almost equitable partitions and new necessary conditions for network controllability abstract in this paper we consider the controllability problem for multi agent networked control systems the main results of the paper are new graph theoretic necessary conditions for controllability involving almost equitable graph vertex partitions we generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple leaders and we also consider the broadcasted control scenario our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number theoretic properties of the communities we show via examples that our results can be used to account for a large portion of uncontrollable inducing leader selections that could not have otherwise been accounted for using symmetry results

the role of network topology on extremism propagation with the relative agreement opinion dynamics abstract in deffuant et al j artif soc soc simulation 5 2002 4 we proposed a simple model of opinion dynamics which we used to simulate the influence of extremists in a population simulations were run without any specific interaction structure and varying the simulation parameters we observed different attractors such as predominance of centrism or of extremism we even observed in certain conditions that the whole population drifts to one extreme of the opinion even if initially there are an equal number of extremists at each extreme of the opinion axis in the present paper we study the influence of the social networks on the presence of such a dynamical behavior in particular we use small world networks with variable connectivity and randomness of the connections we find that the drift to a single extreme appears only beyond a critical level of connectivity which decreases when the randomness increases

graph homology and stability of coupled oscillator networks there are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph laplacian some examples of such models include the kuramoto and kuramoto sakaguchi equations as well as the swing equations which govern the behavior of generators coupled in an electrical network we show that the index calculation can be related to a dual calculation which is done on the first homology group of the graph rather than the vertex space we also show that this representation is computationally attractive for relatively sparse graphs where the dimension of the first homology group is low as is true in many applications we also give explicit formulae for the dimension of the unstable manifold to a phase locked solution for graphs containing one or two loops as an application we present some novel results for the kuramoto model defined on a ring and compute the longest possible edge length for a stable 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

collision free consensus in multi agent networks this paper addresses the collision free consensus problem in a network of agents with single integrator dynamics distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision free among agents during the evolution of the multi agent networks the novelty of the proposed algorithms lies in the definition of neighbors for each agent which is different from the usual sense that neighbors are selected by the distance between agents in the state space in the proposed strategies the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order the consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis meanwhile by realizing the relations between order preservation and collision free a systematic analysis framework on order preservation and hence collision free for agents in arbitrary dimension is provided based on tools from monotone systems theory illustrated numerical examples are presented to validate the effectiveness of the proposed strategies

on the controllability properties of circulant networks this paper examines the controllability of a group of first order agents adopting a weighted consensus type coordination protocol over a circulant network specifically it is shown that a circulant network with laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes our approach leverages on the cauchy binet formula which in conjunction with the popov belevitch hautus test leads to new insights on structural aspects of network controllability

threshold undeniable signature scheme based on conic recently undeniable signature has received a significant attention and has been extensively researched in the cryptographic community many undeniable schemes have been proposed however most of previous proposed schemes are based on discrete logarithm cryptosystems in this paper we present conic analogy of the first undeniable rsa signature scheme proposed by gennaro krawczyk and rabin at crypto 97 and propose the first threshold undeniable signature scheme based on conic

optimal domain splitting for interpolation by chebyshev polynomials polynomial interpolants defined using chebyshev extreme points as nodes converge uniformly at a geometric rate when sampling a function that is analytic on an interval however the convergence rate can be arbitrarily close to unity if the function has a singularity close to the interval when extended to the complex plane in such cases splitting the interval and doing piecewise interpolation may be more efficient in the total number of nodes than the global interpolant because the convergence rate is determined by bernstein ellipses obtained through a joukowski conformal map relative efficiency of splitting at any point in the interval can be calculated and then optimized over the interval the optimal splitting may be applied recursively the chebfun software project uses a simple rule of thumb without prior singularity information to create a binary search that can be shown to do an excellent job of finding the optimal splitting in most cases however the process can use a large number of intermedi

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

efficient generation of shared rsa keys we describe efficient techniques for a number of parties to jointly generate an rsa key at the end of the protocol an rsa modulus n pq is publicly known none of the parties know the factorization of n in addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption our protocols are efficient in computation and communication all results are presented in the honest but curious scenario passive adversary

on nonsmooth solutions of linear hyperbolic systems initial value problems for linear hyperbolic systems with smooth 2 periodic coefficients are solved numerically by a modified fourier galerkin method when the initial values are nonsmooth the described approach is seen to give substantially improved accuracy compared to more traditional methods the discontinuities are accurately resolved already on coarse grids and the fine structure of structured solutions is resolved on relatively coarse grids as well the accuracy is seen to be of high order and even for very long term integrations the global error can be kept very small if the grid is sufficiently refined

