metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

distributed consensus for multi agent systems with delays and noises in transmission channels this paper studies the distributed consensus problem for linear discrete time multi agent systems with delays and noises in transmission channels due to the presence of noises and delays existing techniques such as the lifting technique and the stochastic lyapunov theory are no longer applicable to the analysis of consensus in this paper a novel technique is introduced to overcome the difficulties induced by the delays and noises a consensus protocol with decaying gains satisfying persistence condition is adopted necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non leader follower and leader follower cases under a fixed topology under dynamically switching topologies and randomly switching topologies sufficient conditions for strong consensus and mean square consensus are also obtained numerical examples are given to demonstrate the effectiveness of the proposed protocols

asynchronous distributed algorithms for solving linear algebraic equations two asynchronous distributed algorithms are presented for solving a linear equation of the form ax b with at least one solution the equation is simultaneously and asynchronously solved by m agents assuming that each agent knows only a subset of the rows of the partitioned matrix a b the estimates of the equation s solution generated by its neighbors and nothing more neighbor relationships are characterized by a time dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays the event time sequences of different agents are not assumed to be synchronized it is shown that for any matrix vector pair a b for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents event times the algorithms cause all agents estimates to converge exponentially fast to the same solution to ax b the first algorithm requires a specific initialization step at each agent and the second algorithm works for arbitrary initializations explicit expressions for convergence rates are provided and a relation between local initializations and limiting consensus solutions is established which is used to solve the least 2 norm solution

opinion dynamics in social networks with hostile camps consensus vs polarization most of the distributed protocols for multi agent consensus assume that the agents are mutually cooperative and trustful and so the couplings among the agents bring the values of their states closer opinion dynamics in social groups however require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents which are usually characterized by repulsive couplings and may lead to clustering of the opinions a simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by c altafini who examined first order consensus algorithms over static signed graphs this protocol establishes modulus consensus where the opinions become the same in modulus but may differ in signs in this paper we extend the modulus consensus model to the case where the network topology is an arbitrary time varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph for cut balanced graphs not only sufficient but also necessary conditions for modulus consensus are given

reaching a consensus in a dynamically changing environment convergence rates measurement delays and asynchronous events this paper uses recently established properties of compositions of directed graphs together with results from the theory of nonhomogeneous markov chains to derive worst case convergence rates for the headings of a group of mobile autonomous agents which arise in connection with the widely studied vicsek consensus problem the paper also uses graph theoretic constructions to solve modified versions of the vicsek problem in which there are measurement delays asynchronous events or a group leader in all three cases the conditions under which consensus is achieved prove to be almost the same as the conditions under which consensus is achieved in the synchronous delay free leaderless case

multiple fixed sign solutions for a system of difference equations with sturm liouville conditions we consider the following system of difference equations d mu i k p i k u 1 k u 2 k u n k 0 k 0 1 n i 1 2 ntogether with sturm liouville boundary conditions d ju i 0 0 0 2 n m 1 z 0 w 0 h 0 d w z w n 1 z d h w 0 by using two different fixed point theorems we develop criteria for the existence of three solutions of the system which are of fixed signs on 0 1 n m examples are also included to illustrate the results obtained

a distributed algorithm for solving a linear algebraic equation a distributed algorithm is described for solving a linear algebraic equation of the form ax b assuming the equation has at least one solution the equation is simultaneously solved by m agents assuming each agent knows only a subset of the rows of the partitioned matrix matrix a b the current estimates of the equation s solution generated by its neighbors and nothing more each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors neighbor relations are characterized by a time dependent directed graph bbn t whose vertices correspond to agents and whose arcs depict neighbor relations it is shown that for any matrix a for which the equation has a solution and any sequence of repeatedly jointly strongly connected graphs bbn t t 1 2 ldots the algorithm causes all agents estimates to converge exponentially fast to the same solution to ax b it is also shown that under mild assumptions the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured a worst case convergence rate bound is derived for the case when ax b has a unique solution it is demonstrated that with minor modification the algorithm can track the solution to ax b even if a and b are changing with time provided the rates of change of a and b are sufficiently small it is also shown that in the absence of communication delays exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors a modification of the algorithm is outlined which enables it to obtain a least squares solution to ax b in a distributed manner even if ax b does not have a solution

