formation control of mobile agents based on inter agent distance dynamics we propose a novel formation control strategy based on inter agent distances for single integrator modeled agents in the plane attempting to directly control the inter agent distances we derive a control law from the distance dynamics the proposed control law achieves the local asymptotic stability of infinitesimally rigid formations triangular infinitesimally rigid formations are globally asymptotically stable under the proposed control law with all squared distance errors exponentially and monotonically converging to zero as an extension of existing results the stability analysis in this paper reveals that any control laws related with the gradient law by multiplication of a positive matrix ensure the local asymptotic stability of infinitesimally rigid formations

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

consensus of multi agent networks with aperiodic sampled communication via impulsive algorithms using position only measurements in this technical note an impulsive consensus algorithm is proposed for second order continuous time multi agent networks with switching topology the communication among agents occurs at sampling instants based on position only measurements by using the property of stochastic matrices and algebraic graph theory some sufficient conditions are obtained to ensure the consensus of the controlled multi agent network if the communication graph has a spanning tree jointly a numerical example is given to illustrate the effectiveness of the proposed algorithm

zeroth order method for distributed optimization with approximate projections this paper studies the problem of minimizing a sum of possible nonsmooth convex functions that are corresponding to multiple interacting nodes subject to a convex state constraint set time varying directed network is considered here two types of computational constraints are investigated in this paper one where the information of gradients is not available and the other where the projection steps can only be calculated approximately we devise a distributed zeroth order method the implementation of which needs only functional evaluations and approximate projection in particular we show that the proposed method generates expected function value sequences that converge to the optimal value provided that the projection errors decrease at appropriate rates

on impulsive control of a periodically forced chaotic pendulum system we consider impulsive control of a periodically forced pendulum system which has rich chaos and bifurcation phenomena a new impulsive control method for chaos suppression of this pendulum system is developed some simple sufficient conditions for driving the chaotic state to its zero equilibrium are presented and some criteria for eventually exponentially asymptotical stability are established this work provides a rigorous theoretical analysis to support some early experimental observations on controlling chaos in the periodically forced pendulum system

the variable selection problem abstract the problem of variable selection is one of the most pervasive model selection problems in statistical applications often referred to as the problem of subset selection it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors but there is uncertainty about which subset to use this vignette reviews some of the key developments that have led to the wide variety of approaches for this problem

estimation of error rates in discriminant analysis with selection of variables accurate estimation of misclassification rates in discriminant analysis with selection of variables by for example a stepwise algorithm is complicated by the large optimistic bias inherent in standard estimators such as those obtained by the resubstitution method application of a bootstrap adjustment can reduce the bias of the resubstitution method however the bootstrap technique requires the variable selection procedure to be repeated many times and is therefore difficult to compute in this paper we propose a smoothed estimator that requires relatively little computation and which on the basis of a monte carlo sampling study is found to perform generally at least as well as the bootstrap method

from fixed x to random x regression bias variance decompositions covariance penalties and prediction error estimation in statistical prediction classical approaches for model selection and model evaluation based on covariance penalties are still widely used most of the literature on this topic is based on what w

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

multi consensus of multi agent systems with various intelligences using switched impulsive protocols in this paper multi consensus refers to that the states of multi agent systems asymptotically converge to several consistent values the concept of intelligence degree is introduced to characterize the level of agent intelligence based on that some distributed switched impulsive protocols are proposed using sampled position data and sampled velocity data alternately at sampling instants the continuous time multi agent system using the proposed protocols is equivalently transformed into a discrete time system some necessary and sufficient conditions on the communication network topology are obtained three types of multi consensus can be asymptotically achieved if and only if the directed network has a spanning tree and the feedback gains and sampling periods are chosen appropriately moreover the final states of multi consensus are analytically determined for second order multi agent systems which depend on the initial states of the agents the communication network topology and the feedback gains in the protocols numerical examples are finally presented to show the effectiveness of the proposed protocols and to verify the theoretical results

formation control and network localization via orientation alignment we propose a formation control strategy based on inter agent displacements for single integrator modeled agents in the plane since the orientations of the local reference frames of the agents are not aligned with each other due to the absence of a common sense of orientation the proposed strategy consists of an orientation alignment law and a formation control law under the proposed strategy if the interaction graph is uniformly connected and all the initial orientation angles belong to an interval with length less than the orientations are exponentially aligned and the formation exponentially converges to the desired formation we also show that the proposed strategy can be utilized for network localization as a dual problem

