convergence results for the linear consensus problem under markovian random graphs this paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph the switching is determined by a finite state markov process each topology corresponding to a state of the process we address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time we show that if the consensus matrices are doubly stochastic average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the markov process is strongly connected the aim of this paper is to show how techniques from the theory of markovian jump linear systems in conjunction with results inspired by matrix and graph theory can be used to prove convergence results for stochastic consensus problems

further results on the asymptotic agreement problem the problem of reaching a concensus between two decision makers provided with different information is considered the problem in which the decision makers may have different underlying probability models is studied results are developed to characterize the likelihood of an agreement being reached eventually in terms of the nature of the inter decision maker communications the problem in which the decision makers are aware of the possibility that they may have different models is treated it is found that in this case a deadlock can be reached where neither decision maker can learn additional information from the concensus process and they cannot reach a concensus decision this result indicates that incorporating human uncertainty in probability assessment into the asymptotic agreement problem can lead to outcomes not anticipated in the general theory previously developed

distributed detection in sensor networks with limited range multimodal sensors we consider a multiobject detection problem over a sensor network snet with limited range multimodal sensors the general problem complements the widely considered decentralized detection problem where all sensors observe the same object we develop a distributed detection approach based on recent development of the false discovery rate fdr and the associated benjamini hochberg bh procedure which rank orders scalar test statistics we first develop scalar test statistics for multidimensional data to handle multimodal sensor observations and establish its optimality in terms of the bh procedure we then propose a distributed algorithm for an idealized model to detect the sensors that are in the immediate vicinity of an object we show that the number of binary messages that need to be transmitted communication cost is upper bounded by the number of sensors that are in the vicinity of objects and is independent of the total number of sensors in the snet this brings forth an important principle for evaluating the performance of an snet namely the need for scalability of communications and performance with respect to the number of objects or events in an snet irrespective of the network size we then account for nonideal models by developing robust extensions to our developments under the idealized model the robustness properties ensure that both the error performance and communication cost degrade gracefully with interference

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

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

consensus based linear distributed filtering we address the consensus based distributed linear filtering problem where a discrete time linear stochastic process is observed by a network of sensors we assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable i e for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors without noise is asymptotically stable next we develop a distributed sub optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost in the stationary case we provide sufficient conditions under which this scheme converges conditions expressed in terms of the convergence properties of a set of coupled riccati equations

stochastic nestedness and the belief sharing information pattern solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time horizon thus leading to non tractability of classical dynamic programming a common joint information state supplied to each of the agents leads to a tractable recursion as is evident in the one step delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure however communication requirements for such conditions require exchange of very large data noiselessly hence these assumptions are generally impractical in this paper we present a weaker notion of nestedness which we term as stochastic nestedness which is characterized by a sequence of markov chain conditions it is shown that if the information structure is stochastically nested then an optimization problem is tractable and in particular for lqg problems the team optimal solution is linear despite the lack of deterministic nestedness or partial nestedness one other contribution of this paper is that by regarding the multiple decision makers as a single decision maker and using witsenhausen s equivalent model for discrete stochastic control it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions a pattern we refer to as k stage belief sharing pattern we discuss the minimum amount of information exchange required to achieve such an information pattern for k 1 the information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies in view of nestedness we present a discussion on the monotone values of information channels

adaptive coordinated tracking of multi agent systems with quantized information abstract in this paper we study the adaptive coordinated tracking problem for continuous time first order integrator systems with quantized information under switching undirected and fixed directed communication graphs respectively the combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated both the logarithmic quantizers and uniform quantizers are considered it is shown that when logarithmic quantizers are used exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter simulation examples are provided to illustrate the results

consensus of second order discrete time multi agent systems with fixed topology abstract this paper studies the consensus of second order discrete time multi agent systems with fixed topology first we formulate the problem and give some preliminaries then by algebraic graph theory and matrix theory the convergence of system matrix is analyzed our main results indicate that the consensus of second order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters satisfy a range the eigenvalues of the corresponding laplacian matrix play a key role in reaching consensus finally numerical simulations are given to illustrate the results