coarse differentiation of quasi isometries ii rigidity for sol and lamplighter groups in this paper we prove quasi isometric rigidity results concerning lattices in sol and lamplighter groups the paper builds in a substantial way on our earlier paper coarse dierentiation of quasi isometries i spaces not quasi isometric to cayley graphs

second order global consensus in multiagent networks with random directional link failure in this paper we consider the second order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time averaged system a criterion for the second order consensus is derived by constructing a lyapunov function for the time averaged network by associating the solution of random switching nonlinear system with the constructed lyapunov function a sufficient condition for second order globally nonlinear consensus in a multiagent network with random directed interconnections is also established it is required that the second order consensus can be achieved in the time averaged network and the lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments a numerical example is presented to justify the correctness of the theoretical results

fixed sign solutions of a system of higher order difference equations abstract we consider the following system m u i k f i k u 1 k u 2 k u n k 0 k 0 1 t j u i 0 0 0 j m 3 i m 2 u i 0 i m 1 u i 0 0 i m 2 u i t 1 i m 1 u i t 1 0 i 1 2 n where m 2 t m 1 and for each 1 i n i 0 i 0 i 0 i i and i i t 1 i i i i 0 criteria are offered for the existence of single and double fixed sign solutions of the system

multiagent systems with compasses this paper investigates agreement protocols over cooperative and cooperativeantagonistic multiagent networks with coupled continuous time nonlinear dynamics to guarantee convergence for such syste

existence of positive solutions of bvps for third order discrete nonlinear difference systems in this paper we consider the following boundary value problem of discrete email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some new results of the existence nonexistence and multiplicity are obtained by using krasnosel skii s fixed point theorem in a cone in particular it is proved that the above boundary value problem has n positive solutions under suitable conditions where n is an arbitrary positive integer

robust consensus for continuous time multiagent dynamics this paper investigates consensus problems for continuous time multiagent systems with time varying communication graphs subject to input noise based on input to state stability and integral input to state stability robust consensus and integral robust consensus are defined with respect to l and l1 norms of the noise function respectively sufficient and or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions the results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance the convergence time is obtained for the consensus computation on directed and k bidirectional graphs

nodes selection strategy in cooperative tracking problem in this paper a new optimization problem is addressed for node selection that has application potentials in input output switches for sensors in control system design and leader determination in social networks the purpose of the addressed problem is to develop a strategy for selecting a subset of nodes as controlled nodes in order to minimize certain objective function consisting of the convergence speed and the energy of control action over a finite time horizon for networks with fixed controlled nodes an upper bound of the objective function is obtained which is shown to be convex and independent of the time horizon for networks with switched controlled nodes a greedy algorithm is proposed to reduce the computation complexity resulting from the length of the time horizon where the nodes selection is carried out over divided small time intervals the cost gap is also analyzed between the strategy of optimizing over the whole time horizon and the strategy of optimizing over the small intervals finally the proposed nodes selection strategy is validated through simulations and two regions are found in which the number of optimal controlled nodes is determined

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

positive solutions of bvps for third order nonlinear difference systems abstract in this paper we consider the following discrete system boundary value problems 3 u 1 k f 1 k u 1 k u 2 k 0 k o t 3 u 2 k f 2 k u 1 k u 2 k 0 k o t with the dirichlet boundary condition u 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using a nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

randomized optimal consensus of multi agent systems in this paper we formulate and solve a randomized optimal consensus problem for multi agent systems with stochastically time varying interconnection topology the considered multi agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z r email protected i 1 nf i z in which the optimal solution set of objective function f i can only be observed by agent i itself at each time step simply determined by a bernoulli trial each agent independently and randomly chooses either taking an average among its neighbor set or projecting onto the optimal solution set of its own optimization component both directed and bidirectional communication graphs are studied connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions the convergence analysis is carried out using convex analysis we compare the randomized algorithm with the deterministic one via a numerical example the results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade off between following its neighbors or sticking to its own opinion at each time step

