global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

on scaling laws of diversity schemes in decentralized estimation this paper is concerned with decentralized estimation of a gaussian source using multiple sensors we consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center using the analog amplify and forwarding technique the fusion centre reconstructs a minimum mean squared error mmse estimate of the source based on the received measurements a distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered we derive asymptotic expressions for the expected distortion of the mmse estimate at the fusion centre of these schemes as the number of sensors becomes large for comparison asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived it is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme where the expected distortion decays as 1 m m being the number of sensors the expected distortion decays only as 1 ln m for the diversity schemes this reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes respectively we study for the diversity schemes the optimal power allocation for minimizing the expected distortion subject to average power constraints the effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied it is proved that for rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme whereas it is observed that optimizing the sensor transmission probability with or without optimal power allocation in the distributed case makes very little difference to the asymptotic scaling laws

adaptive finite time consensus in multi agent networks abstract this paper is concerned with the finite time consensus problem of distributed agents having non identical unknown nonlinear dynamics to a leader agent that also has unknown nonlinear control input signal by parameterization of unknown nonlinear dynamics a lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite time consensus control protocol in undirected networks homogeneous lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous theoretical analysis shows that leader following consensus can be achieved in finite time meanwhile finite time parameter convergence can be also guaranteed under the proposed control scheme an example is given to validate the theoretical results

consistent estimation of minimal sujbset dimension for a general paramnetric model we consider the problem of consistently estimating that permissible subset of the parameter space that contains the true parameter point and has smallest dimension the subset selection is done by means of a model selection criterion of

consensus of multi agent systems based on sampled data control this article studies the consensus problem in directed networks assuming that each agent is with double integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants we propose a protocol based on sampled data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol in virtue of this equivalent characterisation we further consider two cases fixed topology and switching topology for the first case we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem for the second case we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals respectively finally simulations are provided to illustrate the effectiveness of the theoretical results

measures of conditional linear dependence and feedback between time series abstract measures of linear dependence and feedback for two multiple time series conditional on a third are defined the measure of conditional linear dependence is the sum of linear feedback from the first to the second conditional on the third linear feedback from the second to the first conditional on the third and instantaneous linear feedback between the first and second series conditional on the third the measures are non negative and may be expressed in terms of measures of unconditional feedback between various combinations of the three series the measures of conditional linear feedback can be additively decomposed by frequency estimates of these measures are straightforward to compute and their distribution can be routinely approximated by bootstrap methods an empirical example involving real output money and interest rates is presented

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

nonsingular fixed time consensus tracking for second order multi agent networks this paper investigates the fixed time consensus tracking problem for second order multi agent systems in networks with directed topology global well defined nonlinear consensus protocols are constructed with the aid of a newly designed sliding surface for each double integrator agent dynamics in particular the proposed framework eliminates the singularity and the settling time is assignable for any initial conditions this makes it possible for network consensus problems to design and estimate the convergence time off line finally simulation is included to demonstrate the performance of the new protocols

large sample properties of posterior densities bayesian information criterion and the likelihood principle in nonstationary time series models asymptotic normality of the posterior is a well understood result for dynamic as well as nondynamic models based on sets of abstract conditions whose actual applicability is hardly known especially for the case of nonstationarity in this paper we provide a set of conditions by which we can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity this result reinforces and generalizes the point of sims and uhlig 1991 that inference based on the likelihood principle explained by berger and wolpert 1988 will be unchanged regardless of whether the data are generated by a stationary process or by a unit root process on the other hand our conditions allow us to generalize the bayesian information criterion known as the schwarz criterion to the case of possible nonstationarity in addition we have shown that consistency of the maximum likelihood estimator not the asymptotic normality of the estimator with some minor additional assumptions is sufficient for asymptotic posterior normality

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

min max time consensus tracking with communication guarantee in this paper a collection of double integrator agents with bounded inputs is considered communication is possible between any two agents only if the inter agent distance is less than a fixed threshold a special node referred to as the leader generates an unknown reference trajectory to which all the other agents are required to converge in the shortest possible time assuming the initial communication graph to be connected a directed spanning tree rooted at the leader is identified using a local algorithm the dynamics of any two agents connected by an edge in the selected tree are modeled as a time optimal pursuit evasion game while maintaining the inter agent communication link using the corresponding feedback saddle point strategies local min max time control laws for each pair of agents are formulated for the selected tree the proposed collection of local min max time control strategies is shown to be the communication preserving global min max time strategy