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems interval branch and bound algorithms for finding all roots use a combination of a computational existence uniqueness procedure and a tessellation process generalized bisection such algorithms identify with mathematical rigor a set of boxes that contains unique roots and a second set within which all remaining roots must lie though each root is contained in a box in one of the sets the second set may have several boxes in clusters near a single root thus the output is of higher quality if there are relatively more boxes in the first set in contrast to previously implemented similar techniques a box expansion technique in this paper based on using an approximate root finder epsilon inflation and exact set complementation decreases the size of the second set increases the size of the first set and never loses roots in addition to the expansion technique use of second order extensions to eliminate small boxes that do not contain roots and interval slopes versus interval derivative matrices are studied these items are evaluated empirically on a significant test problem set within a fortran 90 environment designed for such purposes the results are compared with previous results and show that careful incorporation of the techniques yields both quantitatively and qualitatively superior computer codes

technical communique a linear distributed filter inspired by the markovian jump linear system filtering problem in this paper we introduce a consensus based distributed filter executed by a sensor network inspired by the markovian jump linear system filtering theory we show that the optimal filtering gains of the markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem this parallel allows us to interpret each filtering gain corresponding to a mode of operation of the markovian jump linear system as a filtering gain corresponding to a sensor in the network the approximate solution can be implemented distributively and guarantees a quantifiable level of performance

a consensus algorithm in cat 0 space and its application to distributed fusion of phylogenetic trees abstract based on convex analysis a novel consensus algorithm of dynamical points in a cat 0 space is developed in this paper in which the associated communication graph uniformly contains a directed spanning tree the proposed algorithm provides an efficient method of solving consensus problems in a general cat 0 space while having certain robustness against weak communication the application of the new algorithm to the distributed fusion of phylogenetic trees is shown with demonstrative case simulations together with a study on the algorithm s robustness and efficiency

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

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

consensus on complete riemannian manifolds in finite time abstract in view of the fact that prototypes of riemannian manifolds range from euclidean surfaces to lie groups operator spaces etc the paper explores common consensus schemes for connected complete riemannian manifolds after studying the restriction exponential map we introduce a local consensus protocol with switching communication topologies for the manifolds via the isometric mapping based on one of the euclidean consensus protocols equipped with the compression decompression functions we extend the local consensus protocol and put forth a global consensus algorithm for any such manifolds these consensus schemes can provide common solutions to the consensus problems arising from various nonlinear spaces or abstract spaces belonging to connected complete riemannian manifolds in particular they are simple and concise and can converge in finite time simulation on the unit sphere is provided to verify our consensus schemes and to demonstrate the usage of our proposed techniques

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

finite time consensus using stochastic matrices with positive diagonals we discuss the possibility of reaching consensus in finite time using only linear iterations with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure we show that finite time average consensus can always be achieved for connected undirected graphs for directed graphs we show some necessary conditions for finite time consensus including strong connectivity and the presence of a simple cycle of even length

distributed coordination for second order multi agent systems with nonlinear dynamics using only relative position measurements in this paper we study the distributed coordination for second order multi agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the agents or followers both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader are considered by introducing a distributed filter for each agent or follower the proposed control algorithms use only relative position measurements in the absence of communication in the special case without the intrinsic nonlinear dynamics i e for multi agent systems with double integrator dynamics we further derive a necessary and sufficient condition for the leaderless consensus problem under a general directed graph finally simulation examples are provided to show the effectiveness of the proposed control algorithms

the asymptotic consensus problem on convex metric spaces a consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest the agents exchange information according to a communication network modeled as a directed time varying graph and evolve in a convex metric space a metric space endowed with a convex structure in this paper we generalize the asymptotic consensus problem to convex metric spaces under weak connectivity assumptions we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the generalized convex hull generated by the agent s current state and the states of its neighbors then agreement is achieved asymptotically in addition we present several examples of convex metric spaces and their corresponding agreement algorithms