on metric ramsey type phenomena the main question studied in this article may be viewed as a nonlinear analogue of dvoretzky s theorem in banach space theory or as part of ramsey theory in combinatorics given a finite metric space on n points we seek its subspace of largest cardinality which can be embedded with a given distortion in hilbert space we provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion our main theorem states that for any 0 every n point metric space contains a subset of size at least n1 which is embeddable in hilbert space with o log 1 distortion the bound on the distortion is tight up to the log 1 factor we further include a comprehensive study of various other aspects of this problem

brief paper convergence speed in distributed consensus over dynamically switching random networks characterizing convergence speed is one of the most important research challenges in the design of distributed consensus algorithms for networked multi agent systems in this paper we consider a group of agents that communicate via a dynamically switching random information network each link in the network which represents the directed undirected information flow between any ordered unordered pair of agents could be subject to failure with a certain probability hence we model the information flow using dynamically switching random graphs we characterize the convergence speed for the distributed discrete time consensus algorithm over a variety of random networks with arbitrary weights in particular we propose the asymptotic and per step mean square convergence factors as measures of the convergence speed and derive the exact value for the per step mean square convergence factor numerical examples are also given to illustrate our theoretical results

consensus of high order multi agent systems with switching topologies abstract in this paper a consensus problem is investigated for high order multi agent systems with switching communication networks through which only output information instead of full state information can be transmitted to neighbors based on self state feedback and neighbor output feedback a new consensus protocol is proposed which can realize arbitrary convergence rate furthermore as an application a nonlinear heading consensus protocol is designed for a multi vehicle model finally numerical simulations are given to illustrate the theoretical results

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

bifurcation techniques and positive solutions of discrete lidstone boundary value problems abstract let n 1 t n 5 be two positive integers and t n n n 1 t we consider the existence of solutions of the discrete lidstone boundary value problem 1 n 2 n u t n f t u t 2 u t 1 2 n 2 u t n 1 t t n 2 i u n i 1 2 i u t i 1 0 i 0 1 n 1 where f t n r n r is continuous

three positive solutions of boundary value problems for p laplacian difference equations in this paper existence criteria for three positive solutions of p laplacian difference equation f p u t 1 a t f u t 0 t 1 t 1 u 0 u t 2 0 oru 0 u t 1 0 are established by using the five functionals fixed point theorem as an application one example is given to illustrate the main result in this paper

multiple positive solutions of bvps for third order discrete difference systems this paper is concerned with the following email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

convergence rates of distributed average consensus with stochastic link failures we consider a distributed average consensus algorithm over a network in which communication links fail with independent probability in such stochastic networks convergence is defined in terms of the variance of deviation from average we first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures we then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise we give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks we also present simulation free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

hermitian normalized laplacian matrix for directed networks abstract in this paper we extend and generalize the spectral theory of undirected networks towards directed networks by introducing the hermitian normalized laplacian matrix for directed networks in order to start we discuss the courant fischer theorem for the eigenvalues of hermitian normalized laplacian matrix based on the courant fischer theorem we obtain a similar result towards the normalized laplacian matrix of undirected networks for each i 1 2 n any eigenvalue of hermitian normalized laplacian matrix i 0 2 moreover we prove some special conditions if 0 or 2 is an eigenvalue of the hermitian normalized laplacian matrix l x on top of that we investigate the symmetry of the eigenvalues of l x and the edge version for the eigenvalue interlacing result finally we present two expressions for the coefficients of the characteristic polynomial of the hermitian normalized laplacian matrix as an outlook we sketch some novel and intriguing problems to which our apparatus could generally be applied