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

the little bootstrap and other methods for dimensionality selection in regression x fixed prediction error abstract when a regression problem contains many predictor variables it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables usually a regression equation based on a few variables will be more accurate and certainly simpler there are various methods for picking good subsets of variables and programs that do such procedures are part of every widely used statistical package the most common methods are based on stepwise addition or deletion of variables and on best subsets the latter refers to a search method that given the number of variables to be in the equation say five locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations all of these procedures generate a sequence of regression equations the first based on one variable the next based on two variables and so on each member of this sequence is called a submodel and the number of variables in the e

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

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

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

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

cross validation the jackknife and the bootstrap excess error estimation in forward logistic regression abstract given a prediction rule based on a set of patients what is the probability of incorrectly predicting the outcome of a new patient call this probability the true error an optimistic estimate is the apparent error or the proportion of incorrect predictions on the original set of patients and it is the goal of this article to study estimates of the excess error or the difference between the true and apparent errors i consider three estimates of the excess error cross validation the jackknife and the bootstrap using simulations and real data the three estimates for a specific prediction rule are compared when the prediction rule is allowed to be complicated overfitting becomes a real danger and excess error estimation becomes important the prediction rule chosen here is moderately complicated involving a variable selection procedure based on forward logistic regression

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

robust nonparametric methods the terms nonparametric statistics and distributionfree methods have historically referred to a collection of statistical tests whose null distributions do not depend on the underlying distribution of the data the area has been expanded to include estimates and confidence intervals derived from the tests and includes asymptotically distribution free tests for complex models as well it is now generally recognized that these statistical methods are highly efficient over large sets of possible models and are robust as well this was not always the case the earliest work was by hotelling and pabst in 1936 references to works in this paragraph can be found in the books cited in the next paragraph on rank correlation and by friedman in 1937 on rank tests in a two way design followed in 1945 with the introduction of the signed rank and rank sum tests by wilcoxon in 1947 mann and whitney extended the ideas of wilcoxon all of these rank tests were considered quick and dirty but not competitive with the presumably more efficient t tests this perspective was about to change in 1948 pitman developed efficiency concepts in a set of lecture notes that although never published were widely disseminated during the 1950s and 1960s lehmann working with hodges and with his students at berkeley showed that rank tests are surprisingly efficient and robust in fact the wilcoxon rank tests are essentially efficient at the normal model and can be much more efficient than least squares methods when the underlying distribution of the data has heavy tails in the early 1960s hodges and lehmann derived estimates and confidence intervals from rank test statistics and also introduced aligned rank tests for use in the regression model in 1967 hajek and sid published their seminal book on the theory of rank tests it is impossible to mention all of the contributions to this early development hence we cite several key mono

on the stable equilibrium points of gradient systems this paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f in particular it is shown that under the assumption that f is real analytic local minimality is necessary and sufficient for stability under the weaker assumption that f is indefinitely continuously differentiable local minimality is neither necessary nor sufficient for stability

global and robust formation shape stabilization of relative sensing networks this paper proposes a simple distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology assuming the network runs an initialization procedure to equally orient all agent reference frames convergence to the desired formation shape is guaranteed even in partially asynchronous settings we characterize the algorithm robustness against several sources of errors link failures measurement errors and frame initialization errors the technical approach combines algebraic graph theory multidimensional scaling and distributed linear iterations

estimating erosion risk on forest lands using improved methods of discriminant analysis a population of 638 timber harvest areas in northwestern california was sampled for data related to the occurrence of critical amounts of erosion 153 m3 within 0 81 ha separate analyses were done for forest roads and logged areas linear discriminant functions were computed in each analysis to contrast site conditions at critical plots with randomly selected controls bootstrapping was used extensively in the development and testing of the equations in estimating prediction bias and in placing confidence limits around parameters and posterior probabilities the resulting three variable equations had classification accuracy corrected for prediction bias of 77 7 for road plots and 69 2 for logged area plots the use of linear discriminant functions facilitates the explicit consideration of erosion risk when planning land disturbing activities

on hybrid impulsive and switching systems and application to nonlinear control in this note a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated using switched lyapunov functions some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established in addition a new hybrid impulsive and switching control strategy for nonlinear systems is developed a typical example the unified chaotic system is given to illustrate the theoretical results