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

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

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

formation control using binary information in this paper we study the problem of formation keeping of a network of strictly passive systems when very coarse information is exchanged we assume that neighboring agents only know whether their relative position is larger or smaller than the prescribed one this assumption results in very simple control laws that direct the agents closer or away from each other and take values in finite sets we show that the task of formation keeping while tracking a desired velocity and rejecting matched disturbances is still achievable under the very coarse information scenario in contrast with other results of practical convergence with coarse or quantized information here the control task is achieved exactly

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

the effect of correlated observations on the performance of distributed estimation estimating unknown signal in wireless sensor networks wsns requires sensor nodes to transmit their observations of the signal over a multiple access channel to a fusion center fc the fc uses the received observations which is corrupted by observation noise and both channel fading and noise to find the minimum mean square error mse estimate of the signal in this paper we investigate the effect of the source node correlation the correlation between sensor node observations and the source signal and the inter node correlation the correlation between sensor node observations on the performance of the linear minimum mean square error lmmse estimator for three correlation models in the presence of channel fading first we investigate the asymptotic behavior of the achieved distortion i e mse resulting from both the observation and channel noise in a non fading channel then the effect of channel fading is considered and the corresponding distortion outage probability the probability that the distortion exceeds a certain value is found by representing the distortion as a ratio of indefinite quadratic forms a closed form expression is derived for the outage probability that shows its dependency on the correlation finally the new representation of the outage probability allows us to propose an iterative solution for the power allocation problem to minimize the outage probability under total and individual power constraints numerical simulations are provided to verify our analytic results

finite time distributed linear equation solver for solutions with minimum l_1 norm this paper proposes a continuous time distributed algorithm for multiagent networks to achieve a solution with the minimum l 1 norm to underdetermined linear equations the proposed algorithm comes from a combination of the filippov set valued map with the projection consensus flow given the underlying network is undirected and fixed it is shown that the proposed algorithm drives all agents individual states to converge in finite time to a common value which is the minimum l 1 norm solution

distributed estimation using reduced dimensionality sensor observations we derive linear estimators of stationary random signals based on reduced dimensionality observations collected at distributed sensors and communicated to a fusion center over wireless links dimensionality reduction compresses sensor data to meet low power and bandwidth constraints while linearity in compression and estimation are well motivated by the limited computing capabilities wireless sensor networks are envisioned to operate with and by the desire to estimate random signals from observations with unknown probability density functions in the absence of fading and fusion center noise ideal links we cast this intertwined compression estimation problem in a canonical correlation analysis framework and derive closed form mean square error mse optimal estimators along with coordinate descent suboptimal alternatives that guarantee convergence at least to a stationary point likewise we develop estimators based on reduced dimensionality sensor observations in the presence of fading and additive noise at the fusion center nonideal links performance analysis and corroborating simulations demonstrate the merits of the novel distributed estimators relative to existing alternatives

low level interpretability and high level interpretability a unified view of data driven interpretable fuzzy system modelling this paper aims at providing an in depth overview of designing interpretable fuzzy inference models from data within a unified framework the objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real world systems whose first principle models are unknown because system behaviour can be described naturally as a series of linguistic rules data driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose however fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability model accuracy and interpretability are two conflicting objectives so interpretation preservation during adaptation in data driven fuzzy system modelling is a challenging task which has received much attention in fuzzy system modelling community in order to clearly discriminate the different roles of fuzzy sets input variables and other components in achieving an interpretable fuzzy model a taxonomy of fuzzy model interpretability is first proposed in terms of low level interpretability and high level interpretability in this paper the low level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level while the high level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage completeness and consistency of the rules in terms of the criteria on fuzzy rule level some criteria for low level interpretability and high level interpretability are identified respectively different data driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low level interpretability and high level interpretability furthermore some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested

brief paper stability analysis for multi agent systems using the incidence matrix quantized communication and formation control the spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi agent control problems in particular we consider the problem of state agreement with quantized communication and the problem of distance based formation control in both cases stabilizing control laws are provided when the communication graph is a tree it is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi agent control problems

implicit lyapunov krasovski functionals for stability analysis and control design of time delay systems the method of implicit lyapunov krasovski functional ilkf for stability analysis of time delay systems is introduced theorems on lyapunov asymptotic hyper exponential finite time and fixed time stability analysis using ilkf are presented the hyper exponential stabilization algorithm for a time delay system is presented the theoretical result is supported by numerical simulation

a finite time particle swarm optimization algorithm for odor source localization abstract this paper is concerned with a finite time particle swarm optimization algorithm for odor source localization first a continuous time finite time particle swarm optimization fpso algorithm is developed based on the continuous time model of the particle swarm optimization pso algorithm since the introduction of a nonlinear damping item the proposed continuous time fpso algorithm can converge over a finite time interval furthermore in order to enhance its exploration capability a tuning parameter is introduced into the proposed continuous time fpso algorithm the algorithm s finite time convergence is analyzed by using the lyapunov approach second the discrete time fpso algorithm is obtained by using a given dicretization scheme the corresponding convergence condition is derived by using a linear matrix inequality lmi approach finally the features and performance of the proposed fpso algorithm are illustrated by using two ill posed functions and twenty five benchmark functions respectively in numerical simulation results the problem of odor source localization is presented to validate the effectiveness of the proposed fpso algorithm

methods and criteria for model selection model selection is an important part of any statistical analysis and indeed is central to the pursuit of science in general many authors have examined the question of model selection from both frequentist and bayesian perspectives and many tools for selecting the best model have been suggested in the literature this paper considers the various proposals from a bayesian decision theoretic perspective

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

an alternative quasi likelihood approach bayesian analysis and data based inference for model specification abstract this paper studies an alternative quasi likelihood approach under possible model misspecification we derive a filtered likelihood from a given quasi likelihood ql called a limited information quasi likelihood li ql that contains relevant but limited information on the data generation process our li ql approach in one hand extends robustness of the ql approach to inference problems for which the existing approach does not apply our study in this paper on the other hand builds a bridge between the classical and bayesian approaches for statistical inference under possible model misspecification we can establish a large sample correspondence between the classical ql approach and our li ql based bayesian approach an interesting finding is that the asymptotic distribution of an li ql based posterior and that of the corresponding quasi maximum likelihood estimator share the same sandwich type second moment based on the li ql we can develop inference methods that are useful for practical applications under possible model misspecification in particular we can develop the bayesian counterparts of classical ql methods that carry all the nice features of the latter studied in white 1982 in addition we can develop a bayesian method for analyzing model specification based on an li ql

multiterminal source channel communication over an orthogonal multiple access channel we consider the problem of multiterminal source channel communication where a number of distributed and possibly correlated sources are transmitted through an orthogonal multiple access channel to a common destination we provide a characterization of the optimal tradeoff between the transmission cost gamma and the distortion vector d as measured against individual sources our approach consists of two steps 1 a multiple letter characterization of the rate distortion region of the multiterminal source coding and 2 a source channel separation theorem ensuring that all achievable pairs of gamma d can be obtained by combining the rate distortion region and the orthogonal multiple access channel capacity region as a corollary we determine the optimal power and distortion tradeoff in a quadratic gaussian sensor network under orthogonal multiple access and show that separate source and channel coding strictly outperforms the uncoded amplify forward transmission and is in fact optimal in this case this result is in sharp contrast to the case of nonorthogonal multiple access for which separate source and channel coding is not only suboptimal but also strictly inferior to uncoded transmission

distributed exponential finite time coordination of multi agent systems containment control and consensus in this paper exponential finite time coordination problems of multi agent systems are investigated including containment control and consensus the theoretical basis is that a class of nonlinear systems has favourable finite time convergence characteristic for the objective of containment control the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time for the objective of consensus a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time the distinguished features of this paper lie in the following two points 1 a smaller settling time of the lyapunov function is obtained which manifests in a faster convergence rate than the traditional one and 2 the weakly connected topology considered in this paper is more general than the o

minimal energy decentralized estimation via exploiting the statistical knowledge of sensor noise variance we study the problem of minimal energy decentralized estimation via sensor networks with the best linear unbiased estimator fusion rule while most of the existing solutions require the knowledge of instantaneous noise variances for energy allocation the proposed approach instead relies on an associated statistical model the minimization of total energy is subject to a performance constraint in terms of the reciprocal of mean square errors averaged over the considered distribution a closed form formula for such a mean distortion metric as well as an associated tractable lower bound is derived by imposing a target distortion constraint in terms of this bound and further through feasible set relaxation the problem can be reformulated in the form of convex optimization and is then analytically solved the proposed method shares several attractive features of the existing designs via instantaneous noise variances through simulations it is seen to significantly improve the energy efficiency against the uniform allocation scheme

optimal finite time consensus on fixed and periodic graphs synthesis of optimal controllers achieving finite time consensus for multiagent networks described by fixed or periodic connectivity graphs is considered the solution procedure involves posing a partially nested finite horizon decentralized control problem and converting it to a static convex optimization problem by a quadratic invariance argument the dynamic feedback controller thus synthesized optimizes a transient performance measure and guarantees consensus within a minimal number of steps

finite time weighted average consensus with respect to a monotonic function and its application abstract the consensus state is an important and fundamental quantity for consensus problems of multi agent systems which indicates where all the dynamical agents reach in this paper weighted average consensus with respect to a monotonic function which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values is studied for a group of kinematic agents with time varying topology by constructing a continuous nonlinear distributed protocol such a consensus problem can be solved in finite time even though the time varying topology involves unconnected graphs then the distributed protocol is employed to compute the maximum likelihood estimation of unknown parameters over sensor networks compared with the existing results the estimate scheme proposed here may reduce the costs of data communication storage memory book keeping and computational overheads

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

duality and network theory in passivity based cooperative control this paper presents a class of passivity based cooperative control problems that have an explicit connection to convex network optimization problems the new notion of maximal equilibrium independent passivity is introduced and it is shown that networks of systems possessing this property asymptotically approach the solutions of a dual pair of network optimization problems namely an optimal potential and an optimal flow problem this connection leads to an interpretation of the dynamic variables such as system inputs and outputs to variables in a network optimization framework such as divergences and potentials and reveals that several duality relations known in convex network optimization theory translate directly to passivity based cooperative control problems the presented results establish a strong and explicit connection between passivity based cooperative control theory on the one side and network optimization theory on the other and they provide a unifying framework for network analysis and optimal design the results are illustrated on a nonlinear traffic dynamics model that is shown to be asymptotically clustering

constrained nonlinear programming for volatility estimation with garch models this paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity garch volatility estimation models in financial econometrics these models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature whereas they actually fall into the domain of nonconvex nonlinear programming our results demonstrate that constrained nonlinear programming is a worthwhile exercise for garch models especially for the bivariate and trivariate cases as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal vech and the bekk representations of the multivariate garch model

revisiting normalized gradient descent fast evasion of saddle points the paper considers normalized gradient descent ngd a natural modification of classical gradient descent gd in optimization problems it is shown that contrary to gd ngd escapes saddle points quickly a serious shortcoming of gd in nonconvex problems is that it can take arbitrarily long to escape from the neighborhood of a saddle point in practice this issue can significantly slow the convergence of gd particularly in high dimensional nonconvex problems the paper focuses on continuous time dynamics it is shown that 1 ngd almost never converges to saddle points and 2 the time required for ngd to escape from a ball of radius r about a saddle point x is at most 5 sqrt kappa r where kappa is the condition number of the hessian of f at x as a simple application of these results a global convergence time bound is established for ngd under mild assumptions

estimating cross section common stochastic trends in nonstationary panel data this paper studies large dimension factor models with nonstationary dynamic factors also referred to as cross section common stochastic trends we consider the problem of estimating the dimension of the common stochastic trends and the stochastic trends themselves we derive the rates of convergence and the limiting distributions for the estimated common trends and for the estimated loading coefficients generalized dynamic factor models with nonstationary factors are also considered cointegration among the factors is permitted the method is applied to the study of employment fluctuations across 60 industries for the u s we examine the hypothesis that these fluctuations can be explained by a small number of aggregate factors we also test whether some observable macroeconomic variables are the underlying factors

type based estimation over multiaccess channels we study the problem of communicating sensor readings over a gaussian multiaccess channel we focus on the scenario that each sensor observes a single random variable and transmits it using certain signaling in a shared channel the objective is the design of channel waveforms i e the signal constellation to facilitate the estimation of field parameters from the channel output we propose a communication scheme in which sensors transmit according to the type of their observations type based multiple access tbma and show that the tbma is asymptotically optimal in the limit of large number of sensors if the sensor channel gains are identical in particular we show that tbma together with a variant of the maximum likelihood estimator achieves the cramer rao bound asymptotically we then extend the asymptotic analysis of tbma to fading channels and compare the performance of tbma with other orthogonal allocation methods such as time division multiple access

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

distributed control of angle constrained cyclic formations using bearing only measurements abstract this paper studies distributed control of multi vehicle formations with angle constraints using bearing only measurements it is assumed that each vehicle can only measure the local bearings of their neighbors and there are no wireless communications among the vehicles the desired formation is a cyclic one whose underlying information flow is described by an undirected cycle graph we propose a distributed bearing only formation control law that ensures local exponential or finite time stability collision avoidance between any vehicles can be locally guaranteed in the absence of inter vehicle distance measurements

distributed finite time tracking of multiple non identical second order nonlinear systems with settling time estimation this paper investigates the distributed finite time consensus tracking problem for a group of autonomous agents modeled by multiple non identical second order nonlinear systems first a class of distributed finite time protocols are proposed based on the relative position and relative velocity measurements by providing a topology dependent lyapunov function it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded then a new class of observer based algorithms are designed to solve the finite time consensus tracking problem without using relative velocity measurements the main contribution of this paper is that by computing the value of the lyapunov function at the initial point the finite settling time can be theoretically estimated for second order multi agent systems with the proposed control protocols finally the effectiveness of the analytical results is illustrated by an application in low earth orbit spacecraft formation flying

finite time formation control for linear multi agent systems a motion planning approach abstract this paper investigates the problem of finite time formation control for multi agent systems with general linear dynamics first of all the considered formation problem is converted into the motion planning problem where the systems are steered from initial positions to the desired terminal configurations then by using pontryagin maximum principle an optimal formation control law is developed for multi agent systems based on some invertible conditions with the designed control law the multi agent systems can achieve the desired formation in finite time where the formation configurations and the settling time can be specified in advance according to task requirements meanwhile a performance index is guaranteed to be optimal further it is proved that the formation problem concerned is solved if and only if the linear systems are controllable finally a possible application of the proposed control law to spacecraft formation flying with circular and near circular reference orbit is illustrated

finite time coordination in multiagent systems using sliding mode control approach abstract finite time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time in this paper we use the notion of finite time stability to apply it to the problem of coordinated motion in multiagent systems specifically we consider a group of agents described by fully actuated euler lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady state distances between the neighboring agents in finite time we use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph laplacian matrix furthermore using sliding mode control approach we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state sliding mode control is known to drive the system states to the sliding surface in finite time the key feature of our approach is in the design of non smooth sliding surfaces such that while on the sliding surface the error states converge to the origin in finite time thus ensuring finite time coordination among the agents in the network in addition we discuss the case of switching communication topologies in multiagent systems finally we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents

asymptotic optimality of generalized cl cross validation and generalized cross validation in regression with heteroskedastic errors abstract the problem considered here is that of using a data driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter in contrast to other papers on this subject we consider models with heteroskedastic errors the results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators nearest neighbor estimators and local regression estimators among others generalized c l gc l cross validation cv and generalized cross validation gcv procedures are analyzed the gc l and cv criteria are shown to be asymptotically optimal under general conditions a feasible version of gc l however is available only in some applications the gcv criterion is found to be asymptotically optimal only under a condition that is satisfied in some applications but not in others for example it is satisfied in the nearest neighbor estimation context but not in the series estimation local regression estimation or model selection contexts thus the cv criterion is the only feasible criterion of the three that is asymptotically optimal under general conditions the proofs rely heavily on results of li 1987

estimating regression models of finite but unknown order abstract this paper considers some problems associated with estimation and inference in the normal linear regression model y t j 1 m0 j x tj e t var e t 2 when m 0 is unknown the regressors are taken to be stochastic and assumed to satisfy v grenander s 1954 conditions almost surely it is further supposed that estimation and inference are undertaken in the usual way conditional on a value of m 0 chosen to minimize the estimation criterion function ec m t 2 m mg t with respect to m where 2m is the maximum likelihood estimate of 2 it is shown that subject to weak side conditions if g t a s 0 and tg t a s then this estimate is weakly consistent it follows that estimates conditional on the chosen value of m 0 are asymptotically efficient and inference undertaken in the usual way is justified in large samples when g t converges to a positive constant with probability one then in large samples m 0 will never be chosen too small but the probability of choosing m 0 too large remains positive the results of the paper are stronger than similar ones r shibata 1976 r j bhansali and d y downham 1977 in that a known upper bound on m 0 is not assumed the strengthening is made possible by the assumptions of strictly exogenous regressors and normally distributed disturbances the main results are used to show that if the model selection criteria of h akaike 1974 t amemiya 1980 c l mallows 1973 or e parzen 1979 are used to choose m 0 in 1 then in the limit the probability of choosing m 0 too large is at least 0 2883 the approach taken by g schwarz 1978 leads to a consistent estimator of m 0 however these results are illustrated in a small sampling experiment

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

distributed average tracking for reference signals with bounded accelerations in this technical note the distributed average tracking dat problem for reference signals with bounded accelerations is considered a sliding mode surface is designed such that trajectories on the surface will achieve dat a discontinuous control algorithm is then proposed to guarantee that the surface can be reached in finite time it is shown that if the switching network topology is connected at all time then dat can be solved by properly choosing a gain parameter of the algorithm

risk and rationality uncovering heterogeneity in probability distortion it has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types we present a parsimonious characterization of risk taking behavior by estimating a finite mixture model for three different experimental data sets two swiss and one chinese over a large number of real gains and losses we find two major types of individuals in all three data sets the choices of roughly 80 of the subjects exhibit significant deviations from linear probability weighting of varying strength consistent with prospect theory twenty percent of the subjects weight probabilities near linearly and behave essentially as expected value maximizers moreover individuals are cleanly assigned to one type with probabilities close to unity the reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on the stabilization in finite time of locally controllable systems by means of continuous time varying feedback law it is proven that if for any positive time t there exists an open loop control u a t depending continuously on the initial data a vanishing for a 0 and steering a small neighborhood of 0 into 0 in time t then the control system can be locally stabilized in small time by means of continuous time varying feedback law provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation in this paper we study the energy efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise corrupted channels we assume a gaussian network model where i the data samples being sensed at different sensors have a correlated gaussian distribution and the correlation matrix is known at the fusion center ii the links between the local sensors and the fusion center are subject to fading and additive white gaussian noise awgn and the fading gains are known at the fusion center and iii the central node uses the squared error distortion metric we consider two different distortion criteria i individual distortion constraints at each node and ii average mean square error distortion constraint across the network we determine the achievable power distortion regions under each distortion constraint taking the delay constraint into account we investigate the performance of an uncoded transmission strategy where the noisy observations are only scaled and transmitted to the fusion center at the fusion center two different estimators are considered i the best linear unbiased estimator blue that does not require knowledge of the correlation matrix and ii the minimum mean square error mmse estimator that exploits the correlations for each estimation method we determine the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate under both distortion criteria the numerical comparisons between the two schemes indicate that the mmse estimator requires less power to attain the same distortion provided by the blue and this performance gap becomes more dramatic as correlations between the observations increase furthermore comparisons between power distortion region achieved by the theoretically optimum system and that achieved by the uncoded system indicate that the performance gap between the two systems becomes small for low levels of correlation between the sensor observations if observations at all sensor nodes are uncorrelated the uncoded system with mmse estimator attains the theoretically optimum system performance

fixed time consensus tracking for multiagent systems with high order integrator dynamics this paper addresses the fixed time leader follower consensus problem for high order integrator multiagent systems subject to matched external disturbances a new cascade control structure based on a fixed time distributed observer is developed to achieve the fixed time consensus tracking control a simulation example is included to show the efficacy and the performance of the proposed control structure with respect to different initial conditions

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity

small sample properties of dimensionality statistics for fitting var models to aggregate economic data a monte carlo study abstract the analysis of aggregate economic phenomena by var s as suggested by sims often results in a small sample relative to the number of estimated parameters since the model is identified by a dimensionality criterion the small sample properties of available criteria are important this paper presents a study of small sample properties for six criteria with monte carlo methods it is found that no criterion performs well and that underfitting of models may be quite common

model selection in the presence of nonstationarity abstract this paper studies model selection methods in the presence of nonstationarity we focus on the bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice first we derive each of these criteria in the presence of nonstationarity in particular we study the bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity one important feature of the bayesian model selection criterion bmsc is that bmsc gives different weights to the stationary and nonstationary components of a model while the other criteria do not this feature of bmsc is a desirable property for a model selection rule in the presence of possible nonstationarity second we compare these criteria with regard to parsimony and power we have found that bmsc shows the highest parsimony aic is the second and c p and r 2 having the same level of parsimony are the third with regard to power the order is not clearly established however for the size adjusted power bmsc becomes dominant as the sample size increases without size adjustment the order in the power is exactly the opposite to that in parsimony also we find that bmsc is a consistent selection rule while the other criteria are not third we consider four different cases of practical interest for which bmsc with some of the other criteria is applicable we discuss how our bmsc can be used in these cases of practical interest results of an extensive monte carlo simulation for models in these four cases show that overall the bmsc outperforms other criteria

finite time consensus for controlled dynamical systems in network abstractthe key challenges in networked dynamical systems are the component heterogeneities nonlinearities and the high dimension of the formulated vector of state variables in this paper the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift for each model structure that defines homogeneous and heterogeneous multi system behaviour we derive protocols leading to finite time consensus for each model evolving in networks forming a homogeneous or heterogeneous multi system protocols integrating sufficient conditions are derived leading to finite time consensus likewise for the networking topology we make use of fixed directed and undirected graphs to prove our approaches finite time stability theory and lyapunov methods are considered as illustrative examples the homogeneous multi unicycle kinematics and the homogeneous heterogeneous multi second order dynamics in networks are studied

the conditional autoregressive wishart model for multivariate stock market volatility abstract we propose a conditional autoregressive wishart caw model for the analysis of realized covariance matrices of asset returns our model assumes an autoregressive moving average structure for the scale matrix of the wishart distribution it accounts for positive definiteness of covariance matrices without imposing parametric restrictions and can be estimated by maximum likelihood we also propose extensions of the caw model obtained by including a mixed data sampling midas component and heterogeneous autoregressive har dynamics for long run fluctuations the caw models are applied to realized variances and covariances for five new york stock exchange stocks

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

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

feedback stabilization and lyapunov functions given a locally defined nondifferentiable but lipschitz lyapunov function we employ it in order to construct a discontinuous feedback law which stabilizes the underlying system to any given tolerance a converse result shows that suitable lyapunov functions of this type exist under mild assumptions we also establish that the feedback in question possesses a robustness property relative to measurement error despite the fact that it may not be continuous

finite time connectivity preserving consensus of networked nonlinear agents with unknown lipschitz terms this technical note studies finite time consensus problem for a team of networked nonlinear agents with unknown lipschitz terms under communication constraints where each agent has a limited sensing range because the induced interaction graph is typically state dependent and dynamic we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns by using tools from nonsmooth analysis sufficient conditions are obtained such that finite time consensus can be reached an upper bound of the convergence time is derived via a two step analysis the validity of the theoretical result is shown by one simulation example

uncoded transmission is exactly optimal for a simple gaussian sensor network a single memoryless gaussian source is observed by many terminals subject to independent gaussian observation noises the terminals are linked to a fusion center via a standard gaussian multiple access channel the fusion center needs to recover the underlying gaussian source with respect to mean squared error in this correspondence a theorem of witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission i e each terminal s channel input is merely a scaled version of its noisy observation

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

distributed average tracking of multiple time varying reference signals with bounded derivatives we present a distributed discontinuous control algorithm for a team of agents to track the average of multiple time varying reference signals with bounded derivatives we use tools from nonsmooth analysis to analyze the stability of the system for time invariant undirected connected network topologies we prove that the states of all agents will converge to the average of the time varying reference signals with bounded derivatives in finite time provided that the control gain is properly chosen the validity of this result is also established for scenarios with switching undirected connected network topologies for time invariant directed network topologies with a directed spanning tree we show that all agents will still reach a consensus in finite time but the convergent value is generally not the average of the time varying reference signals with bounded derivatives simulation examples are presented to show the validity of the above results

finite time consensus with disturbance rejection by discontinuous local interactions in directed graphs in this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous time first order integrator dynamics affected by bounded disturbances the topology of the network is described by a directed graph the proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time an upper bound to the convergence time is explicitly derived in the technical note simulation results referring to a network of coupled kuramoto like oscillators are illustrated to corroborate the theoretical analysis

asymptotic capacity analysis for adaptive transmission schemes under general fading distributions asymptotic comparisons of ergodic channel capacity at high and low snrs are provided for several adaptive transmission schemes over fading channels with general distributions including optimal power and rate adaptation rate adaptation only channel inversion and its variants analysis of the high snr pre log constants of the ergodic capacity reveals the existence of constant capacity difference gaps among the schemes with a pre log constant of 1 closed form expressions for these high snr capacity difference gaps are derived which are proportional to the snr loss between these schemes in db scale the largest one of these gaps is found to be between the optimal power and rate adaptation scheme and the channel inversion scheme based on these expressions it is shown that the presence of space diversity or multi user diversity makes channel inversion arbitrarily close to achieving optimal capacity at high snr with sufficiently large number of antennas or users a low snr analysis also reveals that the presence of fading provably always improves capacity at sufficiently low snr compared to the additive white gaussian noise awgn case numerical results are shown to corroborate our analytical results

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

decentralized formation control of mobile agents a unified framework abstract this paper studies the formation control problem for systems consisting of multiple mobile agents that are described by first order differential equations and second order differential equations respectively the following issues are investigated bounded input disturbance and time delay in derivation of the main results a blend of graph theoretic and system theoretic tools is employed where local potential functions and lasalle s invariant principle play central roles finally numerical examples which support the analytical results very well are also included

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

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

fixed time stable gradient flows applications to continuous time optimization this paper proposes novel gradient flow schemes that yield convergence to the optimal point of a convex optimization problem within a fixed time from any given initial condition for unconstrained optimization constrained optimization and min max problems it is shown that the solution of the modified gradient flow dynamics exists and is unique under certain regularity conditions on the objective function while fixed time convergence to the optimal point is shown via lyapunov based analysis the application of the modified gradient flow to unconstrained optimization problems is studied under the assumption of gradient dominance a relaxation of strong convexity then a modified newton s method is presented that exhibits fixed time convergence under some mild conditions on the objective function building upon this method a novel technique for solving convex optimization problems with linear equality constraints that yields convergence to the optimal point in fixed time is developed finally the general min max problem is considered and a modified scheme to obtain the optimal solution of saddle point dynamics in fixed time is developed

consensus dynamics with arbitrary sign preserving nonlinearities abstract this paper studies consensus problems for multi agent systems defined on directed graphs where the consensus dynamics involves general nonlinear and discontinuous functions sufficient conditions only involving basic properties of the nonlinear functions and the topology of the underlying graph are derived for the agents to converge to consensus

nonlinear consensus via continuous sampled and aperiodic updates we consider a first order multi agent system with nonlinear control protocols performing consensus we first address the convergence properties of the continuous system then periodically sampled control inputs are treated where we derive explicit upper bounds on the sampling interval to preserve global stability moreover we design an aperiodic and event triggered updating law to reduce the control efforts even further while ensuring the closed loop stability and providing a strictly positive lower bound on the inter execution time finally the robustness of this approach with respect to additive disturbances is examined by applying 2 gain analysis

non linear regression with discrete explanatory variables with an application to the earnings function abstract in this paper it will be shown that regression models with discrete explanatory variables take the form of a polynominal of a linear function of the regressors a two stage estimation procedure and various model specification tests will be developed in close harmony with an empirical application to the earnings function