling safety assessment collision probability probabilistic reachability Monte-Carlo method
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