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

geometric analysis of the formation problem for autonomous robots in the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation a local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a lyapunov based approach besides the target formation the closed loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations this note addresses a global stability analysis of the closed loop formation control dynamics we pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds these theoretical results are then applied to the well known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

brief paper a connection between formation infeasibility and velocity alignment in kinematic multi agent systems in this paper a feedback control strategy that achieves convergence of a multi agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle type kinematics when inter agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible it is shown that under certain assumptions formation infeasibility forces the agents velocity vectors to a common value at steady state this provides a connection between formation infeasibility and flocking behavior for the multi agent system we finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility

distributed formation stabilization using relative position measurements in local coordinates in this paper we present a novel distributed method to stabilize a set of agents moving in a two dimensional environment to a desired rigid formation in our approach each agent computes its control input using the relative positions of a set of formation neighbors but contrary to most existing works this information is expressed in the agent s own independent local coordinate frame without requiring any common reference the controller is based on the minimization of a lyapunov function that includes locally computed rotation matrices which are required due to the absence of a common orientation our contribution is that the proposed distributed coordinate free method achieves global stabilization to a rigid formation with the agents using only partial information of the team does not require any leader units and is applicable to both single integrator or unicycle agents to guarantee global stability we require that the network induced by the agent interactions belongs to a certain class of undirected rigid graphs in two dimensions which we explicitly characterize the performance of the proposed method is illustrated with numerical simulations

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

consensus in correlated random wireless sensor networks this contribution studies the convergence of consensus algorithms in random wireless sensor networks with spatially correlated links aiming at reducing the convergence time we adopt an optimization criterion based on the minimization of the spectral radius of a matrix for which we derive closed form expressions for both directed and undirected topologies we show that the minimization of the spectral radius assuming constant link weights is a convex optimization problem the expressions derived subsume known protocols found in literature

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

predictive value of statistical models a review is given of different ways of estimating the error rate of a prediction rule based on a statistical model a distinction is drawn between apparent optimum and actual error rates moreover it is shown how cross validation can be used to obtain an adjusted predictor with smaller error rate a detailed discussion is given for ordinary least squares logistic regression and cox regression in survival analysis finally the splitsample approach is discussed and demonstrated on two data sets

stabilisation of infinitesimally rigid formations of multi robot networks this article considers the design of a formation control for multivehicle systems that uses only local information the control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation a potential function is obtained from the graph from which a gradient control is derived under this controller the target formation becomes a manifold of equilibria for the multivehicle system it is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold a complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well finally the controller is validated experimentally

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

consensus of second order multi agent systems via impulsive control using sampled hetero information in this paper the consensus problem for second order multi agent systems using impulsive control with sampled hetero information is investigated necessary and sufficient conditions for sampling interval to achieve consensus for the second order multi agent systems are obtained analysis for the upper bound of sampling interval convergence performance and communication cost of the proposed control protocols are also discussed some numerical examples are given to demonstrate the effectiveness of the proposed control protocols

minimal and redundant bearing rigidity conditions and applications this article studies the notions of minimal and 1 redundant bearing rigidity a necessary and sufficient condition for the numbers of edges in a graph of n n geq 3 vertices to be minimally bearing rigid mbr in mathbb r d d geq 2 is proposed if 3 leq n leq d 1 a graph is mbr if and only if it is the cycle graph in case n d 1 a generically bearing rigid graph is minimal if it has precisely 1 lfloor frac n 2 d 1 rfloor times d text mod n 2 d 1 text sgn text mod n 2 d 1 edges then several conditions for 1 redundant bearing rigidity are derived based on the mathematical conditions some algorithms for generating generically minimally and 1 redundantly bearing rigid graphs are given furthermore two applications of the new notions to optimal network design and formation merging are also reported

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper