Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems.This has fascinated numerous scientific groups for their promising applications as they have th...Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems.This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions.Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics.Therefore,while sustaining the significance of both directed and undirected graphs,this research emphases on the demonstration of a distributed average consensus algorithm.It uses the harmonic mean in the domain of multi-agent systems with directed and undirected graphs under static topologies based on a control input scheme.The proposed agreement protocol focuses on achieving a constant consensus on directional and undirected graphs using the exchange of information between neighbors to update their status values and to be able to calculate the total number of agents that contribute to the communication network at the same time.The proposed method is implemented for the identical networks that are considered under the directional and non-directional communication links.Two different scenarios are simulated and it is concluded that the undirected approach has an advantage over directed graph communication in terms of processing time and the total number of iterations required to achieve convergence.The same network parameters are introduced for both orientations of the communication graphs.In addition,the results of the simulation and the calculation of various matrices are provided at the end to validate the effectiveness of the proposed algorithm to achieve consensus.展开更多
In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,ha...In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.展开更多
In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages o...In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages of postpositive attributive are complex and variable, especially three categories： present participle phrase, past participle phrase, and preposition phrase as postpositire attributive, which always bring the difficulties of automatic parsing. We summarize these categories and annotate the semantic information. Compared with dependency structure, feature structure, being recursive directed graph, enhances semantic information extraction in biomedical field. The annotation results show that recursive directed graph is more suitable to extract complex semantic relations for biomedical text mining.展开更多
To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the l...To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.展开更多
This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, ...This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.展开更多
This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected gr...This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected graphs,two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric,and the derived weight error systems exist n-step delays.Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying(LTV)systems with different phenomena including the nonsymmetric Laplacian matrix and time delays.Subsequently,an adaptive neural network(NN)control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law.Then,by using two novel lemmas on the extended exponential convergence of LTV systems,estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced.The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the“mod”function and proper time series.A simulation comparison is shown to demonstrate the validity of the proposed DCL method.展开更多
Web service composition lets developers create applications on top of service-oriented computing and its native description, discovery, and communication capabilities. This paper mainly focuses on the QoS when the con...Web service composition lets developers create applications on top of service-oriented computing and its native description, discovery, and communication capabilities. This paper mainly focuses on the QoS when the concrete composition structure is unknown. A QoS model of service composition is presented based on the fuzzy directed graph theory. According to the model, a recursive algorithm is also described for calculating such kind of QoS. And, the feasibility of this QoS model and the recursive algorithm is verified by a case study. The proposed approach enables customers to get a possible value of the QoS before they achieve the service.展开更多
This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential d...This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.展开更多
It is difficult to analyze semantic relations automatically, especially the semantic relations of Chinese special sentence patterns. In this paper, we apply a novel model feature structure to represent Chinese semanti...It is difficult to analyze semantic relations automatically, especially the semantic relations of Chinese special sentence patterns. In this paper, we apply a novel model feature structure to represent Chinese semantic relations, which is formalized as ＂recursive directed graph＂. We focus on Chinese special sentence patterns, including the complex noun phrase, verb-complement structure, pivotal sentences, serial verb sentence and subject-predicate predicate sentence. Feature structure facilitates a richer Chinese semantic information extraction when compared with dependency structure. The results show that using recursive directed graph is more suitable for extracting Chinese complex semantic relations.展开更多
Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-w...Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.展开更多
