brief paper distributed containment control for lagrangian networks with parametric uncertainties under a directed graph in this paper we study the distributed containment control problem for networked lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers we propose a distributed adaptive control algorithm combined with distributed sliding mode estimators a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically as a byproduct we show a necessary and sufficient condition on leaderless consensus for networked lagrangian systems under a directed graph numerical simulation results are given to show the effectiveness of the proposed control algorithms

power law subordinacy and singular spectra i half line operators we study hausdorff dimensional spectral properties of certain whole line quasiperiodic discrete schrodinger operators by using the extension of the gilbert pearson subordinacy theory that we previously developed in 19

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

two dimensional linear prediction and its application to adaptive predictive coding of images this paper summarizes a study on two dimensional linear prediction of images and its application to adaptive predictive coding of monochrome images the study was focused on three major areas two dimensional linear prediction of images and its performance implementation of an adaptive predictor and adaptive quantizer for use in image coding and linear prediction and adaptive predictive coding of density logarithm of intensity images among the issues investigated are autoregressive modeling of 2 d image sequences estimation of the nonzero average bias of the image samples stability of the inverse prediction error filter and estimation of the parameters of a 2 d separable linear predictor the implementation of the adaptive predictor is based on the results of linear predictive analysis the adaptive quantization of the prediction error signal is done by using a flexible three level quantizer for code words of fixed or variable length the above ideas are further applied to density images for exploiting the multiplicative structure of images the results of this research indicate that by using adaptive prediction and quantization intensity and density coded images of high quality can be obtained at information rates as low as 0 7 bits pixel

asymptotic behavior of orthogonal polynomials without the carleman condition abstract our goal is to find an asymptotic behavior as n of orthogonal polynomials p n z defined by the jacobi recurrence coefficients a n b n we suppose that the off diagonal coefficients a n grow so rapidly that the series a n 1 converges that is the carleman condition is violated with respect to diagonal coefficients b n we assume that b n a n a n 1 1 2 2 for some 1 the asymptotic formulas obtained for p n z are quite different from the case a n 1 when the carleman condition is satisfied in particular if a n 1 then the phase factors in these formulas do not depend on the spectral parameter z c the asymptotic formulas obtained in the cases 1 and 1 are also qualitatively different from each other as an application of these results we find necessary and sufficient conditions for the essential self adjointness of the corresponding minimal jacobi operator

the asep and determinantal point processes we introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line with correlation kernels defined via spectral projections for the associated jacobi matrices for classical weights we show how such ensembles arise as limits of various hypergeometric orthogonal polynomial ensembles we then prove that the q laplace transform of the height function of the asep with step initial condition is equal to the expectation of a simple multiplicative functional on a discrete laguerre ensemble a member of the new family this allows us to obtain the large time asymptotics of the asep in three limit regimes a for finitely many rightmost particles b gue tracy widom asymptotics of the height function c kpz asymptotics of the height function for the asep with weak asymmetry we also give similar results for two instances of the stochastic six vertex model in a quadrant the proofs are based on limit transitions for the corresponding determinantal point processes

brief paper target containment control of multi agent systems with random switching interconnection topologies in this paper the distributed containment control is considered for a second order multi agent system guided by multiple leaders with random switching topologies the multi leader control problem is investigated via a combination of convex analysis and stochastic process the interaction topology between agents is described by a continuous time irreducible markov chain a necessary and sufficient condition is obtained to make all the mobile agents almost surely asymptotically converge to the static convex leader set moreover conditions on the tracking estimation are provided for the convex target set determined by moving multiple leaders

distributed adaptive coordination for multiple lagrangian systems under a directed graph without using neighbors velocity information in this paper we study the distributed coordination problem for multiple lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors velocity information in the absence of communication we consider two cases namely the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem in both cases distributed adaptive control algorithms without using neighbors velocity information are proposed the control gains in the algorithms are varying with distributed updating laws furthermore necessary and sufficient conditions on the directed graph are presented respectively such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem finally simulation examples are provided to show the effectiveness of the proposed control algorithms

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

bounded rank one perturbations in sampling theory sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points in this paper we derive an orthogonal sampling theory and associated lagrange interpolation formulae from a family of bounded rank one perturbations of a self adjoint operator that has only discrete spectrum of multiplicity one