preconditioners for the interval gauss seidel method interval newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box bf x subset bf r n of a system of nonlinear equations f x 0 with mathematical certainty even in finite precision arithmetic in such methods the system f x 0 is transformed into a linear interval system 0 f m bf f bf x bf bar x m if interval arithmetic is then used to bound the solutions of this system the resulting box bf bar x contains all roots of the nonlinear system the interval gauss seidel method is a reasonable way of finding such solution bounds for the overall interval newton bisection algorithm to be efficient the image box bf bar x should be as small as possible to do this the linear interval system is multiplied by a preconditioner matrix y before the interval gauss seidel method is applied in this paper a technique for computing such preconditioner matrices y is described this te

network based consensus averaging with general noisy channels this paper focuses on the consensus averaging problem on graphs under general imperfect communications we study a particular class of distributed consensus algorithms based on damped updates and using the ordinary differential equation method we prove that the updates converge almost surely to the consensus average for various models of perturbation of data exchanged between nodes the convergence is not asymptotic in the size of the network our analysis applies to various types of stochastic disturbances to the updates including errors in update calculations dithered quantization and imperfect data exchange among nodes under a suitable stability condition we prove that the error between estimated and true averages is asymptotically gaussian and we show how the asymptotic covariance is specified by the graph laplacian for additive perturbations we show how the scaling of the asymptotic mse is controlled by the spectral gap of the laplacian

asynchronous rendezvous analysis via set valued consensus theory this paper presents the design and analysis result for asynchronous rendezvous control of multiagent systems with continuous time dynamics and intermittent interactions the protocol designing strategies only impose weak restrictions on anticipated way point sets from which the way points are selected and path planning of each agent and can be applied to the networks of arbitrary dimensional subsystems explicitly the anticipated way point sets are in a polytope like form and the path between any two consecutive way points is required to be included within the minimum convex region covering the two associated anticipated way point sets under the assumption of directed and switching interaction topology and the assumption of intermittent and asynchronous interactions with time varying delays we perform the set valued consensus analysis on the evolution of anticipated way point sets with respect to update times and provide mild sufficient conditions for the solvability of the asynchronous rendezvous problem the proof techniques rely much on graph theory and nonnegative matrix theory the obtained result extends greatly the existing work in the literature and several examples demonstrate its broad potential applications particularly additional distributed control rules different from the circumcenter algorithm are devised for network connectivity maintenance

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

group consensus control for heterogeneous multi agent systems with fixed and switching topologies abstractin this paper the group consensus problems of heterogeneous multi agent systems with fixed and switching topologies are investigated first a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi agent systems by using the neighbours information then some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus rigorous proofs are given by using graph theory matrix theory and lyapunov theory finally numerical simulations are also given to verify the theoretical analysis

on the consensus of homogeneous multi agent systems with arbitrarily switching topology abstract in this paper we investigate the consensus problem under arbitrary switching for homogeneous multi agent systems with switching communication topology by assuming that each agent is described by a single input stabilizable state space model and that the communication graph is connected at every time instant under these assumptions we construct a common quadratic positive definite lyapunov function for the switched system describing the evolution of the disagreement vector thus showing that the agents always reach consensus in addition the proof leads to the explicit construction of a constant state feedback matrix that allows the multi agent system to achieve consensus

stochastic consensus seeking with noisy and directed inter agent communication fixed and randomly varying topologies we consider consensus seeking of networked agents on directed graphs where each agent has only noisy measurements of its neighbors states stochastic approximation type algorithms are employed so that the individual states converge both in mean square and almost surely to the same limit we further generalize the algorithm to networks with random link failures and prove convergence results

consensus in time delayed multi agent systems with quantized dwell times abstract this paper investigates the effects of quantized dwell times in solving consensus problems in time delayed multi agent systems with the asynchronous property of unpredictable quantization jumps in inter agent communications the quantized dwell times can be introduced on purpose or be inherent from quantizing devices they beneficially avoid undesirable fast chattering of quantizers outputs and mathematical difficulties in convergence analysis the main result shows that the largest eigenvalue of the interaction graph laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time varying transmission delays simulations are presented to show the effectiveness of the main result

homotopies for solving polynomial systems within a bounded domain abstract the problem considered in this paper is the computation of all solutions of a given polynomial system in a bounded domain proving rouche s theorem by homotopy continuation concepts yields a new class of homotopy methods the so called regional homotopy methods these methods rely on isolating a part of the system to be solved which dominates the rest of the system on the border of the domain as the dominant part has a sparser structure it is easier to solve it will be used as start system in the regional homotopy the paper further describes practical homotopy construction methods by presenting estimators to obtain bounds for polynomials over a bounded domain applications illustrate the usefulness of the approach