A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast dominat...A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast domination is a generalization of domination in which a set of broadcasting vertices emits signals of strength t that decrease by 1 as they traverse each edge, and we require that every vertex in the graph receives a cumulative signal of at least r from its set of broadcasting neighbors. In this paper, we extend the study of (t, r) broadcast domination to directed graphs. Our main result explores the interval of values obtained by considering the directed (t, r) broadcast domination numbers of all orientations of a graph G. In particular, we prove that in the cases r = 1 and (t, r) = (2, 2), for every integer value in this interval, there exists an orientation of G which has directed (t, r) broadcast domination number equal to that value. We also investigate directed (t, r) broadcast domination on the finite grid graph, the star graph, the infinite grid graph, and the infinite triangular lattice graph. We conclude with some directions for future study.展开更多
This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured va...This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured value is smaller than a fixed threshold.Meanwhile,the“intermittent”scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process.Using this kind of coarse measurement,the authors propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph.As is well-known,many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents.However,in practical engineering,achieving doublestochasticity,especially for directed graphs,is not always feasible or desirable.To overcome this limitation,the authors design a row-stochastic matrix and a column-stochastic matrix as weight matrices in the proposed algorithm instead of relying on doubly-stochasticity.Under some mild conditions,the authors rigorously prove that agents can reach the average consensus and ultimately find the optimal solution.Finally,the authors provide a numerical example to illustrate the effectiveness of the algorithm.展开更多
Reconfigurable battery systems(RBSs)provide a promising alternative to traditional battery systems due to their flexible and dynamically changeable topological structures that can be adapted to different battery charg...Reconfigurable battery systems(RBSs)provide a promising alternative to traditional battery systems due to their flexible and dynamically changeable topological structures that can be adapted to different battery charging and discharging strategies.A critical system parameter known as the maximum allowable current(MAC)is pivotal to RBS operation.This parameter is instrumental in maintaining the current of each individual battery within a safe range and serves as a guiding indicator for the system’s reconfiguration,ensuring its safety and reliability.This paper proposes a method for calculating the MAC of an arbitrary RBS using a greedy algorithm in conjunction with a directed graph model of the RBS.Using the shortest path of the battery,the greedy algorithm transforms the exhaustion of the switch states in the brute-force algorithm or variable search without utilizing structures in the heuristic algorithms in the combination of the shortest paths.The directed graph model,based on an equivalent circuit,provides a specific method for calculating the MAC of a given structure.The proposed method is validated using 2 previously published RBS structures and an additional one with a more complex structure.The results are the same as those from the brute-force algorithm,but the proposed method substantially improves the computational efficiency,being theoretically N_(s)2^(N_(s))−^(N_(b))log_(10)N_(b) times faster than the brute-force algorithm for an RBS with N_(b) batteries and N_(s) switches.Another advantage of the proposed method is its ability to calculate the MAC of RBSs with arbitrary structures and variable batteries,even in scenarios with random isolated batteries.展开更多
A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which...A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.展开更多
Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive intege...Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.展开更多
This communique introduces a simple technique,which enables the Laplacian-like matrix of a directed graph to be diagonalisable.Thus many results on multi-agent systems over undirected graphs can be extended to directe...This communique introduces a simple technique,which enables the Laplacian-like matrix of a directed graph to be diagonalisable.Thus many results on multi-agent systems over undirected graphs can be extended to directed graphs.As an example,we show how to make this extension of a popular Automatica paper.展开更多
We present a directed graph-based method for distribution network reconfiguration considering distributed generation. Two reconfiguration situations are considered: operation mode adjustment with the objective of mini...We present a directed graph-based method for distribution network reconfiguration considering distributed generation. Two reconfiguration situations are considered: operation mode adjustment with the objective of minimizing active power loss(situation Ⅰ) and service restoration with the objective of maximizing loads restored(situation Ⅱ). These two situations are modeled as a mixed integer quadratic programming problem and a mixed integer linear programming problem, respectively. The properties of the distribution network with distributed generation considered are reflected as the structure model and the constraints described by directed graph. More specifically, the concepts of "in-degree" and "out-degree"are presented to ensure the radial structure of the distribution network, and the concepts of "virtual node" and"virtual demand" are developed to ensure the connectivity of charged nodes in every independent power supply area.The validity and effectiveness of the proposed method are verified by test results of an IEEE 33-bus system and a 5-feeder system.展开更多