on a high order numerical method for functions with singularities by splitting a given singular function into a relatively smooth part and a specially structured singular part it is shown how the traditional fourier method can be modified to give numerical methods of high order for calculating derivatives and integrals singular functions with various types of singularities of importance in applications are considered relations between the discrete and the continuous fourier series for the singular functions are established of particular interest are piecewise smooth functions for which various important applications are indicated and for which numerous numerical results are presented

controllability analysis for a networked dynamic system with autonomous subsystems this technical note investigates the controllability of networked dynamic systems of which some subsystems are not directly affected by external inputs i e autonomous the topology can be arbitrary and every subsystem can have different dynamics and even different number of states inputs and outputs we show that to guarantee the controllability of the whole system every subsystem should be controllable when isolated we establish some necessary and sufficient conditions for the system to be controllable these conditions essentially depend on the parameters of every subsystem separately or the strongly connected autonomous subsystems which reduce significantly computation complexity for large scale networked systems we reveal that heterogenous networked systems under some assumptions can be separated into several independent subnetworks such that the controllability of the whole system is equal to the controllability of each subnetwork based on these conditions criteria that can be easily verified are given for the controllability of networked systems with some special topologies

optimal filter and mollifier for piecewise smooth spectral data we discuss the reconstruction of piecewise smooth data from its pseudo spectral information spectral projections enjoy superior resolution provided the function is globally smooth while the presence of jump discontinuities is responsible for spurious o 1 gibbs oscillations in the neighborhood of edges and an overall deterioration of the convergence rate to the unacceptable first order classical filters and mollifiers are constructed to have compact support in the fourier frequency and physical time spaces respectively and are dilated by the projection order or the width of the smooth region to maintain this compact support in the appropriate region here we construct a noncompactly supported filter and mollifier with optimal joint time frequency localization for a given number of vanishing moments resulting in a new fundamental dilation relationship that adaptively links the time and frequency domains not giving preference to either space allows for a more balanced error decomposition which when minimized yields an optimal filter and mollifier that retain the robustness of classical filters yet obtain true exponential accuracy

bipartite and cooperative output synchronizations of linear heterogeneous agents this paper investigates cooperative output synchronization and bipartite output synchronization of a group of linear heterogeneous agents in a unified framework for a structurally balanced signed graph we prove that the bipartite output synchronization is equivalent to the cooperative output synchronization over an unsigned graph whose adjacency matrix is obtained by taking the absolute value of each entry in the adjacency matrix of the signed graph we obtain a new h criterion which is sufficient for both cooperative output synchronization and bipartite output synchronization

approximating the jump discontinuities of a function by its fourier jacobi coefficients in the present paper we generalize eckhoff s method i e the method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its fourier chebyshev coefficients a new method enables us to approximate the locations of discontinuities and the associated jumps of a discontinuous function which belongs to a restricted class of the piecewise smooth functions by means of its fourier jacobi coefficients for arbitrary indices approximations to the locations of discontinuities and the associated jumps are found as solutions of algebraic equations it is shown as well that the locations of discontinuities and the associated jumps are recovered exactly for piecewise constant functions with a finite number of discontinuities in addition we study the accuracy of the approximations and present some numerical examples

zero forcing sets and controllability of dynamical systems defined on graphs in this technical note controllability of systems defined on graphs is discussed we consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph a one to one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established to illustrate the proposed results special cases including path cycle and complete graphs are discussed moreover as shown for graphs with a tree structure the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

persistent flows in deterministic chains this paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents an arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l 1 norm convergence of the infinite backward products to a rank one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states we discuss two balance conditions on the interactions between agents which generalize the arc balance and cut balance conditions in the literature respectively the proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant we prove that in both cases global consensus is reached if and only if the persistent graph which consists of all the persistent arcs contains a directed spanning tree the convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place the results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self confidence of the agents

distributed averaging with random network graphs and noises we consider a discrete time distributed averaging algorithm over multi agent networks with measurement noises and time varying random graphs each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises the network structure is modeled by a sequence of time varying random digraphs which may be spatially and temporally dependent by stochastic lyapunov method and the combination of algebraic graph theory and martingale convergence theory we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus we prove that all states of the agents converge to a common random variable whose mathematical expectation is the average of initial values in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected an upper bound of the variance of the limit random variable that is the mean square steady state error for stochastic average consensus is given quantitatively related to the weights the algorithm gain and the energy level of the noises