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

parameter estimation in stochastic systems some recent results and applications some recent work on the characterization of almost sure limit sets for maximum likelihood estimates for stochastic systems is reviewed applications to allied topics such as input selection for identification model selection self tuning etc are briefly discussed

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

asymptotic stability of ltv systems with applications to distributed dynamic fusion we investigate the behavior of linear time varying ltv systems with randomly appearing sub stochastic system matrices motivated by dynamic fusion over mobile networks we develop conditions on the system matrices that lead to asymptotic stability of the underlying ltv system by partitioning the sequence of system matrices into slices we obtain the stability conditions in terms of slice lengths and introduce the notion of unbounded connectivity i e the time intervals over which the multi agent network is connected do not have to be bounded as long as they do not grow faster than a certain exponential rate we further apply the above analysis to derive the asymptotic behavior of a dynamic leader follower algorithm

mean field stochastic linear quadratic optimal control with markov jump parameters abstract this paper considers a class of mean field stochastic linear quadratic optimal control problems with markov jump parameters the new feature of these problems is that means of state and control are incorporated into the systems and the cost functional based on the modes of markov chain the corresponding decomposition technique of augmented state and control is introduced it is shown that under some appropriate conditions there exists a unique optimal control which can be explicitly given via solutions of two generalized difference riccati equations a numerical example sheds light on the theoretical results established

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

on consensus speed of multi agent systems with double integrator dynamics the performance of multi agent systems is an important issue in this paper it is focused on consensus speed for multi agent systems with double integrator dynamics and fixed undirected graphes under a kind of consensus protocols it is revealed that under some conditions the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the laplacian matrix of the undirected connected graph based on the mentioned results arbitrary desired consensus speed can be achieved by choosing suitable feedback gains numerical simulations are given to illustrate the main results

convergence and asymptotic agreement in distributed decision problems we consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements possibly at different random times related to the same uncertain random vector each agent has the same objective function and prior probability distribution we assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received possibly at random times by a subset of other agents conditions for asymptotic convergence of each agent s decison sequence and asymptotic agreement of all agents decisions are derived

distributed consensus of second order multi agent systems with heterogeneous unknown inertias and control gains under a directed graph in this paper we study the consensus problem for second order multi agent systems with heterogeneous unknown inertias and control gains under a general directed graph unlike the existing consensus algorithms for second order multi agent systems in which all agents are assumed to have common unit inertias or share common control gains we allow the inertias and the control gains to be heterogeneous and time varying for each agent we propose fully distributed consensus algorithms over a general directed graph when there exist respectively absolute velocity damping and relative velocity damping novel integral type lyapunov functions are proposed to study the consensus convergence moreover the adaptive sigma modification schemes for the gain adaptation are proposed which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence furthermore we show that one proposed algorithm also works for consensus of agents with intrinsic lipschitz nonlinear dynamics the control gains are varying and updated by distributed adaptive laws as a result the proposed algorithms require no global information and thus can be implemented in a fully distributed manner

a matrix approach to graph maximum stable set and coloring problems with application to multi agent systems using the semi tensor product of matrices this paper investigates the maximum weight stable set and vertex coloring problems of graphs with application to the group consensus of multi agent systems and presents a number of new results and algorithms firstly by defining a characteristic logical vector and using the matrix expression of logical functions an algebraic description is obtained for the internally stable set problem based on which a new algorithm to find all the internally stable sets is established for any graph secondly the maximum weight stable set problem is considered and a necessary and sufficient condition is presented by which an algorithm to find all the maximum weight stable sets is obtained thirdly the vertex coloring problem is studied by using the semi tensor product method and two necessary and sufficient conditions are proposed for the colorability based on which a new algorithm to find all the k coloring schemes and minimum coloring partitions is put forward finally the obtained results are applied to multi agent systems and a new protocol design procedure is presented for the group consensus problem the study of illustrative examples shows that the results algorithms presented in this paper are very effective

