Consensus of high-order continuous-time multi-agent systems with time-delays and switching topologies

Consensus problems of high-order continuous-time multi-agent systems with time-delays and switching topologies are studied.The motivation of this work is to extend second-order continuous-time multi-agent systems from the literature.It is shown that consensus can be reached with arbitrarily bounded time-delays even though the communication topology might not have spanning trees.A numerical example is included to show the theoretical results.     

Linear and nonlinear generalized consensuses of multi-agent systems

Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus （GC）, which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov＇s direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.     

Calculation of disconnected quark loops in lattice QCD

Calculation of disconnected quark loops in lattice QCD is very time consuming. Stochastic noise methods are generally used to estimate these loops. However, stochastic estimation gives large errors in the calculations of disconnected diagrams. We use the symmetric multi-probing source(SMP) method to estimate the disconnected quark loops, and compare the results with the Z(2) noise method and the spin-color explicit(SCE) method on a quenched lattice QCD ensemble with lattice volume 12~3× 24 and lattice spacing a ≈ 0.1 fm.. The results show that the SMP method is very suitable for the calculation of pseudoscalar disconnected quark loops. However, the SMP and SCE methods do not have an obvious advantage over the Z(2) noise method in the evaluation of the scalar disconnected loops.     

Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays

A new method in which the consensus algorithm is used to solve the coordinate control problems of leaderless multiple autonomous underwater vehicles(multi-AUVs) with double independent Markovian switching communication topologies and time-varying delays among the underwater sensors is investigated.This is accomplished by first dividing the communication topology into two different switching parts,i.e.,velocity and position,to reduce the data capacity per data package sent between the multi-AUVs in the ocean.Then,the state feedback linearization is used to simplify and rewrite the complex nonlinear and coupled mathematical model of the AUVs into a double-integrator dynamic model.Consequently,coordinate control of the multi-AUVs is regarded as an approximating consensus problem with various time-varying delays and velocity and position topologies.Considering these factors,sufficient conditions of consensus control are proposed and analyzed and the stability of the multi-AUVs is proven by Lyapunov-Krasovskii theorem.Finally,simulation results that validate the theoretical results are presented.     

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.     

Finite-time consensus for leader-following multi-agent systems over switching network topologies

Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper.Based on the graph theory,matrix theory,homogeneity with dilation,and LaSalle’s invariance principle,the control protocol of each agent using local information is designed,and the detailed analysis of the leaderfollowing finite-time consensus is provided.Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Consensus of leader-followers system of multi-missile with time-delays and switching topologies

The consensus problem in directed networks with arbitrary finite time-varying communication delays under both fixed topology and switching topologies is investigated in this article. The dynamics of each missile in this leader-followers system is with linear form. Feedback linearization is used here to attain linear guidance law for each missile, which is the base law for cooperative. Based on graph theory, the consensus problem can be converted to the stability of corresponding error system. Then Lyapunov function method is used to analyze the stability of the error system. Consensus of networks with time-delays under switching topologies is proved using common Lyapunov function method. Simulations indicate the excellent performances of the algorithms in terms of accuracy and efficiency.     

Adaptive approach to global synchronization of directed networks with fast switching topologies

Global synchronization of directed networks with switching topologies is investigated. It is found that if there exists at least one directed spanning tree in the network with the fixed time-average topology and the time-average topology is achieved sufficiently fast, the network will reach global synchronization for appreciate coupling strength. Furthermore, this appreciate coupling strength may be obtained by local adaptive approach. A sufficient condition about the global synchronization is given. Numerical simulations verify the effectiveness of the adaptive strategy.     

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies. We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point, while their control inputs are constrained in their own nonconvex region. It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term. By utilizing the nonnegative matrix theory, it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected. Finally, a numerical simulation example is used to demonstrate the acquired theoretical results.     

Leader-following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies

We consider multi-agent systems with time-varying delays and switching interconnection topologies.By constructing a suitable Lyapunov-Krasovskii functional and using the reciprocally convex approach,new delay-dependent consensus criteria for the systems are established in terms of linear matrix inequalities(LMIs),which can be easily solved by using various effective optimization algorithms.Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Order Topology Orthosummability in Quantum Logics

By using the Antosik–Mikusinski infinite matrix convergence theorem in quantum logics, we prove a theorem on orthosummability with respect to order topology in quantum logics.     