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

asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients abstract we study solutions of three term recurrence relations whose n step transfer matrices belong to the uniform stolz class in particular we derive the first order of their uniform asymptotics for orthonormal polynomials we show more namely we find the constructive formula for the density of their orthogonality measure in terms of turan determinants and we determine their exact asymptotic behavior we treat both bounded and unbounded cases in a unified way

interval bipartite consensus of networked agents associated with signed digraphs this paper solves consensus problems for networked agents whose interactions with each other are described by signed digraphs the laplacian matrix of a signed digraph is studied by introducing rooted cycles and the relationship between it and the spanning tree condition is addressed in particular the laplacian matrix of a signed digraph with spanning trees is positive stable if and only if there is at least one negative rooted cycle otherwise it has exactly one zero eigenvalue if and only if either there exist no rooted cycles or all existing rooted cycles are positive it is shown that all agents reach interval bipartite consensus if their associated signed digraph has a spanning tree further the consensus values of all agents depend only on the initial states of those agents which are associated with root vertices the developed consensus results are applicable for multi agent systems with both continuous time and discrete time dynamics illustrative examples are provided to demonstrate interval bipartite consensus performances for multi agent systems associated with different signed digraphs which all contain spanning trees but are not strongly connected

a fuzzy logic based predictor for predictive coding of images in this paper we present a fuzzy logic based nonlinear predictor for predictive coding of images we define five local structure patterns of images uniform area horizontal contour 0 spl deg vertical contour 90 spl deg 45 spl deg and 135 spl deg diagonal contours their membership functions are derived with the gradient based edge detection method and predicted values for different patterns are defined by linear extrapolation from available neighborhood pixel values the predicted value of the current pixel can be obtained based on the membership functions and the defined predicted values for the different patterns a set of parameters to characterize the proposed fuzzy predictor are determined from empirical data success in the use of the proposed predictor is demonstrated by using simulation results through the reduction in the entropy as compared to those of existing linear and nonlinear ones it is also shown that the proposed fuzzy predictor can be efficiently implemented

containment control of continuous time linear multi agent systems with aperiodic sampling in this paper the containment control problem of continuous time linear multi agent systems is investigated an aperiodic sampled data based protocol is induced by using neighboring information with uncertainly time varying sampling intervals by utilizing the proposed protocol and properties of laplacian matrix the containment control problem of continuous time linear multi agent systems is equivalently transformed into a stability problem of discrete time linear systems the stability analysis is based on the robustness of related discrete time systems against perturbation caused by the variation of sampling intervals by using small gain theorem sufficient conditions are obtained to guarantee the stability of uncertain discrete time systems furthermore two special cases are given to illustrate the method proposed in this paper the theoretical results are verified by some simulations

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

bipartite containment tracking of signed networks abstract this paper considers a class of bipartite containment tracking problems for leader following networks associated with signed digraphs it admits multiple leaders which can be not only stationary but also dynamically changing via interactions between them and their neighbored leaders it is shown that the followers can converge to the convex hull containing each leader s trajectory as well as its symmetric trajectory which is the same as it in modulus but different in sign in particular if the adjacency weight matrix of the digraph is not signed but nonnegative then the leader following network achieves the traditional containment tracking simulation tests are performed to illustrate the observed bipartite containment tracking performances of signed networks

leader follower containment control over directed random graphs the leader follower consensus problem for multi agent systems over directed random graphs is investigated motivated by the fact that inter agent communication can be subject to random failure when agents perform tasks in a complex environment a directed random graph is used to model the random loss of communication between agents where the connection of the directed edge in the graph is assumed to be probabilistic and evolves according to a two state markov model in the leader follower network the leaders maintain a constant desired state and the followers update their states by communicating with local neighbors over the random communication network based on convex properties and a stochastic version of lasalle s invariance principle almost sure convergence of the followers states to the convex hull spanned by the leaders states is established for the leader follower random network a numerical simulation is provided to demonstrate the developed result

fuzzy logic based matching pursuits for lossless predictive coding of still images this paper presents an application of fuzzy logic techniques to the reversible compression of grayscale images with reference to a spatial differential pulse code modulation dpcm scheme prediction may be accomplished in a space varying fashion either as adaptive i e with predictors recalculated at each pixel or as classified in which image blocks or pixels are labeled in a number of classes for which fitting predictors are calculated here an original tradeoff is proposed a space varying linear regression prediction is obtained through fuzzy logic techniques as a problem of matching pursuit in which a predictor different for every pixel is obtained as an expansion in series of a finite number of prototype nonorthogonal predictors that are calculated in a fuzzy fashion as well to enhance entropy coding the spatial prediction is followed by context based statistical modeling of prediction errors a thorough comparison with the most advanced methods in the literature as well as an investigation of performance trends and computing times to work parameters highlight the advantages of the proposed fuzzy approach to data compression

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

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

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

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

jacobi matrices with power like weights grouping in blocks approach the paper deals with jacobi matrices with weights k given by k k 1 k where 12 1 and limk k 0 the main question studied here concerns when the spectrum of the operator j defined by the jacobi matrix has absolutely continuous component covering the real line a sufficient condition is given for a positive answer to the above question the method used in the paper is based on a detailed analysis of generalized eigenvectors of j in turn this analysis relies on the so called grouping in blocks approach to a large product of the transfer matrices associated to j

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