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
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
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
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
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
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
Graph partition is a classical combinatorial optimization and graph theory problem,and it has a lot of applications,such as scientific computing,VLSI design and clustering etc.In this paper,we study the partition prob...Graph partition is a classical combinatorial optimization and graph theory problem,and it has a lot of applications,such as scientific computing,VLSI design and clustering etc.In this paper,we study the partition problem on large scale directed graphs under a new objective function,a new instance of graph partition problem.We firstly propose the modeling of this problem,then design an algorithm based on multi-level strategy and recursive partition method,and finally do a lot of simulation experiments.The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS.In addition,our algorithm is better than METIS on unbalanced ratio.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
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
In this paper,we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game.Motivated by the recent consensus-based designs,we present a distribute...In this paper,we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game.Motivated by the recent consensus-based designs,we present a distributed algorithm with a proportional gain for weight-balanced directed graphs.By further embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the graph Laplacian,we extend it to the case with arbitrary strongly connected directed graphs having possible unbalanced weights.In both cases,the Nash equilibrium is proven to be exactly reached with an exponential convergence rate.An example is given to illustrate the validity of the theoretical results.展开更多
In this paper, the cycle structures for directed graphs on surfaces are studied. If G is a strongly connected graph, C is a ∏-contractible directed cycle of G, then both of Int（C,∏） and Ext（C,∏） are strongly co...In this paper, the cycle structures for directed graphs on surfaces are studied. If G is a strongly connected graph, C is a ∏-contractible directed cycle of G, then both of Int（C,∏） and Ext（C,∏） are strongly connected graph; the dimension of cycles space of G is identified. If G is a strongly connected graph, then the structure of MCB in G is unique. Let G be a strongly connected graph, if G has been embedded in orientable surface Sg with fw（G） ≥ 2（fw（G） is the face-width of G）, then any cycle base of G must contain at least 2g noncontractible directed cycles; if G has been embedded in non-orientable surface Ng, then any cycle base of G must contain at least g noncontractible directed cycles.展开更多
Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously,which have received much attention lately.Scott(2005)asked the following natural question:What is the maximum c...Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously,which have received much attention lately.Scott(2005)asked the following natural question:What is the maximum constant cdsuch that every directed graph D with m arcs and minimum outdegree d admits a bipartition V(D)=V_1∪V_2 satisfying min{e(V_1,V_2),e(V_2,V_1)}cdm?Here,for i=1,2,e(V_i,V_(3-i))denotes the number of arcs in D from V_i to V_(3-i).Lee et al.(2016)conjectured that every directed graph D with m arcs and minimum outdegree at least d 2 admits a bipartition V(D)=V_1∪V_2 such that min{e(V_1,V_2),e(V_2,V_1)}≥((d-1)/(2(2 d-1))+o(1))m.In this paper,we show that this conjecture holds under the additional natural condition that the minimum indegree is also at least d.展开更多
The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bou...The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.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
To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successf...To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.展开更多
Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback com...Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.展开更多
Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under dir...Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under directed graph to estimate the relative information between each follower robot and the leader robot.Then the formation control problem is transformed into the tracking problem and a finite-time tracking controller is proposed based on the robot model feature.展开更多
The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ...The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.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 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 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.
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.
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supported by National Numerical Windtunnel Project(No.NNW2019ZT5-B16)National Natural Science Foundation of China(Nos.11871256,12071194)the Basic Research Project of Qinghai(No.2021-ZJ-703).
文摘Graph partition is a classical combinatorial optimization and graph theory problem,and it has a lot of applications,such as scientific computing,VLSI design and clustering etc.In this paper,we study the partition problem on large scale directed graphs under a new objective function,a new instance of graph partition problem.We firstly propose the modeling of this problem,then design an algorithm based on multi-level strategy and recursive partition method,and finally do a lot of simulation experiments.The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS.In addition,our algorithm is better than METIS on unbalanced ratio.
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.
基金This work was partially supported by the National Natural Science Foundation of China under Grants 61973043,62003239,and 61703368Shanghai Sailing Program under Grant 20YF1453000+1 种基金Shanghai Municipal Science and Technology Major Project No.2021SHZDZX0100Shanghai Municipal Commission of Science and Technology Project No.19511132101.
文摘In this paper,we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game.Motivated by the recent consensus-based designs,we present a distributed algorithm with a proportional gain for weight-balanced directed graphs.By further embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the graph Laplacian,we extend it to the case with arbitrary strongly connected directed graphs having possible unbalanced weights.In both cases,the Nash equilibrium is proven to be exactly reached with an exponential convergence rate.An example is given to illustrate the validity of the theoretical results.
基金Supported by NSFC(Grant No.10771225)Fundamental Research Funds for the Central University
文摘In this paper, the cycle structures for directed graphs on surfaces are studied. If G is a strongly connected graph, C is a ∏-contractible directed cycle of G, then both of Int（C,∏） and Ext（C,∏） are strongly connected graph; the dimension of cycles space of G is identified. If G is a strongly connected graph, then the structure of MCB in G is unique. Let G be a strongly connected graph, if G has been embedded in orientable surface Sg with fw（G） ≥ 2（fw（G） is the face-width of G）, then any cycle base of G must contain at least 2g noncontractible directed cycles; if G has been embedded in non-orientable surface Ng, then any cycle base of G must contain at least g noncontractible directed cycles.
基金supported by National Natural Science Foundation of China (Grant No. 11671087)supported by National Science Foundation of USA (Grant No. DMS1600738)+2 种基金the Hundred Talents Program of Fujian Provincesupported by the Shandong Provincial Natural Science Foundation of China (Grant No. ZR2014JL001)the Excellent Young Scholars Research Fund of Shandong Normal University of China
文摘Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously,which have received much attention lately.Scott(2005)asked the following natural question:What is the maximum constant cdsuch that every directed graph D with m arcs and minimum outdegree d admits a bipartition V(D)=V_1∪V_2 satisfying min{e(V_1,V_2),e(V_2,V_1)}cdm?Here,for i=1,2,e(V_i,V_(3-i))denotes the number of arcs in D from V_i to V_(3-i).Lee et al.(2016)conjectured that every directed graph D with m arcs and minimum outdegree at least d 2 admits a bipartition V(D)=V_1∪V_2 such that min{e(V_1,V_2),e(V_2,V_1)}≥((d-1)/(2(2 d-1))+o(1))m.In this paper,we show that this conjecture holds under the additional natural condition that the minimum indegree is also at least d.
文摘The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.
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.
文摘To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.
基金supported by the National Science and Technology Innovation 2030-Major Program(2022ZD 0115403)the National Natural Science Foundation of China(61991414)+1 种基金Chongqing Natural Science Foundation(CSTB2023NSCQJQX0018)Beijing Natural Science Foundation(L221005)
文摘Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.
基金supported by the National Natural Science Foundation of China(62073113,62003122,62303148)the Fundamental Research Funds for the Central Universities(MCCSE2023A01,JZ2023HGTA0201,JZ2023HGQA0109)the Anhui Provincial Natural Science Foundation(2308085QF204)
文摘Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under directed graph to estimate the relative information between each follower robot and the leader robot.Then the formation control problem is transformed into the tracking problem and a finite-time tracking controller is proposed based on the robot model feature.
文摘The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.