This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth.Given that there exists an exosystem wh...This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth.Given that there exists an exosystem whose state information is not available to all agents,the authors develop distributed adaptive event-triggered observers for the followers based on relative information between neighboring agents.It should be pointed out that,two kinds of time-varying gains are introduced to avoid relying on any global information associated with the network,and dynamic triggering conditions are designed to get rid of continuous communications.On the basis of the designed observers,the authors devise a local controller for each agent.Compared with the existing related works,the main contribution of the current paper is that the cooperative output regulation problem for general directed graphs is solved requiring neither global information nor continuous communications.展开更多
In this paper,we investigate the observer-based event-triggered consensus problem for linear multi-agent systems(MASs)under a directed graph and denial-of-service(DoS)attacks.A type of DoS attacks launched by maliciou...In this paper,we investigate the observer-based event-triggered consensus problem for linear multi-agent systems(MASs)under a directed graph and denial-of-service(DoS)attacks.A type of DoS attacks launched by malicious attackers at irregular intervals is considered,which can cause communication channel disruption.A novel event-triggered secure control scheme based on a closed-loop observer is proposed to determine the scheduling of the controller update,and a separation method with less conservativeness is employed to design the controller and observer gains.Then,the frequency and duration of DoS attacks that can be tolerated are analysed for the observer-based secure consensus problem.In addition,a strictly positive minimal event-triggered time interval for each agent is designed with the help of the proposed eventtriggered condition to eliminate the Zeno behaviour.Finally,a numerical simulation is given to verify the theoretical analysis.展开更多
This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Bot...This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.展开更多
文摘Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems.This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions.Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics.Therefore,while sustaining the significance of both directed and undirected graphs,this research emphases on the demonstration of a distributed average consensus algorithm.It uses the harmonic mean in the domain of multi-agent systems with directed and undirected graphs under static topologies based on a control input scheme.The proposed agreement protocol focuses on achieving a constant consensus on directional and undirected graphs using the exchange of information between neighbors to update their status values and to be able to calculate the total number of agents that contribute to the communication network at the same time.The proposed method is implemented for the identical networks that are considered under the directional and non-directional communication links.Two different scenarios are simulated and it is concluded that the undirected approach has an advantage over directed graph communication in terms of processing time and the total number of iterations required to achieve convergence.The same network parameters are introduced for both orientations of the communication graphs.In addition,the results of the simulation and the calculation of various matrices are provided at the end to validate the effectiveness of the proposed algorithm to achieve consensus.
基金Supported by the Science and Technological Tackling Project of Heilongjiang Province(GB06A106)
文摘In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.
基金Supported by the National Natural Science Foundation of China(61202193,61202304)the Major Projects of Chinese National Social Science Foundation(11&ZD189)the Chinese Postdoctoral Science Foundation(2013M540593,2014T70722)
文摘In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages of postpositive attributive are complex and variable, especially three categories： present participle phrase, past participle phrase, and preposition phrase as postpositire attributive, which always bring the difficulties of automatic parsing. We summarize these categories and annotate the semantic information. Compared with dependency structure, feature structure, being recursive directed graph, enhances semantic information extraction in biomedical field. The annotation results show that recursive directed graph is more suitable to extract complex semantic relations for biomedical text mining.
基金the National Natural Science Foundation of China(No.61371024)the Aviation Science Fund of China(No.2013ZD53051)+1 种基金the IndustryAcademy-Research Project of Aviation Industry Corporation of China(No.cxy2013XGD14)the Space Support Technology Fund of China
文摘To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.
基金Project supported by Science Foundation of Shanghai MunicipalConmission of Education (Grant No .03A203)
文摘This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.
基金supported in part by the Guangdong Natural Science Foundation(2019B151502058)in part by the National Natural Science Foundation of China(61890922,61973129)+1 种基金in part by the Major Key Project of PCL(PCL2021A09)in part by the Guangdong Basic and Applied Basic Research Foundation(2021A1515012004)。
文摘This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected graphs,two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric,and the derived weight error systems exist n-step delays.Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying(LTV)systems with different phenomena including the nonsymmetric Laplacian matrix and time delays.Subsequently,an adaptive neural network(NN)control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law.Then,by using two novel lemmas on the extended exponential convergence of LTV systems,estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced.The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the“mod”function and proper time series.A simulation comparison is shown to demonstrate the validity of the proposed DCL method.