chebyshev polynomials in distributed consensus applications in this paper we analyze the use of chebyshev polynomials in distributed consensus applications it is well known that the use of polynomials speeds up the convergence to the consensus in a significant way however existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known we propose a distributed algorithm based on the second order difference equation that describes the chebyshev polynomials of first kind the contributions of our algorithm are three i since the evaluation of chebyshev polynomials is stable there is no limitation in the degree of the polynomial ii instead of the knowledge of the whole network topology it only requires a partial knowledge or an approximation to it iii it can be applied to time varying topologies in the paper we characterize the main properties of the algorithm for both fixed and time varying communication topologies theoretical results as well as experiments with synthetic data show the benefits of using our algorithm compared to existing methods

global and robust formation shape stabilization of relative sensing networks this paper proposes a simple distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology assuming the network runs an initialization procedure to equally orient all agent reference frames convergence to the desired formation shape is guaranteed even in partially asynchronous settings we characterize the algorithm robustness against several sources of errors link failures measurement errors and frame initialization errors the technical approach combines algebraic graph theory multidimensional scaling and distributed linear iterations

convergence speed of unsteady distributed consensus decay estimate along the settling spanning trees results for estimating the convergence rate of nonstationary distributed consensus algorithms are provided on the basis of qualitative mainly topological as well as basic quantitative information lower bounds on the matrix entries the results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples the main idea is to follow propagation of information along certain spanning trees which arise in the communication graph

quasi isometric classification of graph manifold groups we show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi isometric we also classify the quasi isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite twocolored graphs a corollary is the quasi isometric classification of artin groups whose presentation graphs are trees in particular any two right angled artin groups whose presentation graphs are trees of diameter greater than 2 are quasi isometric further this quasi isometry class does not include any other right angled artin groups a finitely generated group can be considered geometrically when endowed with a word metric up to quasi isometric equivalence such metrics are unique in this article only finitely generated groups are considered given a collection of groups g gromov 11 proposed the fundamental questions of identifying which groups are quasi isometric to those in g rigidity and which groups in g are quasi isometric to each other classification in this article we focus on the classification question for graph manifold groups and right angled artin groups a compact 3 manifold m is called geometric if m m admits a geometric structure in the sense of thurston i e a complete locally homogeneous riemannian metric of finite volume thurston s geometrization conjecture see 29 17 21 23 22 provides that every irreducible 3 manifold of zero euler characteristic i e with boundary consisting only of tori and klein bottles admits a decomposition along tori and klein bottles into geometric pieces the minimal such decomposition being called the geometric decomposition there is a considerable literature on quasi isometric rigidity and classification of 3 manifold groups the rigidity results can be briefly summarized in the following form

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

coordination of multiagents interacting under independent position and velocity topologies we consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs different algorithms are proposed and analyzed for different settings including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies as well as the case with a group velocity reference signal under switching velocity interaction it is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory matrix analysis as well as the lyapunov stability theory

existence of positive solutions of bvps for second order nonlinear difference systems this paper is concerned with the following system d 2u i k f i k u 1 k u 2 k u n k 0 k 0 t i 1 2 nwith the dirichlet boundary conditionu i 0 u i t 2 0 i 1 2 n some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem in particular it proves that the above system has n positive solutions under suitable conditions where n is an arbitrary integer

generalized sarymsakov matrices within the set of stochastic indecomposable aperiodic sia matrices the class of sarymsakov matrices is the largest known subset that is closed under matrix multiplication and more critically whose compact subsets are all consensus sets this paper shows that a larger subset with these two properties can be obtained by generalizing the standard definition for sarymsakov matrices the generalization is achieved by introducing the notion of the sia index of a stochastic matrix whose value is 1 for sarymsakov matrices and then exploring those stochastic matrices with larger sia indices in addition to constructing the larger set this paper introduces another class of generalized sarymsakov matrices which contains matrices that are not sia and studies their products sufficient conditions are provided for an infinite product of matrices from this class converging to a rank one matrix finally as an application of the results just described and to confirm their usefulness a necessary and sufficient combinatorial condition the avoiding set condition for deciding whether or not a compact set of stochastic matrices is a consensus set is revisited in addition a necessary and sufficient combinatorial condition is established for deciding whether or not a compact set of doubly stochastic matrices is a consensus set

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

exponential consensus of general linear multi agent systems under directed dynamic topology this paper aims to investigate the consensus control of generic linear multi agent systems mass under directed dynamic topology nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which are widely used for multiple integrator agents is explored to deal with the convergence analysis of generic linear mass it is finally shown that the exponential consensus can be reached under very relaxed conditions i e the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough moreover a least convergence rate and a bound for the unstable mode of the individual agent system both of which are independent of the switching mode can be explicitly specified

the multi agent rendezvous problem part 2 the asynchronous case this paper is concerned with the collective behavior of a group of n 1 mobile autonomous agents labelled 1 through n which can all move in the plane each agent is able to continuously track the positions of all other agents currently within its sensing region where by an agent s sensing region we mean a closed disk of positive radius r centered at the agent s current position the multi agent rendezvous problem is to devise local control strategies one for each agent which without any active communication between agents cause all members of the group to eventually rendezvous at a single unspecified location this paper describes a family of unsynchronized strategies for solving the problem correctness is established appealing to the concept of analytic synchronization

on the quantitative quasi isometry problem transport of poincare inequalities and different types of quasi isometric distortion growth abstract we consider a quantitative form of the quasi isometry problem we discuss several arguments which lead us to a number of results and bounds of quasi isometric distortion comparison of volumes connectivity etc then we study the transport of poincare constants by quasi isometries and we give sharp lower and upper bounds for the homotopy distortion growth for a certain class of hyperbolic metric spaces a quotient of a heintze group r r n by z n we also prove the linear distortion growth between hyperbolic space h n n 3 and a tree

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

robust distributed average consensus via exchange of running sums we consider a multi component system in which each component node can send receive information to from sets of neighboring nodes via communication links edges that form a fixed strongly connected possibly directed communication topology digraph we analyze a class of distributed iterative algorithms that allow the nodes to asymptotically compute the exact average of their initial values despite a variety of challenging scenarios including possible packet drops in the communication links and imprecise knowledge of the network the algorithms in this class run the two linear iterations of the so called ratio consensus algorithm modified so that messages sent by one node to another are encoded as running sums this convolutional encoding allows the receiving node l to infer information about past messages that node j meant to send to node l but may have been lost due to packet drops imprecise knowledge of the network unknown out neighborhoods can be handled at the cost of memory and communication overhead by also having each node track the progress of running sums of other nodes and forward to its out neighboring nodes the updated value of one such running sum that it randomly selects our analysis relies on augmenting the digraph that describes the communication topology by introducing additional virtual nodes and showing that the dynamics of each of the two iterations in the augmented digraph is mathematically equivalent to a finite inhomogeneous markov chain almost sure convergence to exact average consensus is then established via weak ergodicity analysis of the resulting inhomogeneous markov chain

a system of ni pi boundary value problems with positive nonpositive nonlinearities abstract we consider the system of boundary value problems u n i i t f i t u 1 t u 2 t u m t 0 t 0 1 u j i 0 0 u p i i 1 0 j n i 2 i 1 2 m where ni 2 1 pi ni 1 1 i m several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs

orlicz spaces and the large scale geometry of heintze groups we consider an orlicz space based cohomology for metric measured spaces with bounded geometry we prove the quasi isometry invariance for a general young function in the hyperbolic case we prove that the degree one cohomology can be identified with an orlicz besov function space on the boundary at infinity we give some applications to the large scale geometry of homogeneous spaces with negative curvature heintze groups as our main result we prove that if the heintze group is not of carnot type any self quasi isometry fixes a distinguished point on the boundary and preserves a certain foliation on the complement of that point

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

degree fluctuations and the convergence time of consensus algorithms we consider a consensus algorithm in which every node in a sequence of undirected b connected graphs assigns equal weight to each of its neighbors under the assumption that the degree of each node is fixed except for times when the node has no connections to other nodes we show that consensus is achieved within a given accuracy e on n nodes in time b 4n3 bln 2n e because there is a direct relation between consensus algorithms in time varying environments and in homogeneous random walks our result also translates into a general statement on such random walks moreover we give a simple proof of a result of cao spielman and morse that the worst case convergence time becomes exponentially large in the number of nodes n under slight relaxation of the degree constancy assumption

coordinated path following in the presence of communication losses and time delays this paper addresses the problem of steering a group of vehicles along given spatial paths while holding a desired time varying geometrical formation pattern the solution to this problem henceforth referred to as the coordinated path following cpf problem unfolds in two basic steps first a path following pf control law is designed to drive each vehicle to its assigned path with a nominal speed profile that may be path dependent this is done by making each vehicle approach a virtual target that moves along the path according to a conveniently defined dynamic law in the second step the speeds of the virtual targets also called coordination states are adjusted about their nominal values so as to synchronize their positions and achieve indirectly vehicle coordination in the problem formulation it is explicitly considered that each vehicle transmits its coordination state to a subset of the other vehicles only as determined by the communications topology adopted it is shown that the system that is obtained by putting together the pf and coordination subsystems can be naturally viewed as either the feedback or the cascade connection of the latter two using this fact and recent results from nonlinear systems and graph theory conditions are derived under which the pf and the coordination errors are driven to a neighborhood of zero in the presence of communication losses and time delays two different situations are considered the first captures the case where the communication graph is alternately connected and disconnected brief connectivity losses the second reflects an operational scenario where the union of the communication graphs over uniform intervals of time remains connected uniformly connected in mean to better root the paper in a nontrivial design example a cpf algorithm is derived for multiple underactuated autonomous underwater vehicles auvs simulation results are presented and discussed

analysis and applications of spectral properties of grounded laplacian matrices for directed networks abstract in depth understanding of the spectral properties of grounded laplacian matrices is critical for the analysis of convergence speeds of dynamical processes over complex networks such as opinion dynamics in social networks with stubborn agents we focus on grounded laplacian matrices for directed graphs and show that their eigenvalues with the smallest real part must be real lower and upper bounds for such eigenvalues are provided utilizing tools from nonnegative matrix theory for those eigenvectors corresponding to such eigenvalues we discuss two cases when we can identify the vertex that corresponds to the smallest eigenvector component we then discuss an application in leader follower social networks where the grounded laplacian matrices arise naturally with the knowledge of the vertex corresponding to the smallest eigenvector component for the smallest eigenvalue we prove that by removing or weakening specific directed couplings pointing to the vertex having the smallest eigenvector component all the states of the other vertices converge faster to that of the leading vertex this result is in sharp contrast to the well known fact that when the vertices are connected together through undirected links removing or weakening links does not accelerate and in general decelerates the converging process

convergence rate for discrete time multiagent systems with time varying delays and general coupling coefficients multiagent systems mass are ubiquitous in our real world there is an increasing attention focusing on the consensus or synchronization problem of mass over the past decade although there are numerous results reported on the convergence of a discrete time mas based on the infinite products of matrices few results are on the convergence rate because of the switching topology the traditional eigenvalue analysis and the lyapunov function methods are both invalid for the convergence rate analysis of an mas with a switching topology therefore the estimation of the convergence rate for a discrete time mas with time varying delays remains a difficult problem to overcome the essential difficulty of switching topology this paper aims at developing a contractive set approach to analyze the convergence rate of a discrete time mas in the presence of time varying delays and generalized coupling coefficients using the proposed approach we obtain an upper bound of the convergence rate under the condition of joint connectivity in particular the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients which have been widely applied in the existing works on this topic as an application of the main results we will show that the classical vicsek model with time delays can realize synchronization if the initial topology is connected

coarse differentiation of quasi isometries i spaces not quasi isometric to cayley graphs in this paper we prove that certain spaces are not quasi isometric to cayley graphs of nitely generated groups in particular we answer a question of woess and prove a conjecture of diestel and leader by showing that certain homogeneous graphs are not quasi isometric to a cayley graph of a nitely generated group this paper is the rst in a sequence of papers proving results announced in our 2007 article quasi isometries and rigidity of solvable groups in particular this paper contains many steps in the proofs of quasi isometric rigidity of lattices in sol and of the quasi isometry classication of lamplighter groups the proofs of those results are completed in coarse dierentiation of quasi isometries ii rigidity for lattices in sol and lamplighter groups the method used here is based on the idea of coarse dierentiation introduced in our 2007 article

agreeing asynchronously this paper formulates and solves a version of the widely studied vicsek consensus problem in which each member of a group of n 1 agents independently updates its heading at times determined by its own clock it is not assumed that the agents clocks are synchronized or that the ldquoeventrdquo times between which any one agent updates its heading are evenly spaced nor is it assumed that heading updates must occur instantaneously using the concept of ldquoanalytic synchronizationrdquo together with several key results concerned with properties of ldquocompositionsrdquo of directed graphs it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous case provided the notion of an agent s neighbor between its event times is appropriately defined however in sharp contrast with the synchronous case where for analysis an n dimensional state space model is adequate for the asynchronous version of the problem a 2n dimensional state space model is required it is explained how to analyze this model despite the fact that unlike the synchronous case the stochastic matrices involved do not have all positive diagonal entries

quasisymmetric maps on the boundary of a negatively curved solvable lie group we describe all the self quasisymmetric maps on the ideal boundary of a particular negatively curved solvable lie group as applications we derive some rigidity properties for quasiisometries of the solvable lie group

second order consensus for multi agent systems with switching topology and communication delay in this paper two kinds of consensus problems for second order agents under directed and arbitrarily switching topologies are investigated that is the cases without and with communication delay for the former by constructing a new kind of digraph and employing a new graphic method we can specify the least convergence rate for all the agents to reach consensus for the latter in virtue of a matrix inequality method a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus this on the other hand shows that consensus can be reached if the delay is small enough finally two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results

on attack resilient distributed formation control in operator vehicle networks this paper tackles a distributed formation control problem where a group of vehicles is remotely controlled by a network of operators each operator vehicle pair is attacked by an adversary who corrupts the commands sent from the operator to the vehicle from the point of view of operators each adversary follows an attacking strategy linearly parameterized by some potentially time varying matrix which is unknown a priori in particular we consider two scenarios depending upon whether adversaries can adapt their attacking tactics online to assure mission completion in such a hostile environment we propose two novel attack resilient distributed control algorithms that allow operators to adjust their policies on the fly by exploiting the latest collected information about adversaries both algorithms enable vehicles to asymptotically achieve the desired formation from any initial configuration and initial estimate of the adversaries strategies it is further shown that the sequence of the distances t

quasi isometries preserve the geometric decomposition of haken manifolds we prove quasi isometry invariance of the canonical decomposition for fundamental groups of haken 3 manifolds with zero euler characteristic we show that groups quasi isometric to haken manifold groups with nontrivial canonical decomposition are finite extensions of haken orbifold groups as a by product we describe all 2 dimensional quasi flats in the universal covers of non geometric haken manifolds

existence theorems for a system of difference equations with n p type conditions we offer criteria for the existence of single and double solutions of fixed signs for the following system of boundary value email protected nu i k q i k u 1 k u 2 k u m k 0 email protected 0 1 n d ju i 0 email protected p iu i n n p i 0 2 n n 1 1

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

further results on fixed sign solutions for a system of higher order difference equations abstract we consider the following system of n th order boundary value problems download full size image where u i k u i k u i k n 2 u i k 1 i m criteria are offered for the existence of single and double fixed sign solutions of the system we also include examples to illustrate the importance of the results obtained

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

convergence and state reconstruction of time varying multi agent systems from complete observability theory we study continuous time consensus dynamics for multi agent systems with undirected switching interaction graphs we establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of complete observability the proof is remarkably simple compared to similar results in the literature and the conditions for consensus are mild this observability based method can also be applied to the case where negatively weighted edges are present additionally as a by product of the observability based arguments we show that the nodes initial value can be recovered from the signals on the edges up to a shift of the network average