controllability of multiplex multi time scale networks the paradigm of layered networks is used to describe many real world systems from biological networks to social organizations and transportation systems while recently there has been much progress in understanding the general properties of multilayer networks our understanding of how to control such systems remains limited one fundamental aspect that makes this endeavor challenging is that each layer can operate at a different time scale thus we cannot directly apply standard ideas from structural control theory of individual networks here we address the problem of controlling multilayer and multi time scale networks focusing on two layer multiplex networks with one to one interlayer coupling we investigate the practically relevant case when the control signal is applied to the nodes of one layer we develop a theory based on disjoint path covers to determine the minimum number of inputs n i necessary for full control we show that if both layers operate on the same time scale then the network structure of both layers equally affect controllability in the presence of time scale separation controllability is enhanced if the controller interacts with the faster layer n i decreases as the time scale difference increases up to a critical time scale difference above which n i remains constant and is completely determined by the faster layer we show that the critical time scale difference is large if layer i is easy and layer ii is hard to control in isolation in contrast control becomes increasingly difficult if the controller interacts with the layer operating on the slower time scale and increasing time scale separation leads to increased n i again up to a critical value above which n i still depends on the structure of both layers this critical value is largely determined by the longest path in the faster layer that does not involve cycles by identifying the underlying mechanisms that connect time scale difference and controllability for a simplified model we provide crucial insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity

upper and lower bounds for controllable subspaces of networks of diffusively coupled agents this technical note studies the controllability of diffusively coupled networks where some agents called leaders are under the influence of external control inputs first we consider networks where agents have general linear dynamics then we turn our attention to infer network controllability from its underlying graph topology to do this we consider networks with agents having single integrator dynamics for such networks we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions respectively we also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders

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

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

a necessary and sufficient condition for consensus of continuous time agents over undirected time varying networks the average consensus problem of continuous time agents in undirected time varying networks is studied the network is allowed to be disconnected a notion called infinite integral connectivity is proposed based on the notion a necessary and sufficient condition for achieving consensus is given that is when the network topology is described by an undirected time varying graph g t the agents achieve consensus if and only if the infinite integral graph of g t over 0 is connected this criterion does not hold for directed networks

detection of edges in spectral data ii nonlinear enhancement we discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities where f x f x f x neq 0 our approach is based on two main aspects localization using appropriate concentration kernels and separation of scales by nonlinear enhancement to detect such edges one employs concentration kernels k epsilon cdot depending on the small scale epsilon it is shown that odd kernels properly scaled and admissible in the sense of having small w 1 infty moments of order cal o epsilon satisfy k epsilon f x f x cal o epsilon thus recovering both the location and amplitudes of all edges as an example we consider general concentration kernels of the form k sigma n t sum sigma k n sin kt to detect edges from the first 1 epsilon n spectral modes of piecewise smooth f s here we improve in generality and simplicity over our previous study in a gelb and e tadmor appl comput harmon anal 7 1999 pp 101 135 both periodic and nonperiodic spectral projections are considered we identify in particular a new family of exponential factors sigma exp cdot with superior localization properties the other aspect of our edge detection involves a nonlinear enhancement procedure which is based on separation of scales between the edges where k epsilon f x sim f x neq 0 and the smooth regions where k epsilon f cal o epsilon sim 0 numerical examples demonstrate that by coupling concentration kernels with nonlinear enhancement one arrives at effective edge detectors

strong structural controllability of systems on colored graphs this article deals with strong structural controllability of leader follower networks the system matrix defining the network dynamics is a pattern matrix in which a priori given entries are equal to zero while the remaining entries take nonzero values these nonzero entries correspond to edges in the network graph the network is called strongly structurally controllable if for all choices of real values for the nonzero entries in the pattern matrix the system is controllable in the classical sense the novelty of this article is that we consider the situation that prespecified nonzero entries in the system s pattern matrix are constrained to take identical nonzero values these constraints can be caused by symmetry properties or physical constraints on the network restricting the system matrices to those satisfying these constraints yields a new notion of strong structural controllability the aim of this article is to establish graph theoretic conditions for this more general property of strong structural controllability