基金Supported by the National Natural Science Foundation of China(60303025 ,60673017)the Natural Science Foundation of Jiangsu Prov-ince (BK2007137)the Program for New Century Excellent Talents in University
文摘Web service composition lets developers create applications on top of service-oriented computing and its native description, discovery, and communication capabilities. This paper mainly focuses on the QoS when the concrete composition structure is unknown. A QoS model of service composition is presented based on the fuzzy directed graph theory. According to the model, a recursive algorithm is also described for calculating such kind of QoS. And, the feasibility of this QoS model and the recursive algorithm is verified by a case study. The proposed approach enables customers to get a possible value of the QoS before they achieve the service.
文摘This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.
基金Supported by the National Natural Science Foundation of China(61202193,61202304)the Major Projects of Chinese National Social Science Foundation(11&ZD189)+2 种基金the Chinese Postdoctoral Science Foundation(2013M540593,2014T70722)the Accomplishments of Listed Subjects in Hubei Prime Subject Developmentthe Open Foundation of Shandong Key Lab of Language Resource Development and Application
文摘It is difficult to analyze semantic relations automatically, especially the semantic relations of Chinese special sentence patterns. In this paper, we apply a novel model feature structure to represent Chinese semantic relations, which is formalized as ＂recursive directed graph＂. We focus on Chinese special sentence patterns, including the complex noun phrase, verb-complement structure, pivotal sentences, serial verb sentence and subject-predicate predicate sentence. Feature structure facilitates a richer Chinese semantic information extraction when compared with dependency structure. The results show that using recursive directed graph is more suitable for extracting Chinese complex semantic relations.
基金supported and funded by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2018R1D1A1B07049321).
文摘Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.
文摘A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast domination is a generalization of domination in which a set of broadcasting vertices emits signals of strength t that decrease by 1 as they traverse each edge, and we require that every vertex in the graph receives a cumulative signal of at least r from its set of broadcasting neighbors. In this paper, we extend the study of (t, r) broadcast domination to directed graphs. Our main result explores the interval of values obtained by considering the directed (t, r) broadcast domination numbers of all orientations of a graph G. In particular, we prove that in the cases r = 1 and (t, r) = (2, 2), for every integer value in this interval, there exists an orientation of G which has directed (t, r) broadcast domination number equal to that value. We also investigate directed (t, r) broadcast domination on the finite grid graph, the star graph, the infinite grid graph, and the infinite triangular lattice graph. We conclude with some directions for future study.
基金supported by the National Natural Science Foundation of China under Grant No.62473272the Natural Science Foundation of Sichuan Province,China under Grant No.2024NSFSC0437。
文摘This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured value is smaller than a fixed threshold.Meanwhile,the“intermittent”scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process.Using this kind of coarse measurement,the authors propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph.As is well-known,many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents.However,in practical engineering,achieving doublestochasticity,especially for directed graphs,is not always feasible or desirable.To overcome this limitation,the authors design a row-stochastic matrix and a column-stochastic matrix as weight matrices in the proposed algorithm instead of relying on doubly-stochasticity.Under some mild conditions,the authors rigorously prove that agents can reach the average consensus and ultimately find the optimal solution.Finally,the authors provide a numerical example to illustrate the effectiveness of the algorithm.
文摘Reconfigurable battery systems(RBSs)provide a promising alternative to traditional battery systems due to their flexible and dynamically changeable topological structures that can be adapted to different battery charging and discharging strategies.A critical system parameter known as the maximum allowable current(MAC)is pivotal to RBS operation.This parameter is instrumental in maintaining the current of each individual battery within a safe range and serves as a guiding indicator for the system’s reconfiguration,ensuring its safety and reliability.This paper proposes a method for calculating the MAC of an arbitrary RBS using a greedy algorithm in conjunction with a directed graph model of the RBS.Using the shortest path of the battery,the greedy algorithm transforms the exhaustion of the switch states in the brute-force algorithm or variable search without utilizing structures in the heuristic algorithms in the combination of the shortest paths.The directed graph model,based on an equivalent circuit,provides a specific method for calculating the MAC of a given structure.The proposed method is validated using 2 previously published RBS structures and an additional one with a more complex structure.The results are the same as those from the brute-force algorithm,but the proposed method substantially improves the computational efficiency,being theoretically N_(s)2^(N_(s))−^(N_(b))log_(10)N_(b) times faster than the brute-force algorithm for an RBS with N_(b) batteries and N_(s) switches.Another advantage of the proposed method is its ability to calculate the MAC of RBSs with arbitrary structures and variable batteries,even in scenarios with random isolated batteries.
基金Supported by the National Natural Science Foundation of China(Grant No.12071260)。
文摘A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.
文摘Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.
基金the National Natural Science Foundation of China(61603314 and 61773322).
文摘This communique introduces a simple technique,which enables the Laplacian-like matrix of a directed graph to be diagonalisable.Thus many results on multi-agent systems over undirected graphs can be extended to directed graphs.As an example,we show how to make this extension of a popular Automatica paper.
基金supported by the National Science and Technology Support Program of China (No. 2013BAA01B02)
文摘We present a directed graph-based method for distribution network reconfiguration considering distributed generation. Two reconfiguration situations are considered: operation mode adjustment with the objective of minimizing active power loss(situation Ⅰ) and service restoration with the objective of maximizing loads restored(situation Ⅱ). These two situations are modeled as a mixed integer quadratic programming problem and a mixed integer linear programming problem, respectively. The properties of the distribution network with distributed generation considered are reflected as the structure model and the constraints described by directed graph. More specifically, the concepts of "in-degree" and "out-degree"are presented to ensure the radial structure of the distribution network, and the concepts of "virtual node" and"virtual demand" are developed to ensure the connectivity of charged nodes in every independent power supply area.The validity and effectiveness of the proposed method are verified by test results of an IEEE 33-bus system and a 5-feeder system.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61973006 and 62103302Shanghai Sailing Program under Grant No. 21YF1450300+2 种基金Shanghai Municipal Science and Technology Major Project under Grant No. 2021SHZDZX0100Shanghai Municipal Commission of Science and Technology Project under Grant No. 19511132101the Fundamental Research Funds for the Central Universities under Grant No. 22120210523
文摘This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth.Given that there exists an exosystem whose state information is not available to all agents,the authors develop distributed adaptive event-triggered observers for the followers based on relative information between neighboring agents.It should be pointed out that,two kinds of time-varying gains are introduced to avoid relying on any global information associated with the network,and dynamic triggering conditions are designed to get rid of continuous communications.On the basis of the designed observers,the authors devise a local controller for each agent.Compared with the existing related works,the main contribution of the current paper is that the cooperative output regulation problem for general directed graphs is solved requiring neither global information nor continuous communications.
基金the National Natural Science Foundation of China[61873338]Natural Science Foundation of Shandong Province[ZR2020KF034]Taishan Scholars[tsqn201812052].
文摘In this paper,we investigate the observer-based event-triggered consensus problem for linear multi-agent systems(MASs)under a directed graph and denial-of-service(DoS)attacks.A type of DoS attacks launched by malicious attackers at irregular intervals is considered,which can cause communication channel disruption.A novel event-triggered secure control scheme based on a closed-loop observer is proposed to determine the scheduling of the controller update,and a separation method with less conservativeness is employed to design the controller and observer gains.Then,the frequency and duration of DoS attacks that can be tolerated are analysed for the observer-based secure consensus problem.In addition,a strictly positive minimal event-triggered time interval for each agent is designed with the help of the proposed eventtriggered condition to eliminate the Zeno behaviour.Finally,a numerical simulation is given to verify the theoretical analysis.
基金supported by National Nature Science Foundation of China (Nos. 61663026, 62066026, 61963028 and 61866023)Jiangxi NSF (No. 20192BAB 207025)。
文摘This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.