基于非准直外腔的单频激光高阶回馈效应研究

对基于非准直外腔的单频激光高阶回馈现象及产生机理进行了研究,获得了调制幅度不均匀的高分辨率多重高阶回馈条纹,分析了多重高阶回馈条纹的特点及产生机制。提出采用基于光路阻挡的实验方法,在回馈镜反射率大于90%的强回馈中,发现了单重高阶回馈效应,获得了调制幅度均匀、无大包络的高分辨率单重高阶回馈条纹,其分辨率达到/10,而且还有进一步提高的潜力。单重高阶回馈条纹不但具有多重高阶回馈时高分辨率的优点,还具有传统弱回馈时调制幅度均匀、类正弦等特性,对进一步研制高精度回馈测量系统具有重要意义。     

Light propagation characteristics in quantum well structures of photonic crystals

Two-dimensional （2D） closed-cavity single quantum well （SQW） and multiple quantum well （MQW） structures are proposed based on the traditional 2D open-cavity SQW structures of photonic crystals. The numerical calculation results show that the proposed structures can greatly improve the optical characteristics compared with the traditional structures. It is found that the barrier thickness has a great impact on the optical characteristics of the closed-cavity MQW structures： when the barrier thickness is narrower, each resonant peak which appears in the SQW would split, the number of split times is just equal to the number of wells, and each well in the MQW structures is a travelling-wave-well, similar to the well in the open-cavity SQW structures; when the barrier thickness is wider, there is no effect of spectral splitting, and each well in the MQW structures is a standing-wave-well, just like the well in the closed-cavity SQW. The physical origin of different field distributions and the effect of the spectral splitting are provided.     

Chaos synchronization in networks of coupled maps with time-varying topologies

Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are: 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.     

Growth and transport properties of CaFeAsF_(1-x) single crystals

Using self-flux method,we have successfully grown the parent phase of the single crystals of CaFeAsF1-x.The X-ray di?raction indicates good crystallinity.In-plane resistivity shows a bad metallic behavior with a sharp drop of resistivity at about T SDW=119K.This anomaly is associated with the possible spin density wave(SDW)order.Interestingly near T SDW,the resistivity exhibits a cusp-like feature,which may be understood as the strong coupling effect between the electrons and the antiferromagnetic(AF)spin fluctuations.A reduction of fluorine or application of a high pressure will suppress the SDW feature and induce superconductivity.Hall effect measurements reveal a positive Hall coefficient below T SDW indicating a dominant role of the hole-like charge carriers in the parent phase.Strong magnetoresistance has been observed below T SDW suggesting multiple conduction channels of the charge carriers.     

基于光线追迹的单频激光多重回馈效应研究

提出一种基于非准直平凹回馈腔的单频激光多重回馈光线追迹模型,采用该模型阐明了单频激光多重回馈效应的产生机理,分析了多重回馈高分辨率条纹的特性,明确了影响多重回馈条纹形状的主要因素,包括回馈镜的倾角、曲率半径、反射率以及回馈外腔长等,获得了回馈镜在不同倾角时的有效回馈阶次及其耦合系数。光线追迹分析与实验结果表明:当回馈镜倾斜角为1.7时,多重回馈效应会产生调制幅度均匀、没有大包络的高分辨率回馈条纹,每个条纹的分辨率可达/50。     

Constrained order in frustrated 2D optical patterns

In 2D optical patterns obtained in a Liquid Crystal Light Valve with optical feedback, we show a new kind of geometrical frustration which comes from the imposed form of the boundaries. The circular section of the incoming laser beam presents a symmetry which belongs to the O(2) group, whereas the optical feedback selects patterns with a symmetry restrained to a dihedral subgroup of O(2). By imposing boundaries which respect the symmetry of the dihedral group, we lift the frustration and obtain perfectly ordered patterns. Received 19 January 2001 and Received in final form 2 June 2001     

Detection limits for single small flaws and groups of flaws when using focussed ultrasonic transducers

The performance of ultrasonic imaging systems, using line-focussed transducers, was evaluated theoretically by employing a simple technique based on convolution. The analysis considered the response of single reflectors, which are mainly voids, and also multiple reflectors located both on a single plane and on multiple planes, which represent a porous layer or bond-line. The limits of detection for each of the above cases, in the presence of different levels of acoustic noise in the object under test were also calculated. The results presented are expressed as a function of a dimensionless flaw size, incorporating the ultrasonic frequency and beam F-number. The results can be used to identify the best match between ultrasonic equipment and a specific imaging problem. They can also serve to guide decisions regarding the most suitable detection method for use with the chosen equipment. If the inspection is properly designed, surprisingly small flaws could be reliably detected — even in objects where significant levels of incoherent acoustic noise are found. The method and results presented in this paper for line-focussed transducers fit qualitatively the case of spherically focussed transducers. The method is highly versatile and it can be extended to cover a range of problems, outside the scope of this paper, including, quantitatively, that of the spherically focussed transducer by employing a formulation which uses more computer time and memory.