stabilization and synchronization for a heterogeneous multi agent system via harmonic control abstract in this paper a class of heterogeneous multi agent systems with directed cycle graphs is investigated the stabilization and synchronization problems via harmonic control are solved under some conditions and the feedback control gains are constructively designed several numerical examples are presented to demonstrate the effectiveness of the proposed method

stochastic frontier models a bayesian perspective abstract a bayesian approach to estimation prediction and model comparison in composed error production models is presented a broad range of distributions on the inefficiency term define the contending models which can either be treated separately or pooled posterior results are derived for the individual efficiences as well as for the parameters and the differences with the usual sampling theory approach are highlighted the required numerical integrations are handled by monte carlo methods with importance sampling and an empirical example illustrates the procedures

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

asymptotic agreement in distributed estimation each of several agents updates his estimate of the same random variable whenever he makes a new observation or receives the estimate made by another agent in turn each agent transmits his estimate to a randomly chosen subset of the other agents a subset of agents forms a communicating ring if for every pair underline m underline p of ring members there is a sequence of ring members underline m underline m 1 underline m 2 underline m n 1 underline p such that underline m i sends his estimate to underline m i 1 infinitely often if each ring member knows that he is a ring member then the estimates of all the ring members asymptotically agree however this common limit can depend upon the order in which estimates are transmitted

calculation of multivariate chebyshev type inequalities abstract a general multivariate chebyshev inequality has been obtained by whittle and olkin and pratt application of their inequality is made difficult because of the presence of a certain intractable matrix equation dharmadhikari and joag dev have obtained a bivariate gauss inequality in this paper we extend the bivariat gauss inequality to the general multivariate case encountering the same intractable matrix equation we develop a general method for the solution of this equation applying recent results in the solution of systems of nonlinear equations

global consensus for discrete time multi agent systems with input saturation constraints in this paper we consider the global consensus problem for discrete time multi agent systems with input saturation constraints under fixed undirected topologies we first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents we then focus on two special cases where the agent model is either neutrally stable or a double integrator for the neutrally stable case any linear protocol of a particular form which solves the consensus problem for the case without input saturation constraints also solves the global consensus problem for the case with input saturation constraints for the double integrator case we show that a subset of linear protocols which solve the consensus problem for the case without saturation constraints also solve the global consensus problem for the case with input saturation constraints the results are illustrated by numerical simulations

decomposing stochastic frontier efficiency into secular and organisational efficiency abstract in this article we propose to decompose the frontier efficiency into two distinct parts namely a secular part long term and an organisational part short term a product life cycle model for twelve industries of the belgian manufacturing sector has been tested for the period 1979 1983 by using cluster analysis filtering out the secular effect for each cluster groups of fimrs makes it possible to decompose the overall technical efficiency it turns out that for 27 out of 44 groups of firms the organisational part is larger than the secular part considering the status of the firms organisational efficiency differences could be analysed directy for groups of similar firms

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

computation of topological degree using interval arithmetic and applications a method is described for computing the topological degree of a mapping from rn into rn defined by n functions of n variables on a region specified as a product of n intervals a generalized box b the method is an adaptation of kearfott s method to boxes and begins by checking the signs of the n functions on the boundary of b with interval arithmetic on the basis of this check a portion b 1 of the boundary of b is designated for further investigation and one of the n functions defining the mapping is dropped the signs of the remaining functions are checked on the boundary of b 1 again a portion b 2 of the boundary of b 1 is designated for further investigation and another of the functions is dropped on the nth cycle of the process the topological degree finally is evaluated by determining the signs of a single function on a collection of isolated points comprising the boundary of a region b n 1 when the topological degree is nonzero there is at least one point inside b where the n functions are simultaneously zero to locate such a point the familiar bisection method for functions f x defined over an interval a b using sign changes of f x is easily generalized to apply to n functions defined over boxes using the topological degree for this application we actually use the topological degree mod 2 the crossing parity because its computation is easier if the n functions have all partial derivatives in the box b with a nonzero jacobian at any point where the functions are simultaneously zero then all such points inside b can be located by another method which also uses the crossing parity

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

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

second order consensus of networked thrust propelled vehicles on directed graphs this technical note addresses the second order consensus problem of multiple underactuated thrust propelled vehicles tpvs on directed graphs containing a directed spanning tree we propose an adaptive control approach to resolve this problem and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the tpvs in addition the resultant complexity is reduced and the requirement on the interaction graph is relaxed using an input output analysis we show that the proposed controller realizes second order consensus of the tpvs i e the position and velocity consensus errors between the tpvs converge to zero and moreover the velocities of the tpvs converge to the weighted average of their initial values the performance of the proposed control approach is shown by a numerical simulation

consensus seeking over random weighted directed graphs we examine the consensus problem for a group of agents that communicate via a stochastic information network communication among agents is modeled as a weighted directed random graph that switches periodically the existence of any edge is probabilistic and independent from the existence of any other edge we further allow each edge to be weighted differently sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights

abstract generalized bisection and a cost bound etude des proprietes des algorithmes de recherche binaires pour la separation de toutes les solutions des systemes d equations non lineaires dans un domaine compact donne

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

a generalized gossip algorithm on convex metric spaces a consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest this problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity in this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces where the communication between agents is controlled by a set of poisson counters we study the convergence properties of the algorithm using stochastic calculus in particular we show that the distances between the states of the agents converge to zero with probability one and in the r th mean sense in the special case of complete connectivity and uniform poisson counters we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents in addition we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations

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

consensus in distributed estimation with inconsistent beliefs two people sequentially revise and exchange their estimates of the same random variable they may have different models of the underlying probability structure the two sets of estimates then will converge to the same value or the people will realize that their beliefs are inconsistent

consensus on compact riemannian manifolds in view of a fact that compact manifolds have the important application in practice this paper provides a local consensus protocol for connected compact riemannian manifolds where communication network can be directed and dynamically switching meanwhile with the help of the compression decompression functions we extend the local protocol and propose a global consensus algorithm for such manifolds furthermore to demonstrate their effectiveness and efficiency the global algorithm is applied to the consensus problem of rotation attitudes together with a case simulation

decentralized parameter estimation by consensus based stochastic approximation in this paper an algorithm for decentralized multi agent estimation of parameters in linear discrete time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy an analysis of the asymptotic properties of the proposed algorithm is presented taking into account both the multi agent network structure and the probabilities of getting local measurements and implementing exchange of inter agent messages in the case of non vanishing gains in the stochastic approximation algorithms an asymptotic estimation error covariance matrix bound is defined as the solution of a lyapunov like matrix equation in the case of asymptotically vanishing gains the mean square convergence is proved and the rate of convergence estimated in the discussion the problem of additive communication noise is treated in a methodologically consistent way it is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence some simulation results illustrate the obtained theoretical results

randomized gradient free method for multiagent optimization over time varying networks in this brief we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but lipschitz continuous functions subject to a convex state constraint set the underlying network topology is modeled as time varying we propose a randomized derivative free method where in each update the random gradient free oracles are utilized instead of the subgradients sgs in contrast to the existing work we do not require that agents are able to compute the sgs of their objective functions we establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the lipschitz constant of each agent s objective function finally a numerical example is provided to demonstrate the effectiveness of the method

robust consensus control with guaranteed rate of convergence using second order hurwitz polynomials abstractthis paper considers homogeneous networks of general linear time invariant second order systems we consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilisable we show that consensus with a guaranteed rate of convergence can always be achieved using linear state feedback to achieve this we provide a new and simple derivation of the conditions for a second order polynomial with complex coefficients to be hurwitz we apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph laplacian matrix may have complex eigenvalues based on the conditions found methods to compute feedback gains are proposed we show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics we also consider the use of static output feedback

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