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

zero forcing linear and quantum controllability for systems evolving on networks we study the dynamics of systems on networks from a linear algebraic perspective the control theoretic concept of controllability describes the set of states that can be reached for these systems our main result says that controllability in the quantum sense expressed by the lie algebra rank condition and controllability in the sense of linear systems expressed by the controllability matrix rank condition are equivalent conditions we also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property if a set of vertices is a zero forcing set the associated dynamical system is controllable these results open up the possibility of further exploiting the analogy between networks linear control systems theory and quantum systems lie algebraic theory this study is motivated by several quantum systems currently under study including continuous quantum walks modeling transport phenomena

tensor graphical lasso teralasso the paper introduces a multiway tensor generalization of the bigraphical lasso which uses a two way sparse kronecker sum multivariate normal model for the precision matrix to model parsimoniously conditional dependence relationships of matrix variate data based on the cartesian product of graphs we call this tensor graphical lasso generalization teralasso we demonstrate by using theory and examples that the teralasso model can be accurately and scalably estimated from very limited data samples of high dimensional variables with multiway co ordinates such as space time and replicates statistical consistency and statistical rates of convergence are established for both the bigraphical lasso and teralasso estimators of the precision matrix and estimators of its support non sparsity set respectively we propose a scalable composite gradient descent algorithm and analyse the computational convergence rate showing that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to the global minimizer of the teralasso objective function finally we illustrate teralasso by using both simulation and experimental data from a meteorological data set showing that we can accurately estimate precision matrices and recover meaningful conditional dependence graphs from high dimensional complex data sets

controllability of multiagent networks with antagonistic interactions this paper addresses the controllability of a class of antagonistic multiagent networks with both positive and negative edges all the agents of the multiagent network run a consensus algorithm using a signed laplacian based on the generalized equitable partition we propose a graph theoretic characterization of an upper bound on the controllable subspace then we provide a necessary condition for the controllability of the system and give an algorithm to compute the partition furthermore we prove that for a structurally balanced network the controllability is equivalent to that of the corresponding all positive network if the leaders are chosen from the same vertex set several examples are given to illustrate these results

convergence acceleration of modified fourier series in one or more dimensions modified fourier series have recently been introduced as an adjustment of classical fourier series for the approximation of nonperiodic functions defined on d variate cubes such approximations offer a number of advantages including uniform convergence however like fourier series the rate of convergence is typically slow in this paper we extend eckhoff s method to the convergence acceleration of multivariate modified fourier series by suitable augmentation of the approximation basis we demonstrate how to increase the convergence rate to an arbitrary algebraic order moreover we illustrate how numerical stability of the method can be improved by utilising appropriate auxiliary functions in the univariate setting it is known that eckhoff s method exhibits an auto correction phenomenon we extend this result to the multivariate case finally we demonstrate how a significant reduction in the number of approximation coefficients can be achieved by using a hyperbolic cross index set

regularity controllability observability of an nds with descriptor form subsystems and generalized lfts abstract this paper investigates regularity controllability and observability for a networked dynamic system nds with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional transformation glft of its parameters except a well posedness condition no any other constraints are put on either parameters or connections of a subsystem based on the kronecker canonical form kcf of a matrix pencil some matrix rank based necessary and sufficient conditions are established respectively for the regularity and complete controllability observability of the nds in which the associated matrix depends affinely on both subsystem parameters and subsystem connections these conditions keep the property that all the involved numerical computations are performed on each subsystem independently which is attractive in the analysis and synthesis of a large scale nds moreover some explicit and easily checkable requirements are derived for subsystem dynamics parameters with which a completely controllable observable nds can be constructed more easily

on discontinuous solutions of hyperbolic equations abstract a modified fourier method which is applicable to numerical simulations of discontinuous solutions of hyperbolic equations is presented truncated fourier series representations are de truncated at every timestep by utilising step functions in the reconstruction of the discontinuous solutions the de truncated expansions are used to eliminate the numerical dispersion and diffusion which normally ruin the discontinuous solutions in a few timesteps when traditional fourier methods are applied

systems of ordinary differential equations which generate an order preserving flow a survey of results this article consists of a survey of results concerning the qualitative behavior of solutions of systems of ordinary differential equations which generate an order preserving flow we restrict our consideration to partial orderings on r n induced by any one of its orthants a flow preserves ordering if any two solutions x t and y t are ordered x t leqq y t for all t 0 whenever x 0 leqq y 0 many of the important results for such systems have only recently been obtained principally by m w hirsch who pointed out the tendency of their solutions to converge to equilibrium less well known are some global geometric constraints on the stable manifold of an equilibrium and the existence of heteroclinic orbits connecting ordered equilibria a particularly striking result for this class of systems is the easily computable necessary and sufficient condition for stability of an equilibrium one of our main goals is to show that by allowing partial orderings on r n generated by orthants

acceleration of algebraically converging fourier series when the coefficients have series in powers of 1 n if the coefficients in a fourier cosine series f x f email protected n 0 a ncos nx decrease as a small negative power of n then one may need millions of terms to sum the series to high accuracy we show that if the a n are known analytically and have a power series in 1 n then it is straightforward to approximate f x as a series of what we shall the lanczos krylov lk functions we describe the similar methodology for sine series general fourier series are merely the sum of a cosine series with a sine series and thus are implicitly handled too for cosine coefficients that involve only even powers of n and sine coefficients that are functions of odd powers of n the lk functions may be expressed in terms of bernoulli polynomials the lk functions for cosine coefficients involving odd powers of n and for sine coefficients in even powers of n are not known explicitly these are also known as clausen functions we provide rapidly convergent series to compute these clausen functions to high accuracy our method includes the endpoint subtraction ideas of lanczos and krylov but is more general the sum n 1 1 n 1 1 email protected cos nx where l 0 is a constant arises in phase transitions in absorbed monolayers on metal surfaces it is easily summed by our method which correctly incorporates the logarithmic singularities at x email protected

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

delay independent asymptotic stability in monotone systems monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties it is known that under the property of quasimonotonicity time delayed systems become monotone and some remarkable properties have been reported for such systems these include for example the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays nevertheless extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity and it has been conjectured that these can be relaxed our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay independent stability in particular one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as t rightarrow infty then the system is globally asymptotically stable for arbitrary bounded time varying delays this follows from a more general result derived in the paper that allows to quantify delay independent regions of attraction which can be used to prove global asymptotic stability for various classes of systems these also recover various known delay independent stability results that are discussed within the paper

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

detecting discontinuity points from spectral data with the quotient difference qd algorithm this paper introduces a new technique for the localization of discontinuity points from spectral data through this work we will be able to detect discontinuity points of a 2 p periodic piecewise smooth function from its fourier coefficients this could be useful in detecting edges and reducing the effects of the gibbs phenomenon which appears near discontinuities and affects signal restitution our approach consists in moving from a discontinuity point detection problem to a pole detection problem then adapting the quotient difference qd algorithm in order to detect those discontinuity points

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

nonlinear second order multi agent systems subject to antagonistic interactions without velocity constraints abstract this paper studies the nonlinear second order multi agent systems without velocity information while subject to antagonistic interactions among the reciprocal agents when being free of nonlinear disturbances a necessary and sufficient condition for the consensus resp stability problem is presented which essentially shows that the coupling weights and topology structure suffice to assure the consensus resp stability of the agents whereas nonzero eigenvalues of the laplacian matrix also act a crucial role provided that merely the absolute information of the auxiliary variable is demanded the derived results implicitly manifest that structurally balanced graph resp isolated structurally balanced graph or containing the in isolated structurally balanced subgraph is merely the necessary condition for the consensus resp stability of the agents within the second order dynamical setting in the presence of nonlinear dynamics we explicitly extend the derived results with the help of the lyapunov based technique under quite mild assumptions furthermore some comparisons are presented in contrast to some of the existing literature finally numerical examples are given to validate the efficiency of the obtained results

controllability and observability of network of networks via cartesian products the paper presents a system theoretic analysis framework for a network of networks formed from smaller factor networks via graph cartesian products we provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network of networks we then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure an example demonstrating the usefulness of our results in the context of social networks with a cartesian product structure is then presented

accurate reconstructions of functions of finite regularity from truncated fourier series expansions kowledge of a truncated fourier series expansion for a 2 periodic function of finite regularity which is assumed to be piecewise smooth in each period is used to accurately reconstruct the corresponding function an algebraic equation of degree m is constructed for the m singularity locations in each period for the function in question the m coefficients in this algebraic equation are obtained by solving an algebraic system of m equations determined by the coefficients in the known truncated expansion if discontinuities in the derivatives of the function are considered in addition to discontinuities in the function itself that algebraic system will be nonlinear with respect to the m unknown coefficients the degree of the algebraic system will depend on the desired order of accuracy for the reconstruction i e a higher degree will normally lead to a more accurate determination of the singularity locations by solving an additional linear algebraic system for the jumps of the function and its derivatives up to the arbitrarily specified order at the calculated singularity locations we are able to reconstruct the 2 periodic function of finite regularity as the sum of a piecewise polynomial function and a function which is continuously differentiab1e up to the specified order

recent directions in matrix stability abstract matrix stability has been intensively investigated in the past two centuries we review work that has been done in this topic focusing on the great progress that has been achieved in the last decade or two we start with classical stability criteria of lyapunov routh and hurwitz and lienard and chipart we then study recently proven sufficient conditions for stability with particular emphasis on p matrices we investigate conditions for the existence of a stable scaling for a given matrix we review results on other types of matrix stability such as d stability additive d stability and lyapunov diagonal stability we discuss the weak principal submatrix rank property shared by lyapunov diagonally semistable matrices we also discuss the uniqueness of lyapunov scaling factors maximal lyapunov scaling factors cones of real positive semidefinite matrices and their applications to matrix stability and inertia preserving matrices

on the consensus and bipartite consensus in high order multi agent dynamical systems with antagonistic interactions abstract the aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents under the assumption that their mutual interactions can be described by a weighted signed connected and structurally balanced communication graph this amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative and hence represented by nonnegative weights while interactions between agents belonging to opposite groups are antagonistic and hence represented by nonpositive weights in this framework bipartite consensus can always be reached under the stabilizability assumption on the state space model describing the dynamics of each agent on the other hand nontrivial standard consensus may be achieved only under very demanding requirements both on the laplacian associated with the communication graph and on the agents description in particular consensus may be achieved only if there is a sort of equilibrium between the two groups both in terms of cardinality and in terms of the weights of the conflicting interactions amongst agents

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

a stability barrier for reconstructions from fourier samples we prove that any stable method for resolving the gibbs phenomenon that is recovering high order accuracy from the first m fourier coefficients of an analytic and nonperiodic function can converge at best root exponentially fast in m any method with faster convergence must also be unstable and in particular exponential convergence implies exponential ill conditioning this result is analogous to a recent theorem of platte trefethen and kuijlaars concerning recovery from pointwise function values on an equispaced m grid the main step in our proof is an estimate for the maximal behavior of a polynomial of degree n with bounded m term fourier series this estimate is related to a conjecture of hrycak and grochenig in the final part of the paper we discuss the implications of our main theorem to polynomial based interpolation and least squares approaches for overcoming the gibbs phenomenon

a criterion for exponential consensus of time varying non monotone nonlinear networks in this technical note we present new results on exponential consensus for continuous time nonlinear time varying networks a key feature in the following is that the monotonicity property is not required unlike most of existing literature on the subject moreover we give an estimate of the exponential rate of convergence towards the agreement manifold finally representative example and counterexample are given

on the reachability and observability of path and cycle graphs in this technical note we investigate the reachability and observability properties of a network system running a laplacian based average consensus algorithm when the communication graph is a path or a cycle specifically we provide necessary and sufficient conditions based on simple rules from number theory to characterize all and only the nodes from which the network system is reachable respectively observable interesting immediate corollaries of our results are i a path graph is reachable observable from any single node if and only if the number of nodes of the graph is a power of two n 2i i n and ii a cycle is reachable observable from any pair of nodes if and only if n is a prime number for any set of control observation nodes we provide a closed form expression for the unreachable unobservable eigenvalues and for the eigenvectors of the unreachable unobservable subsystem

on the resolution power of fourier extensions for oscillatory functions functions that are smooth but non periodic on a certain interval possess fourier series that lack uniform convergence and suffer from the gibbs phenomenon however they can be represented accurately by a fourier series that is periodic on a larger interval this is commonly called a fourier extension when constructed in a particular manner fourier extensions share many of the same features of a standard fourier series in particular one can compute fourier extensions which converge spectrally fast whenever the function is smooth and geometrically fast if the function is analytic much the same as the fourier series of a smooth analytic and periodic function with this in mind the purpose of this paper is to describe analyse and explain the observation that fourier extensions much like classical fourier series also have excellent resolution properties for representing oscillatory functions the resolution power or required number of degrees of freedom per wavelength depends on a user controlled parameter and as we show it varies between 2 and p the former value is optimal and is achieved by classical fourier series for periodic functions for example the latter value is the resolution power of algebraic polynomial approximations thus fourier extensions with an appropriate choice of parameter are eminently suitable for problems with moderate to high degrees of oscillation

uniform approximation of piecewise r smooth and globally continuous functions we study the uniform chebyshev approximation of continuous and piecewise r smooth r ge2 functions f 0 t to mathbb r with a finite number of singular points the approximation algorithms use only n function values at adaptively or nonadaptively chosen points we construct a nonadaptive algorithm mathcal a r n rm non that for the functions with at most one singular point enjoys the best possible convergence rate n r this is in sharp contrast to results concerning discontinuous functions for r ge3 this optimal rate of convergence holds only in the asymptotic sense i e it occurs only for sufficiently large n that depends on f in a way that is practically impossible to verify however it is enough to modify mathcal a r n rm non by using r 1 lfloor r 1 2 rfloor extra 1pt function evaluations to obtain an adaptive algorithm mathcal a r n rm ada with error satisfying f mathcal a r n rm ada f c le c rt r f r l infty n r for all n ge n 0 and n 0 independent of f this result cannot be achieved for functions with more than just one singular point however the convergence rate n r can be recovered asymptotically by a nonadaptive algorithm overline mathcal a r n rm non that is a slightly modified mathcal a r n rm non specifically limsup n to infty f overline mathcal a r n rm non f c cdot n r le c rt r f r l infty for all r smooth functions f with finitely many singular points

intrinsic reduced attitude formation with ring inter agent graph this paper investigates the reduced attitude formation control problem for a group of rigid body agents using feedback based on relative attitude information under both undirected and directed cyc

a robust k n 1 threshold proxy signature scheme based on factoring abstract proxy signature is an active cryptographic research area since mambo et al introduced the concept of proxy signature in 1996 many proxy signature schemes have been proposed however most of these previously proposed schemes are based on discrete logarithm problems in this paper we would like to propose a new robust k n 1 threshold proxy signature scheme based on factoring in this scheme generating a valid proxy signature needs not only any k or more members in n proxy signers but also a trusted dealer to cooperatively sign a message to our best knowledge this is the first k n 1 threshold proxy signature scheme based on factoring

how well does the hermite pade approximation smooth the gibbs phenomenon in order to reduce the gibbs phenomenon exhibited by the partial fourier sums of a periodic function f defined on discontinuous at 0 driscoll and fornberg considered so called singular fourier pade approximants constructed from the hermite pade approximants of the system of functions 1 g1 z g2 z where g1 z log 1 z and g2 z is analytic such that re g2 e it f t convincing numerical experiments have been obtained by these authors but no error estimates have been proven so far in the present paper we study the special case of nikishin systems and their hermite pade approximants both theoretically and numerically we obtain rates of convergence by using orthogonality properties of the functions involved along with results from logarithmic potential theory in particular we ad dress the question of how to choose the degrees of the approximants by considering diagonal and row sequences as well as linear hermite pade approximants our theoretical findings and numerical experiments confirm that these hermite pade approximants are more efficient than the more elementary pade approximants par ticularly around the discontinuity of the goal function f

reduction of the gibbs phenomenon for smooth functions with jumps by the e algorithm recently brezinski has proposed to use wynn s e algorithm in order to reduce the gibbs phenomenon for partial fourier sums of smooth functions with jumps by displaying very convincing numerical experiments in the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions and obtain the rate of column convergence for such functions possibly perturbed by another sufficiently differentiable function we also analyze the connection to pade fourier and pade chebyshev approximants including those recently studied by kaber and maday

on limits of powers of certain absolutely row stochastic matrices abstract we consider limits of powers of matrices that are absolutely row stochastic matrices a such that a is row stochastic we give graph theoretic criteria when such limits exist and if so determine their value in particular we show that for aperiodic connected matrices that satisfy opposition bipartiteness obipness a perron frobenius property holds here we call a obip also called structural balance in the literature when nodes in the graph corresponding to a can be partitioned into two groups such that within group links are non negative and across group links are non positive

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

some studies on nonpolynomial interpolation and error analysis abstract in this paper we propose nonpolynomial and hermite nonpolynomial interpolation with multiple parameters and present method to determine optimal value of parameters which generate minimum error in approximation the generalized error analysis results for nonpolynomial and hermite nonpolynomial interpolations are derived we establish theoretical relationship among nonpolynomial polynomial interpolation and the fourier series and propose solution to runge s phenomenon through nonpolynomial interpolation the hermite nonpolynomial cubic spline nonpolynomial cubic spline interpolation methods and their error analysis are presented numerical simulations are carried out for the analysis of error in cubic spline interpolations proposed method is applied to the analysis of various time series to show comparison in errors between polynomial and nonpolynomial spline interpolations and to empirical mode decomposition emd to illustrate practical usefulness of the results

observability and coarse graining of consensus dynamics through the external equitable partition using the intrinsic relationship between the external equitable partition eep and the spectral properties of the graph laplacian we characterize convergence and observability properties of consensus dynamics on networks in particular we establish the relationship between the original consensus dynamics and the associated consensus of the quotient graph under varied initial conditions and characterize the asymptotic convergence to the synchronization manifold under nonuniform input signals we also show that the eep with respect to a node can reveal nodes in the graph with an increased rate of asymptotic convergence to the consensus value as characterized by the second smallest eigenvalue of the quotient laplacian finally we show that the quotient graph preserves the observability properties of the full graph and how the inheritance by the quotient graph of particular aspects of the eigenstructure of the full laplacian underpins the observability and convergence properties of the system

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

convergence analysis of directed signed networks via an m matrix approach abstractthis paper aims at solving convergence problems on directed signed networks with multiple nodes where interactions among nodes are described by signed digraphs the convergence analysis is

approximation of the discontinuities of a function by its classical orthogonal polynomial fourier coefficients in the present paper we generalize the method suggested in an earlier paper by the author and overcome its main deficiency first we modify the well known prony method which subsequently will be utilized for recovering exactly the locations of jump discontinuities and the associated jumps of a piecewise constant function by means of its fourier coefficients with respect to any system of the classical orthogonal polynomials next we will show that the method is applicable to a wider class of functions namely to the class of piecewise smooth functions for functions which piecewise belong to c 2 1 1 the locations of discontinuities are approximated to within o 1 n by means of their fourier jacobi coefficients unlike the previous one the generalized method is robust since its success is independent of whether or not a location of the discontinuity coincides with a root of a classical orthogonal polynomial in addition the error estimate is uniform for any c d c 1 1 to the end we discuss the accuracy stability and complexity of the method and present numerical examples

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

controllability of multi agent systems with directed and weighted signed networks abstract this paper studies the controllability of multi agent systems with signed networks which are represented by directed weighted signed graphs the adjacency weights of network depict the property of interactions positive weight means cooperative interaction while negative weight antagonistic interaction first by using switching equivalent transformation the controllability of three kinds of signed networks is studied structurally balanced anti balanced and strictly unbalanced it is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network then a graph theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks furthermore some necessary and sufficient conditions are given for the controllability of generic linear multi agent systems in addition several examples are presented to illustrate the theoretical results

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

multivariate modified fourier series and application to boundary value problems in this paper we analyse the approximation theoretic properties of modified fourier series in cartesian product domains with coefficients from both full and hyperbolic cross index sets we show that the number of expansion coefficients may be reduced significantly whilst retaining comparable error estimates in doing so we extend the univariate results of iserles norsett and s olver we then demonstrate that these series can be used in the spectral galerkin approximation of second order neumann boundary value problems which offers some advantages over standard chebyshev or legendre polynomial discretizations

continuous time consensus under persistent connectivity and slow divergence of reciprocal interaction weights in this paper we present new results on consensus for continuous time multiagent systems we introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete time consensus protocols slow divergence of reciprocal interaction weights generalizes the assumption of cut balanced interactions we show that under these two assumptions the continuous time consensus protocol succeeds the states of all the agents converge asymptotically to a common value moreover our proof allows us to give an estimate of the rate of convergence towards the consensus we also provide examples that make us think that both of our assumptions are tight

a simple algorithm for the stable unstable decomposition of a linear discrete time system a simple algorithm that decomposes the dynamics of a linear discrete time system into stable modes unstable modes and those on the unit circle is considered here the relationship between such a decomposition and the stable unstable decomposition of continuous time systems is also established

a class of uncontrollable diffusively coupled multiagent systems with multichain topologies we construct systematically a class of uncontrollable diffusively coupled multiagent systems with a single leader and multichain topologies for studying the controllability of diffusively coupled multiagent systems such identified uncontrollable systems serve as counterexamples that prove the need to modify the existing sufficient condition using graph partitioning characterization the uncontrollability of the constructed multichain structures can be preserved when the structures are further augmented to get better connected the paper also provides an algorithm to obtain the minimal leader invariant relaxed equitable partition for the graph associated with any diffusively coupled multiagent system guided by a single leader

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed

the evolution of beliefs over signed social networks we study the evolution of opinions or beliefs over a social network modeled as a signed graph the sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends positive links or enemies negative links pairs of nodes are randomly selected to interact over time and when two nodes interact each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link this model generalizes the degroot model to account for negative links when two adversaries interact their opinions go in opposite directions we provide conditions for convergence and divergence in expectation in mean square and in almost sure sense and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph we establish a no survivor theorem stating that the difference in opinions of any two nodes diverges whenever opinions in the network diverge as a whole we also prove a live or die lemma indicating that almost surely the opinions either converge to an agreement or diverge finally we extend our analysis to cases where opinions have hard lower and upper limits in these cases we study when and how opinions may become asymptotically clustered to the belief boundaries and highlight the crucial influence of strong or weak structural balance of the underlying network on this clustering phenomenon

stability criteria for matrices in this paper we study the stability of matrices using technologies of special matrices analysis several simple criteria for the stability for the matrix a aij cn n which is not diagonally dominant are obtained by aid of simple algebraic conditions of aij only