Average Convergence for Directed&Undirected Graphs in Distributed Systems

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.

A novel genetic algorithm based on all spanning trees of undirected graph for distribution network reconfiguration

Network reconfiguration is of theoretical and practical significance to guarantee safe and economical operation of distribution system.In this paper,based on all spanning trees of undirected graph,a novel genetic algorithm for electric distribution network reconfiguration is proposed.Above all,all spanning trees of simplified graph of distribution network are found.Tie branches are obtained with spanning tree subtracted from simplified graph.There is one and only one switch open on each tie branch.Decimal identity number of open switch on each tie branch is taken as the optimization variable.Therefore,the length of chromosome is very short.Each spanning tree corresponds to one subpopulation.Gene operations of each subpopulation are implemented with parallel computing method.Individuals of offspring after gene operation automatically meet with radial and connected constraints for distribution network operation.Disadvantages of conventional genetic algorithm for network reconfiguration that a large amount of unfeasible solutions are created after crossover and mutation,which result in very low searching efficiency,are completely overcome.High calculation speed and superior capability of the proposed method are validated by two test cases.

From undirected graphs to directed graphs:a new technique makes it possible for multi-agent systems

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.

The Wiener Index of an Undirected Power Graph

The undirected power graph P(Zn) of a finite group Zn is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if u ≠ v and or . The Wiener index W(P(Zn)) of an undirected power graph P(Zn) is defined to be sum of distances between all unordered pair of vertices in P(Zn). Similarly, the edge-Wiener index We(P(Zn)) of P(Zn) is defined to be the sum of distances between all unordered pairs of edges in P(Zn). In this paper, we concentrate on the wiener index of a power graph , P(Zpq) and P(Zp). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph P(Zn), using m,n and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of Zn.

Generalized Competition Indices of Primitive θ-Graphs

As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.

A DIRECTED GRAPH ALGORITHM OF VARIATIONAL GEOMETRY BASED ON GEOMETRIC REASONING

The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.

Identifying Composite Crosscutting Concerns with Scatter-Based Graph Clustering

Identifying composite crosscutting concerns（CCs） is a research task and challenge of aspect mining.In this paper,we propose a scatter-based graph clustering approach to identify composite CCs.Inspired by the state-of-the-art link analysis tech-niques,we propose a two-state model to approximate how CCs tangle with core modules.According to this model,we obtain scatter and centralization scores for each program element.Espe-cially,the scatter scores are adopted to select CC seeds.Further-more,to identify composite CCs,we adopt a novel similarity measurement and develop an undirected graph clustering to group these seeds.Finally,we compare it with the previous work and illustrate its effectiveness in identifying composite CCs.

Some Indices of Alphabet Overlap Graph

The undirected de Bruijn graph is often used as the model of communication network for its useful properties, such as short diameter, small maximum vertex degree. In this paper, we consider the alphabet overlap graph G（k, d, s）： the vertex set V = {v｜v = （v1...vk）; vi ∈ {1,2,... ,d}, i = 1,2,... ,k}; they are distinct and two vertices u = （ul...uk） and v = （vl... vk） are adjacent if and only if us＋i = vi or vs＋i = ui （i = 1,2,...,k - s）. In particular, when s = 1, G（k,d,s） is just an undirected de Bruijn graph. First, we give a formula to calculate the vertex degree of G（k, d, s）. Then, we use the corollary of Menger＇s theorem to prove that the connectivity of G（k, d, s） is 2d^s - 2d^2s-k for s ≥ k/2.

Cooperative Neuro Adaptive Control of Leader Following Uncertain Multi-Agent Systems with Unknown Hysteresis and Dead-Zone

In this paper,a cooperative adaptive control of leader-following uncertain nonlinear multiagent systems is proposed.The communication network is weighted undirected graph with fixed topology.The uncertain nonlinear model for each agent is a higher-order integrator with unknown nonlinear functions,unknown disturbances and unknown input actuators.Meanwhile,the gains of input actuators are unknown nonlinear functions with unknown sign.Two most common behaviors of input actuators in practical applications are hysteresis and dead-zone.In this paper,backlash-like hysteresis and dead-zone are used to model the input actuators.Using universal approximation theorem proved for neural networks,the unknown nonlinear functions are tackled.The unknown weights of neural networks are derived by proposing appropriate adaptive laws.To cope with modeling errors and disturbances an adaptive robust structure is proposed.Considering Lyapunov synthesis approach not only all the adaptive laws are derived but also it is proved that the closed-loop network is cooperatively semi-globally uniformly ultimately bounded(CSUUB).In order to investigate the effectiveness of the proposed method,it is applied to agents modeled with highly nonlinear mathematical equations and inverted pendulums.Simulation results demonstrate the effectiveness and applicability of the proposed method in dealing with both numerical and practical multi-agent systems.

Decomposition of two classes of structural models

The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 206]. A new approach is proposed to decompose a directed acyclic graph and its optimal properties are studied. We interpret this approach from the perspective of the decomposition of the corresponding conditional independence model and provide an algorithm for identifying the maximal prime subgraphs in a directed acyclic graph.