consensus in ad hoc wsns with noisy links part i distributed estimation of deterministic signals we deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks wsns we cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation different from existing alternatives our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages thus allowing for decentralized computation even of nonlinear estimators including maximum likelihood estimators mle in nonlinear and non gaussian data models we prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal furthermore our decentralized algorithms exhibit resilience in the presence of receiver and or quantization noise in particular we introduce a decentralized scheme for least squares and best linear unbiased estimation blue and establish its convergence in the presence of communication noise our algorithms also exhibit potential for higher convergence rate with respect to existing schemes corroborating simulations demonstrate the merits of the novel distributed estimation algorithms

solving a modified consensus problem of linear multi agent systems a distributed protocol is proposed for a modified consensus problem of a network of agents that have the same continuous time linear dynamics each agent estimates its own state using its output information and then sends the estimated state to its neighbor agents for the purpose of reaching a consensus the modified consensus problem requires the group decision value to be a linear function of initial states and initial estimated states of all agents in the network and the transformation matrix associated with this linear function not to be a zero matrix it is proved that under the proposed control protocol the modified consensus problem can be solved if and only if the system matrices of the agent s dynamics are stabilizable and detectable the input matrix is not a zero matrix and the communication topology graph has a spanning tree the proposed protocol can also be extended to multi agent systems where agents are described by discrete time linear dynamics the corresponding necessary and sufficient conditions are provided as well

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

weighted composition operators from the logarithmic weighted type space to the weighted bergman space in cn let w be a bounded circular strictly convex domain in c n with c 2 boundary and h w the space of all analytic functions on w let u h w and f be a holomorphic self map of w the weighted composition operator uc f on h w is defined by uc f f z u z f f z where f h w and z w let h l o g c b w b 0 c r be the logarithmic weighted type space on w and a a p w p 0 a 1 the weighted bergman space on w here we characterize the boundedness and compactness of the weighted composition operator uc f h l o g c b w a a p w

distributed average consensus with dithered quantization in this paper we develop algorithms for distributed computation of averages of the node data over networks with bandwidth power constraints or large volumes of data distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted we propose a distributed algorithm in which the nodes utilize probabilistically quantized information i e dithered quantization to communicate with each other the algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely in addition we show that the expected value of the consensus is equal to the average of the original sensor data we derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging pqda moreover we show that the convergence of the pqda is monotonic by studying the evolution of the minimum length interval containing the node values we reveal that the length of this interval is a monotonically nonincreasing function with limit zero we also demonstrate that all the node values in the worst case converge to the final two quantization bins at the same rate as standard unquantized consensus finally we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios

a stopping rule for stochastic approximation a stochastic approximation algorithm is a recursive procedure to find the solution to an unknown nonlinear equation via noisy measurements in this paper we present a stopping rule for a stochastic approximation we show that there is a high probability that the distance between the exact solution and the candidate solution is less than a specified tolerance level when the stochastic approximation stops according to our stopping rule furthermore the number of recursions required by the stopping rule is a polynomial function of the problem size

distributed parameter estimation over unreliable networks with markovian switching topologies due to the existence of various uncertainties the design of distributed estimation algorithms with robustness and high accuracy is an urgent demand for sensor network applications this paper is aimed at investigating the design of distributed parameter estimation algorithms and the analysis of their convergence properties in uncertain sensing and communication environments consensus based distributed parameter estimation algorithms for both discrete time and continuous time cases are established which are suitable for unreliable communication networks with stochastic communication noises random link gains and markovian signal losses under mild conditions on stochastic noises gain function and topology switching markov chain we establish both the mean square and almost sure convergence of the designed algorithms by use of probability limit theory algebraic graph theory stochastic differential equation theory and markov chain theory the effect of sensor dependent gain functions on the convergence of the algorithm is also analyzed

nash social and centralized solutions to consensus problems via mean field control theory the purpose of this paper is to synthesize initial mean consensus behavior of a set of agents from the fundamental optimization principles of i stochastic dynamic games and ii optimal control in the stochastic dynamic game model each agent seeks to minimize its individual quadratic discounted cost function involving the mean of the states of all other agents in this formulation we derive the limiting infinite population mean field equation system and explicitly compute its unique solution the resulting mean field mf control strategies drive each agent to track the overall population s initial state distribution mean and by applying these decentralized strategies any finite population system reaches mean consensus asymptotically as time goes to infinity furthermore these control laws possess an en nash equilibrium property where en goes to zero as the population size n goes to infinity finally the analysis is extended to the case of random mean field couplings in the social cooperative formulation the basic objective is to minimize a social cost as the sum of the individual cost functions containing mean field coupling in this formulation we show that for any individual agent the decentralized mean field social mf social control strategy is the same as the mean field nash mf nash equilibrium strategy hence mf nash controls unashn mf social controls usocn on the other hand the solution to the centralized lqr optimal control formulation yields the standard consensus sc algorithm whenever the graph representing the corresponding topology of the network is completely connected cc hence cent lqr controls ucentn sc cc controls uscn moreover a system with centralized control laws reaches consensus on the initial state distribution mean as time and population size n go to infinity hence asymptotically in time mf nash controls unashn mf social controls usocn cent lqr controls ucent sc cc controls usc finally the analysis is extended to the long time average lta cost functions case

continuous inclusions and bergman type operators in n harmonic mixed norm spaces on the polydisc abstract we study anisotropic mixed norm spaces of n harmonic functions in the unit polydisc of c n bergman type reproducing integral formulas are established by means of fractional derivatives and some continuous inclusions it gives us a tool to construct corresponding projections and related operators and prove their boundedness on the mixed norm and besov spaces

norm and essential norm of composition followed by differentiation from α bloch spaces to hμ abstract this note calculates the norm of composition followed by differentiation operator from the bloch and the little bloch space to the weighted space h on the unit disk and gives an upper and a lower bound for the essential norm of the operator from the bloch space b 0 to h

weighted consensus protocols design based on network centrality for multi agent systems with sampled data this technical note aims at constructing and analyzing an efficient framework for the leader following consensus protocol in multi agent systems mass we propose two novel consensus protocols weighted by calculating the betweenness and eigenvector centralities for agent and link which are determined by the interconnection structure of mass the concepts of centrality were introduced in the field of social science ultimately the use of the proposed protocols can be described with regard to not only the number of each agent s neighbors which was utilized in the existing works but also more information about agents through considering two such centralities by utilizing the lyapunov method and some mathematical techniques the leader following guaranteed cost consensus conditions for mass with the proposed protocols and sampled data will be established in terms of linear matrix inequalities lmis based on the result of consensus criteria two new protocol design methods which utilize the betweenness and eigenvector centralities will be proposed finally some simulation results are given to illustrate the advantages of the proposed protocols in point of the robustness on sampling interval and the transient consensus performance

average consensus with packet drop communication average consensus consists in the problem of determining the average of some quantities by means of a distributed algorithm it is a simple instance of problems arising when designing estimation algorithms operating on data produced by sensor networks simple solutions based on linear estimation algorithms have already been proposed in the literature and their performance has been analyzed in detail if the communication links which allow the data exchange between the sensors have some loss then the estimation performance will degrade in this contribution the performance degradation due to this data loss is evaluated

consensus seeking over markovian switching networks with time varying delays and uncertain topologies stochastic consensus problems for linear time invariant multi agent systems over markovian switching networks with time varying delays and topology uncertainties are dealt with by using the linear matrix inequality method and the stability theory of markovian jump linear system we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the markov process provided the union of topologies associated with the positive recurrent states of the markov process admits a spanning tree and the agent dynamics is stabilizable feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying delays numerical examples are given to show the feasibility of theoretical results

riemann hilbert approach to a generalised sine kernel and applications we investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval q q we determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its fredholm determinant further we apply our results to build the resolvent of truncated wiener hopf operators generated by holomorphic symbols finally the leading asymptotics of the fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models

norm of some operators from logarithmic bloch type spaces to weighted type spaces abstract operator norm of weighted composition operators from the iterated logarithmic bloch space b log k k n or the logarithmic bloch type space b log 0 1 to weighted type spaces on the unit ball are calculated it is also calculated norm of the product of differentiation and composition operators among these spaces on the unit disk

norms of some operators on bounded symmetric domains let d be a bounded symmetric domain h d the class of all holomorphic functions on d and u h d operator norm of the multiplication operator on the weighted bergman space a a p d as well as of weighted composition operator from a a p d to a weighted type space are calculated

stochastic consentability of linear systems with time delays and multiplicative noises this paper develops stochastic consentability of linear multiagent systems with time delays and multiplicative noises first the stochastic stability for stochastic differential delay equations driven by multiplicative noises is examined and the existence of the positive definite solution for a class of generalized algebraic riccati equations gares is established then sufficient conditions are deduced for the mean square and almost sure consentability and stabilization based on the developed stochastic stability and gares consensus protocols are designed for linear multiagent systems with undirected and leader following topologies it is revealed that multiagent consentability depends on certain characterizing system parameters including linear system dynamics communication graph channel uncertainties and time delay of the deterministic term it is shown that a second order integrator multiagent system is unconditionally mean square and almost surely consentable for any given noise intensities and time delay and that the mean square and almost sure consensus can be achieved by carefully choosing the control gain according to certain explicit conditions

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

distributed cooperative adaptive identification and control for a group of continuous time systems with a cooperative pe condition via consensus in this paper we first address the uniformly exponential stability ues problem of a group of distributed cooperative adaptive systems in a general framework inspired by consensus theory distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems it is shown that not only is the entire closed loop system stable but also both the identification tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation pe condition of a regressor matrix in each system which is weaker than the traditionally defined pe condition the effects of network topology on ues of the closed loop system are also explored if the topology is time invariant it needs to be undirected and connected however when the topology is time varying it is just required that the integration of the topology over an interval with fixed length is undirected and connected the established results are then employed to identify and control several classes of linearly parameterized systems simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws

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

necessary and sufficient conditions for consensus of double integrator multi agent systems with measurement noises an average consensus protocol is proposed for continuous time double integrator multi agent systems with measurement noises under fixed topologies the time varying control gain is employed to attenuate noises the closed loop system is therefore a time varying linear stochastic differential equation by determining the state transition matrix of this closed loop system the dynamic characteristics of the multi agent system can be fully described it is proved that in the noisy communication environment the average consensus can be achieved if and only if the communication topology is a balanced and strongly connected graph and the time varying control gain satisfies the stochastic approximation type conditions under the proposed protocol the position of each agent is convergent in mean square to a common random variable whose mathematical expectation is the average of initial positions and initial velocities of all agents in the system while each agent s velocity is convergent in mean square to a common random variable whose mathematical expectation and variance are both zero

mitigation of complex behavior over networked systems analysis of spatially invariant structures in this paper we consider a simple distributed averaging system which incorporates various communication constraints including delays noise and link failures it has been shown in wang and elia 2012 that such networked system generates a collective levy flight behavior when part of the system loses mean square ms stability we focus on spatially invariant architectures to gain more insights into how model parameters affect emergence of this complex scale invariant behavior and to seek structures robust to communication constraints specifically we develop a computational expression for checking ms stability which is scalable with the number of unreliable links we derive the closed form formulas from this expression in the limiting case of zero and large delays and in the case of large number of nodes in the limit of large delays we derive various results that are independent of the network size and its specific interconnections we find that small inter agent coupling improves the robustness of the system networks with larger connectivity tend to be more fragile in the presence of fading connections for fixed inter agent coupling that gossiping improves the robustness and that the lattice is the most robust among the spatially invariant systems with generalized circulant interconnections

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

stochastic consensus over noisy networks with markovian and arbitrary switches this paper considers stochastic consensus problems over lossy wireless networks we first propose a measurement model with a random link gain additive noise and markovian lossy signal reception which captures uncertain operational conditions of practical networks for consensus seeking we apply stochastic approximation and derive a markovian mode dependent recursive algorithm mean square and almost sure i e probability one convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition subsequently we consider a model with arbitrary random switching and a common stochastic lyapunov function technique is used to prove convergence finally our method is applied to models with heterogeneous quantizers and packet losses and convergence results are proved

multi consensus of multi agent networks via a rectangular impulsive approach abstract a multi consensus problem is studied in multi agent networks the interaction mechanism of competition abstention cooperation among agents is introduced three rectangular impulsive protocols are proposed to solve multi consensus of second order multi agent networks with a directed topology these algorithms have the performance of dirac impulsive control and discrete time control necessary and sufficient conditions are obtained for the stationary multi consensus and the dynamic multi consensus numerical examples are provided to illustrate the effectiveness of the obtained criteria

products of volterra type operator and composition operator from h and bloch spaces to zygmund spaces the boundedness and compactness of the products of volterra type operators and composition operators from the space of bounded analytic functions and the bloch space to the zygmund space are discussed in this paper

compact differences of weighted composition operators from weighted bergman spaces to weighted type spaces abstract we characterize the compactness of differences of weighted composition operators from the weighted bergman space a p 0 1 to the weighted type space h v of analytic functions on the open unit disk d in terms of inducing symbols 1 2 d d and u 1 u 2 d c for the case 1

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

on a new integral type operator from the bloch space to bloch type spaces on the unit ball abstract we introduce the following integral type operator on the space h b of all holomorphic functions on the unit ball b c n p g f z 0 1 f t z g t z d t t z b where g h b g 0 0 and is a holomorphic self map of b the boundedness and compactness of the operator from the bloch space b or the little bloch space b 0 to the bloch type space b or the little bloch type space b 0 are characterized in the main results we calculate the essential norm of the operators p g b or b 0 b or b 0 in an elegant way

sampled data discrete time coordination algorithms for double integrator dynamics under dynamic directed interaction in this article we study two sampled data based discrete time coordination algorithms for multi vehicle systems with double integrator dynamics under dynamic directed interaction for both algorithms we derive sufficient conditions on the interaction graph the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices when the conditions on the damping gain and the sampling period are satisfied the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval simulation results are presented to show the effectiveness of the theoretical results

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

asymptotic properties of consensus type algorithms for networked systems with regime switching topologies this paper is concerned with asymptotic properties of consensus type algorithms for networked systems whose topologies switch randomly the regime switching process is modeled as a discrete time markov chain with a finite state space the consensus control is achieved by using stochastic approximation methods in the setup the regime switching process the markov chain contains a rate parameter e 0 in the transition probability matrix that characterizes how frequently the topology switches on the other hand the consensus control algorithm uses a stepsize m that defines how fast the network states are updated depending on their relative values three distinct scenarios emerge under suitable conditions we show that when 0 e o m a continuous time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous time markov chain in this case a scaled sequence of tracking errors converges to a system of switching diffusion when 0 email protected email protected the network topology is almost non switching during consensus control transient intervals and hence the limit dynamic system is simply an autonomous differential equation when email protected email protected the markov chain acts as a fast varying noise and only its averaged network matrices are relevant resulting in a limit differential equation that is an average with respect to the stationary measure of the markov chain simulation results are presented to demonstrate these findings

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

almost certain convergence in double arrays for double arrays of constants ani 1 i k n n 1 and i i d random variables x x i i 1 conditions are given under which the row sums sum limits i 1 k n a ni x i xrightarrow text a text c text 0 both cases k n and k n are treated in general the hypotheses involve a trade off between moment requirements on x and the magnitude of the itani a marcinkiewicz zygmund type strong law is obtained for the special case a ni a i mathord left vphantom a i left sum limits j 1 n a j p right 1 p right kern nulldelimiterspace left sum limits j 1 n a j p right 1 p a i 0 text sum limits text 1 n a j p to infty text 0 p 2

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

sampled data based average consensus of second order integral multi agent systems switching topologies and communication noises a distributed sampled data based protocol is proposed for the average consensus of second order integral multi agent systems under switching topologies and communication noises under the proposed protocol it is proved that sufficient conditions for ensuring mean square average consensus are the consensus gain satisfies the stochastic approximation type condition and the communication topology graph at each sampling instant is a balanced graph with a spanning tree moreover if the consensus gain takes some particular forms the proposed protocol can solve the almost sure average consensus problem as well compared with the previous work the distinguished features of this paper lie in that 1 a sampled data based stochastic approximation type protocol is proposed for the consensus of second order integral multi agent systems 2 both communication noises and switching topologies are simultaneously considered and 3 average consensus can be reached not only in the mean square sense but also in the almost sure sense c 2013 elsevier ltd all rights reserved

weighted composition operators from weighted bergman spaces to weighted type spaces on the unit ball we calculate the operator norm of the weighted composition operator from a weighted bergman space to a weighted type space on the unit ball of c n we also characterize the compactness of the operator

stochastic approximation approach for consensus and convergence rate analysis of multiagent systems in this note we study the consensus problem for multiagent systems with measurement noises different from the existing approach the consensus problem is converted to a root finding problem for which the stochastic approximation theory can be applied by choosing an appropriate regression function we propose a consensus algorithm which is applicable to systems with more general measurement noise processes including stationary autoregressive and moving average arma processes and infinite moving average ma processes further we establish a relationship between the convergence rate and the exponent of the step size of the algorithm particularly strong convergence rate for systems with a leader follower topology is studied

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

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

weighted composition operators between fock type spaces in cn motivated by quite recent results by ueki 22 the boundedness and compactness of the weighted composition operators acting between some fock type spaces in c n are characterized we also study weighted composition operators on little weighted fock type spaces norm of some of these operators is calculated in some cases we give some estimates for the essential norm of some of these operators

counting free fermions on a line a fisher hartwig asymptotic expansion for the toeplitz determinant in the double scaling limit we derive an asymptotic expansion for a wiener hopf determinant arising in the problem of counting one dimensional free fermions on a line segment at zero temperature this expansion is an extension of the result in the theory of toeplitz and wiener hopf determinants known as the generalized fisher hartwig conjecture the coefficients of this expansion are conjectured to obey certain periodicity relations which renders the expansion explicitly periodic in the counting parameter we present two methods to calculate these coefficients and verify the periodicity relations order by order the matrix riemann hilbert problem and the painleve v equation we show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

structural modeling and convergence analysis of consensus based time synchronization algorithms over networks this paper raises a quite general problem how to characterize necessary conditions of bounded convergence namely the divergence conditions of a consensus based time synchronization cbts algorithm over a network with random communication delays we firstly present a unified structural model of cbts algorithms then we fit different cbts algorithms such as dcts ats wmts and lsts into the same structural model with just different algorithm parameters to characterize divergence conditions we focus on the algorithm structure and algorithm parameters rather than the topology graph of the network by studying the asymptotic property of the relative drift estimation error of cbts algorithms we discover almost sure divergence conditions and mean square divergence conditions of cbts algorithms using these conditions we clearly point out that the dcts algorithm is divergent the ats algorithm is divergent almost surely the wmts algorithm is mean square divergent but the lsts overcomes all of these divergence conditions the results of this paper provide a fundamental guideline for designing future time synchronization algorithms

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

consensus seeking in multi agent systems with multiplicative measurement noises abstract in this paper the consensus problems of the continuous time integrator systems under noisy measurements are considered the measurement noises which appear when agents measure their neighbors states are modeled to be multiplicative by multiplication of the noises here the noise intensities are proportional to the absolute value of the relative states of an agent and its neighbor by using known distributed protocols for integrator agent systems the closed loop system is described in the vector form by a singular stochastic differential equation for the fixed and switching network topology cases constant consensus gains are properly selected such that mean square consensus and strong consensus can be achieved especially exponential mean square convergence of agents states to the common value is derived for the fixed topology case in addition asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied simulations shed light on the effectiveness of the proposed theoretical results

the riemann hilbert problem associated with the quantum nonlinear schrodinger equation we consider the dynamical correlation functions of the quantum nonlinear schrodinger equation in a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator valued fredholm determinant in this paper we show that a riemann hilbert problem can be associated with this fredholm determinant this riemann hilbert problem formulation permits us to write down completely integrable equations for the fredholm determinant and to perform an asymptotic analysis for the correlation function

distributed stochastic approximation algorithm with expanding truncations in this paper a novel distributed stochastic approximation algorithm dsaa is proposed to seek roots of the sum of local functions each of which is associated with an agent from multiple agents connected over a network at each iteration each agent updates its estimate for the root utilizing the noisy observations of its local function and the information derived from the neighboring agents the key difference of the proposed algorithm from the existing ones consists in the expanding truncations so it is called the dsaawet by which the boundedness of the estimates can be guaranteed without imposing the growth rate constraints on the local functions the estimates generated by the dsaawet are shown to converge almost surely to a consensus set which belongs to a connected subset of the root set of the sum function in comparison with the existing results we impose weaker conditions on the local functions and on the observation noise we then apply the proposed algorithm to two applications one from signal processing and the other one from distributed optimization and establish the almost sure convergence numerical simulation results are also included

composition operators from the weighted bergman space to the nth weighted type space on the upper half plane abstract the boundedness of the composition operator from the weighted bergman space to recently introduced by this author the nth weighted type space on the upper half plane z c im z 0 are characterized here

determinant representation for correlation functions of spin 1 2 xxx and xxz heisenberg magnets we consider zero temperature correlation functions of the spin 1 2 xxz heisenberg chain in the critical regime 1 1 in a magnetic field starting from the algebraic bethe ansatz we derive representations for various correlation functions in term of determinats of fredholm integral operators

norms of multiplication operators on hardy spaces and weighted composition operators from hardy spaces to weighted type spaces on bounded symmetric domains abstract let d be a bounded symmetric domain we calculate operator norm of the multiplication operator on the hardy space h p d as well as of the weighted composition operator from h p d to a weighted type space

a sufficient condition for convergence of sampled data consensus for double integrator dynamics with nonuniform and time varying communication delays this technical note investigates a discrete time second order consensus algorithm for networks of agents with nonuniform and time varying communication delays under dynamically changing communication topologies in a sampled data setting some new proof techniques are proposed to perform the convergence analysis it is finally shown that under certain assumptions upon the velocity damping gain and the sampling period consensus is achieved for arbitrary bounded time varying communication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

essential norm of differences of weighted composition operators between weighted type spaces on the unit ball abstract we find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted type spaces of holomorphic functions on the unit ball in c n as a consequence we characterize the compactness of these operators the boundedness of these operators is also characterized

stochastic approximation for consensus a new approach via ergodic backward products this paper considers both synchronous and asynchronous consensus algorithms with noisy measurements for stochastic approximation based consensus algorithms the existing convergence analysis with dynamic topologies heavily relies on quadratic lyapunov functions whose existence however may be difficult to ensure for switching directed graphs our main contribution is to introduce a new analytical approach we first show a fundamental role of ergodic backward products for mean square consensus in algorithms with additive noise subsequently we develop ergodicity results for backward products of degenerating stochastic matrices converging to a 0 1 matrix via a discrete time dynamical system approach these results complement the existing ergodic theory of stochastic matrices and provide an effective tool for analyzing consensus problems under a joint connectivity assumption our approach may deal with switching topologies delayed measurements and correlated noises and it does not require the double stochasticity condition typically assumed for the existence of quadratic lyapunov functions

a mean square consensus protocol for linear multi agent systems with communication noises and fixed topologies the mean square consensus of linear multi agent systems with communication noises is studied in this note each agent is modeled by a continuous time linear time invariant dynamics and the fixed communication topology is described by a digraph the proposed consensus protocol is composed of two parts the agent s own state feedback and the relative states between agent and its neighbor agents due to the existence of communication noises the relative states cannot be obtained accurately to attenuate the noise effect a time varying gain vector a t k is applied to the inaccurate relative states it is proved that 1 if the communication topology has a spanning tree and every node has at least one parent node then the proposed protocol can solve the mean square consensus problem if and only if a t satisfies 0 a s ds and 0 a2 s ds and all roots of the polynomial whose coefficients are the elements of vector k are in the left half complex plane 2 if the communication topology has a spanning tree and there exists one node without any parent node then the condition 0 a2 s ds is only sufficient but not necessary and 3 if the communication topology has no spanning tree then the proposed protocol cannot solve the mean square consensus problem

exact solvability and asymptotic aspects of generalized xx0 spin chains abstract building on our earlier work saeedian et al 2018 we introduce and study generalized xx0 models we explicitly construct a long range interacting spin chain referred to as the selberg model and study the correlation functions of the selberg and xx0 models using a matrix integral representation of the generalized xx0 model and applying asymptotic analysis in non intersecting brownian motion the phase structure of the selberg model is determined we find that tails of the tracy widom distribution of gaussian unitary ensemble govern a discrete to continuous third order phase transition in selberg model the same method also reproduces the gross witten phase transition of the original xx0 model finally we conjecture universal features for the phase structure of the generalized xx0 model

seeking consensus in networks of linear agents communication noises and markovian switching topologies the stochastic consensus problem of linear multi input multi output mimo multi agent systems mass with communication noises and markovian switching topologies is studied in this technical note the agent s full state is first estimated by the state observer and then the estimated state is exchanged with neighbor agents through a noisy communication environment the communication topology is randomly switching and the switching law is described by a continuous time markovian chain then a consensus protocol is proposed for this mas and some sufficient conditions are obtained for ensuring the mean square and almost sure consensus in addition if the communication topology is fixed some necessary and sufficient conditions for the mean square consensus can be obtained according to whether or not each agent in the system has parents

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

on convergence rate of leader following consensus of linear multi agent systems with communication noises this note further studies the previously proposed consensus protocol for linear multi agent systems with communication noises each agent is allowed to have its own time varying gain to attenuate the effect of communication noises therefore the common assumption that all agents have the same noise attenuation gain is not necessary it has been proved that if all noise attenuation gains are infinitesimal of the same order then the mean square leader following consensus can be reached furthermore the convergence rate of the multi agent system has been investigated if the noise attenuation gains belong to a class of functions which are bounded above and below by t beta beta in 0 1 asymptotically then the second moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t beta asymptotically

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

containment control of multi agent systems in a noisy communication environment the containment problem of first order and second order integral multi agent systems with communication noises is investigated in this paper motivated by the previous work a time varying gain a t is introduced to attenuate the noise effect it is proved that the proposed protocol can solve the mean square containment problem if the following conditions hold 1 the communication topology graph has a spanning forest whose roots are leaders of the multi agent system 2 0 a t dt 3 lim t a t 0 moreover if a t is uniformly continuous these conditions are necessary for ensuring the mean square containment in addition the proposed protocol is also extended to allow the case where each agent has its own gain a i t it is proved that the mean square containment problem can still be solved if all agent dependent gains are infinitesimals of the same order as time goes to infinity finally two simulation examples are provided to demonstrate the effectiveness of the proposed protocols

stochastic approximation based consensus dynamics over markovian networks this paper considers consensus problems with random networks a key object of our analysis is a sequence of stochastic matrices which involve markovian switches and decreasing step sizes we establish ergodicity of the backward products of these stochastic matrices the basic technique is to consider the second moment dynamics of an associated markovian jump linear system and exploit its two scale interaction property resulting from the decreasing step sizes the mean square convergence rate of the backward products is also obtained the ergodicity results are used to prove mean square consensus of stochastic approximation algorithms where agents collect noisy information the approach is further applied to a token scheduled averaging model

consensus conditions of continuous time multi agent systems with additive and multiplicative measurement noises this work is concerned with the consensus problem of multi agent systems with additive and multiplicative measurement noises by developing general stochastic stability lemmas for nonautonomous stochastic differential equations stochastic weak and strong consensus conditions are investigated under fixed and time varying topologies respectively for the case with fixed topologies and additive noises the necessary and sufficient conditions for almost sure strong consensus are given it is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs and almost sure weak consensus implies mean square weak consensus under undirected graphs if multiplicative noises appear then small noise intensities do not affect the control gain to guarantee stochastic strong consensus for the case with time varying topologies sufficient consensus conditions are given under the periodically connected condition of the topology flow

temperature correlators of the impenetrable bose gas as an integrable system it is shown that the temperature equal time correlators of impenetrable bosons in one space dimension are described by a classical integrable system partial differential equations for two point as well as for multipoint correlators are obtained the short distance and low density expansions are constructed

coding with side information for rate constrained consensus average consensus algorithms are protocols to compute the average value of all sensor measurements via near neighbors communications they offer a natural tradeoff between the number of messages exchanged among terminals and the accuracy in the computation most of the models adopted for the message exchange in the literature however neither include explicit rate constraints nor explore the rate distortion tradeoff associated with the algorithm the contribution of our work is in examining the impact of such constraints and in finding strategies to minimize the communication cost in terms of rate the main motivation behind the proposed coding strategies is the observation that consensus algorithms offer the perfect example of a network communication problem where there is an increasing correlation between the data exchanged as the algorithm iterates henceforth it is possible to utilize previously exchanged data and current side information to significantly reduce the demands of quantization bit rate for a certain precision we analyze the case of a network where the links are assumed to be reliable at a constant bit rate we explore the conditions on the quantization noise which lead to a consensus value whose mean squared distance from the initial average is bounded in the case of infinite length vector coding with gaussian states we show that our proposed schemes achieve bounded convergence with vanishing rates as the iteration index tends to infinity

consensus of nonlinear multi agent systems with observer based protocols abstract this paper is concerned with distributed pinning consensus problem for a class of nonlinear multi agent system with observer based protocols two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents according to the state information observed a distributed pinning observer based protocol is proposed for the leader following consensus of the multi agent system furthermore two multi step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively it is shown that under the condition that the pinning joint communication topology contains a directed spanning tree the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable but also guarantee the consensus of the multi agent system to be solved asymptotically finally two numerical examples are provided to demonstrate the effectiveness of the observer based protocols

norms of some operators on the bergman and the hardy space in the unit polydisk and the unit ball let h x be the class of all holomorphic functions on the set x c n and u h x we calculate operator norms of the multiplication operators m u f uf on the weighted bergman space a a p x as well as on the hardy space h p x where x is the unit polydisk d n or the unit ball b in c n we also calculate the norm of the weighted composition operator from the weighted bergman space a a p d n a 1 p 0 and the hardy space h p d n p 0 to a weighted type space on the unit polydisk

large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature abstract asymptotics of the temperature time dependent correlation function of two fields one dimensional bosons with infinite point like repulsion is calculated

admissible l2 consensus for singular time delayed swarm systems with external disturbances abstract admissible consensus analysis and design problems for high order linear time invariant singular swarm systems with time delays and external disturbances are investigated firstly by the state space decomposition a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances which describe the absolute motions of singular swarm systems as a whole then an l 2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents and linear matrix inequality criteria for admissible l 2 consensus and consensualization are shown finally numerical simulations are presented to demonstrate theoretical results

synchronization and convergence of linear dynamics in random directed networks recently methods in stochastic control are used to study the synchronization properties of a nonautonomous discrete time linear system x k 1 g k x k where the matrices g k are derived from a random graph process the purpose of this note is to extend this analysis to directed graphs and more general random graph processes rather than using lyapunov type methods we use results from the theory of inhomogeneous markov chains in our analysis these results have been used successfully in deterministic consensus problems and we show that they are useful for these problems as well sufficient conditions are derived that depend on the types of graphs that have nonvanishing probabilities for instance if a scrambling graph occurs with nonzero probability then the system synchronizes

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

consensus analysis of switching multi agent systems with fixed topology and time delay abstract this paper investigates the average consensus problems of the discrete time markov switching linear multi agent systems lmas with fixed topology and time delay firstly we introduce a concept of the average consensus to adapt the stochastic systems secondly a time delay switching consensus protocol is proposed by developing a new signal mode the switching signal of the systems and the time delay signal of the controller can be merged into one signal thirdly by lyapunov technique two lmis criteria of average consensus are provided and they reveal that the consensus of the multi agent systems relates to the spectral radius of the laplacian matrix furthermore by our results and ccl type algorithms we can get the gain matrices finally a numerical example is given to illustrate the efficiency of our results