fisher information for a complex gaussian random variable beamforming applications for wave propagation in a random medium we derive a general expression for the fisher information for a special class of complex gaussian random variables whose mean and covariance may be expressed in terms of a specific parameterized linear transformation the deterministic unknown parameter case is considered this class is descriptive of signals that propagate in a homogeneous or inhomogeneous medium and also occurs in numerous beamforming applications the fisher information derived here encompasses a wide range of previously derived well known results for complex gaussian signals propagating in a homogeneous medium and is also applicable to more recent models for signals propagating in an inhomogenous medium the conditions for the estimates of the azimuth and elevation to decouple from the estimates of the nuisance parameters are studied for monochromatic plane wave and spherical wave propagation in a random medium for propagation in an anisotropic medium it is found that in general the cramer rao lower bounds crlbs of the entire unknown parameter set will be coupled for special cases of propagation in an isotropic medium it is found that for plane waves the crlbs of the angles of arrival will be approximately decoupled from the crlbs of the other unknowns and for spherical waves the crlbs of the angles of arrival will be always be coupled to the crlbs of all other unknowns although the couplings may be minimized under certain conditions

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

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

linear quadratic optimal control of continuous time lti systems with random input gains this note studies the linear quadratic lq optimal control of continuous time linear time invariant systems with random gains imposed on the input channels we start from the indefinite lq problem in which the cost weighting matrix can be indefinite the definite lq problem is discussed as a special case the main novelty originates from the point of view that in networked control designing the channels and controller jointly often leads to an easier problem and achieves better performance than designing them separately specifically we formulate the lq problem as a channel controller co design problem assuming that the channel capacities can be allocated among the input channels subject to an overall capacity constraint necessary and sufficient conditions are obtained for the well posedness and the attainability of the indefinite lq problem under a given channel capacity allocation satisfying the stabilization requirement the optimal controller is given by a linear state feedback associated with the mean square stabilizing solution of a modified algebraic riccati equation

designing parametric linear quadratic regulators for parametric lti systems via lmis this paper addresses the problem of determining parametric linear quadratic regulators lqrs for continuous time linear time invariant systems affected by parameters through rational functions th

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

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

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

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

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

well posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon abstract this paper is concerned with a stochastic linear quadratic lq problem in an infinite time horizon with multiplicative noises both in the state and the control a distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite a new type of algebraic riccati equation called a generalized algebraic riccati equation gare is introduced which involves a matrix pseudo inverse and two additional algebraic equality inequality constraints it is then shown that the well posedness of the indefinite lq problem is equivalent to a linear matrix inequality lmi condition whereas the attainability of the lq problem is equivalent to the existence of a stabilizing solution to the gare moreover all possible optimal controls are identified via the solution to the gare finally it is proved that the solution to the gare can be obtained via solving a convex optimization problem called semidefinite programming

stable protocol admissible synchronizability for high order singular complex networks with switching topologies abstract stable protocol admissible synchronization analysis and design problems for singular complex networks with both connected switching topologies and jointly connected switching topologies are investigated firstly a singular observer type synchronization protocol is introduced where the errors of protocol states among neighboring agents are applied to make complex networks satisfy a specific separation principle which can simplify synchronization analysis and design problems then by the orthonormal projection operators between the synchronization subspace and the complement synchronization subspace stable protocol admissible synchronization problems are transformed into admissible ones of multiple subsystems with lower dimensions and an approach is given to determine the synchronization function furthermore stable protocol admissible synchronizability criteria for connected switching topology cases and jointly connected switching topology cases are proposed respectively finally two numerical examples are given to demonstrate the effectiveness of theoretical results

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

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

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

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

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

simple and accurate direction of arrival estimator in the case of imperfect spatial coherence we consider the direction finding problem in the imperfect spatial coherence case i e when the amplitude and phase of the wavefront vary randomly along the array aperture this phenomenon can originate from propagation through an inhomogeneous medium it is also encountered in the case of spatially dispersed sources we derive a fast and accurate estimator for the direction of arrival of a single source using a uniform linear array ula of sensors the estimator is based on a reduced statistic obtained from the subdiagonals of the covariance matrix of the array output it only entails computing the fourier transform of an m 1 length sequence where m is the number of array sensors a theoretical analysis is carried out and an expression for the asymptotic variance of the estimator is derived numerical simulations validate the theoretical results and show that the estimator has an accuracy very close to the cramer rao bound

matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts the performance of high resolution direction of arrival doa estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence the original solution to this problem was proposed by paulraj and kailath 1988 but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture a novel solution to this problem is proposed which does not require a priori knowledge of the spatial coherence matrix

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

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

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

leader following exponential consensus of fractional order nonlinear multi agents system with hybrid time varying delay a heterogeneous impulsive method abstract in this paper we study the leader following exponential consensus of multi agent system each agent in the system is described by nonlinear fractional order differential equation both the internal delay and coupling delay are taken into consideration the heterogeneous impulsive control is used for ensuring the consensus of all agents based on lyapunov function method and matrix analysis some sufficient conditions for exponential consensus are obtained finally some illustrative examples are given to show the effectiveness of the obtained results

an efficient approximation of spatial correlation based on gauss hermite quadrature an efficient spatial correlation approximation for clustered multiple input multiple output channels based on a hierarchical angle structure is presented to avoid complicated numerical integrations different approximations have been proposed in the literature one approximation is expressed in a high order series expansion of bessel functions while the other suffers low accuracy for large angle spread an approximation based on gauss hermite quadrature ghq is proposed whose values are shown to match well with theoretical results when the antenna spacing is within a critical range by exploring the properties of the abscissas and the weights of the ghq the proposed approximation can be effectively computed with only a few expansion terms and its validity can be maintained over a large range of angle spread the approximation errors of the proposed and existing methods are analyzed simulation results verify the accuracy of the analysis and the efficiency of the proposed approximation

uniqueness of consensus functions for time delayed swarm systems with time varying topologies abstract this paper shows that consensus functions for high order linear swarm systems with time varying interaction topologies and time delays are uniquely determined by initial states if interaction topologies are balanced in addition an explicit expression of the consensus function is presented and the different influences of initial states of agents and protocols on the consensus function are determined respectively

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

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

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

efficient quadratic detection in perturbed arrays via fourier transform techniques matched field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations unfortunately various array perturbations caused by phase calibration propagation effects or modeling errors can cause the sensor observations to become only partially correlated limiting the performance of traditional matched field beamformers that assume perfect coherence of the signal wavefronts quadratic array processing is optimal for many perturbed array problems however direct implementation poses a significant computational burden we show that under certain conditions the optimal quadratic detector for dealing with perturbed arrays can be approximately realized efficiently and robustly employing only discrete fourier transforms to deal with spatial processing in addition we show that the proposed spatial processing allows for convenient integration of conventional frequency domain methods for angle of arrival searches our proposed array detection structure provides the robustness and performance benefits of complicated quadratic processing at a computational cost comparable with that of traditional matched field beamforming

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

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

direction finding for an extended target with possibly non symmetric spatial spectrum we consider the problem of estimating the direction of arrival doa of an extended target in radar array processing two algorithms are proposed that do not assume that the power azimuthal distribution of the scatterers is symmetric with respect to the mass center of the target the first one is based on spectral moments which are easily related to the target s doa the second method stems from a previous paper by the present authors and consists of a least squares fit on the elements of the covariance matrix both methods are simple and are shown to provide accurate estimates furthermore they extend the range of unambiguous doas that can be estimated compared with the same previous paper

low complexity estimators for distributed sources in antenna array applications the propagation environment is often more complicated than the ordinarily assumed model of plane wavefronts here a low complexity algorithm is suggested for estimating both the doa and the spread angle of a source subject to local scattering using a uniform linear array the parameters are calculated from the estimates obtained using a standard algorithm such as root music to fit a two ray model to the data the algorithm is shown to give consistent estimates and the statistical performance is studied analytically and through simulations

doubly constrained robust capon beamformer with ellipsoidal uncertainty sets the doubly constrained robust dcr capon beamformer with a spherical uncertainty set was introduced and studied by stoica and wang here we consider the generalized dcr problem gdcr in which the uncertainty set is an ellipsoid rather than a sphere although as noted previously by stoica and wang this problem is nonconvex and appears to be intractable we show that it can be solved efficiently in fact we prove that the gdcr beamformer can be obtained as a solution to a convex optimization problem to this end we first derive a strong duality result for nonconvex quadratic programs with two quadratic constraints over the complex domain specializing the results to our context leads to a semidefinite programming formulation of the gdcr beamformer

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

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts eigenstructure subspace methods for direction of arrival estimation are only applicable when each wave front contributes a rank one component to the array covariance this implies that the wave fronts need to have perfect spatial coherence in several practical situations where the wave fronts may only have partial spatial coherence eigenstructure algorithms show poor performance such as overestimation of the number of sources bias and reduced accuracy and resolution in estimating the directions of arrival in this article the performance degradation due to partial spatial coherence is studied and a new approach is proposed that exploits the underlying coherence model to yield asymptotically exact estimates for finite data this method provides improved results only when the number of snapshots exceeds a certain threshold results of computer simulations are also presented

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

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

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

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

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

continuous time stochastic consensus this paper investigates the continuous time multi agent consensus with stochastic communication noises each agent can only use its own and neighbors information corrupted by random noises to design its control input to attenuate the communication noises we consider the stochastic approximation type and the kalman bucy filtering based protocols by using the tools of stochastic analysis and algebraic theory the asymptotic properties of these two kinds of protocols are analyzed firstly for the stochastic approximation type protocol we clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains in both mean square and probability one secondly we propose kalman bucy filtering based consensus protocols each agent uses kalman bucy filters to get asymptotically unbiased estimates of neighbors states and the control input is designed based on the protocol with precise communication and the certainty equivalence principle the iterated logarithm law of estimation errors is developed it is shown that if the communication graph has a spanning tree then the consensus error is bounded above by o t 1 in mean square and by o t 1 2 log log t 1 2 almost surely finally the superiority of the kalman bucy filtering based protocol over the stochastic approximate type protocol is studied both theoretically and numerically

convergence rates of discrete time stochastic approximation consensus algorithms graph related limit bounds abstract in this paper we study the convergence rates of the discrete time stochastic approximation consensus algorithms over sensor networks with communication noises under general digraphs basic results of stochastic analysis and algebraic graph theory are used to investigate the dynamics of the consensus error and the mean square and sample path convergence rates of the consensus error are both given in terms of the graph and noise parameters especially calculation methods to estimate the mean square limit bounds are presented under balanced digraphs and sufficient conditions on the network topology and the step sizes are given to achieve the fast convergence rate for the sample path limit bounds estimation methods are also presented under undirected graphs

estimation of directions of arrival of multiple scattered sources we consider the problem of estimating the directions of arrival doa of multiple sources in the presence of local scattering this problem is encountered in wireless communications due to the presence of scatterers in the vicinity of the mobile or when the signals propagate through a random inhomogeneous medium assuming a uniform linear array ula we develop doa estimation algorithms based on covariance matching applied to a reduced size statistic obtained from the sample covariance matrix after redundancy averaging next a computationally efficient estimator based on ar modelling of the coherence loss function is derived a theoretical expression for the asymptotic covariance matrix of this estimator is derived finally the corresponding cramer rao bounds crbs are derived despite its simplicity the ar based estimator is shown to possess performance that is nearly as good as that of the covariance matching method

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

approximate maximum likelihood estimators for array processing in multiplicative noise environments we consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise this scenario is encountered for example in communications owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media since the exact maximum likelihood ml estimator is computationally intensive two approximate solutions are proposed originating from the analysis of the high and low signal to noise ratio snr cases respectively first starting with the no additive noise case a very simple approximate ml aml sub 1 estimator is derived the performance of the aml sub 1 estimator in the presence of additive noise is studied and a theoretical expression for its asymptotic variance is derived its performance is shown to be close to the cramer rao bound crb for moderate to high snr next the low snr case is considered and the corresponding aml sub 2 solution is derived it is shown that the approximate ml criterion can be concentrated with respect to both the multiplicative and additive noise powers leaving out a two dimensional 2 d minimization problem instead of a four dimensional 4 d problem required by the exact ml numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis

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

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

lqg control for mimo systems over multiple erasure channels with perfect acknowledgment this technical note concerns control applications over lossy data networks sensor data is transmitted to an estimation control unit over a network and control commands are issued to subsystems over the same network sensor and control packets may be randomly lost according to a bernoulli process in this context the discrete time linear quadratic gaussian lqg optimal control problem is considered in schenato a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively here a nontrivial generalization for mimo systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet no aggregation in such a framework it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver moreover the optimal lqg control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels such a dependence is not present in the single channel case considered in mean square in the infinite horizon case stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities lmis

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

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

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

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