containment control for partial differential multi agent systems abstract this paper investigates the containment control problem for a class of partial differential multi agent systems which are governed by the parabolic equations heat equations or the second order hyperbolic equations wave equations the distributed containment based feedback control laws are obtained by constructing an appropriate lyapunov functional and under the action of the feedback control laws the containment errors between the followers states and the convex hull spanned by the leaders states on an appropriate sobolev space can converge to zero as time tends to infinity simulation examples are finally used to show the effectiveness of the theoretical analysis

two sided bounds on the rate of convergence to a stable law we derive necessary and sufficient conditions for several characterizations of the rate of convergence of a sum of independent variables to a stable law the technique used is to obtain upper and lower bounds on the rate in terms of functions depending in a very simple way on the common underlying distribution this permits a general approach to the problem of rates of convergence

modeling and adaptive tracking for a class of stochastic lagrangian control systems this paper focuses on the problem of modeling and adaptive tracking for a class of stochastic lagrangian control systems with unknown parameters by reasonably introducing random noise a method to construct stochastic lagrangian control systems is given under some milder assumptions an adaptive tracking controller is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters the reasonability of assumptions and the efficiency of the controller are demonstrated by a mechanics model in random vibration environment

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

homogeneous observers iterative design and global stabilization of high order nonlinear systems by smooth output feedback we study the problem of global stabilization by smooth output feedback for a class of n dimensional homogeneous systems whose jacobian linearization is neither controllable nor observable a new output feedback control scheme is proposed for the explicit design of both homogeneous observers and controllers while the smooth state feedback control law is constructed based on the tool of adding a power integrator the observer design is new and carried out by developing a machinery which makes it possible to assign the observer gains one by one in an iterative manner such design philosophy is fundamentally different from that of the traditional luenberger observer in which the observer gain is determined by observability in the case of linear systems our design method provides not only a new insight but also an alternative solution to the output feedback stabilization problem for a class of high order nonhomogeneous systems we further show how the proposed design method with an appropriate modification can still achieve global output feedback stabilization examples and simulations are given to demonstrate the main features and effectiveness of the proposed output feedback control schemes

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

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

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

containment control of leader following multi agent systems with markovian switching network topologies and measurement noises this paper investigates the distributed containment tracking control problem for first order agents with multiple dynamic leaders under directed markovian switching network topologies the control input of each agent can only use its local state and the states of its neighbors corrupted by white noises firstly when the dynamic leaders velocities have some special forms which include the stationary leaders as a special case some necessary and sufficient conditions are presented for the containment tracking in the asymptotic unbiased mean square sense secondly for more general leaders velocities necessary and sufficient conditions are provided for the containment tracking with bounded errors in the mean square sense finally a simulation example is given to illustrate the performance of the proposed control scheme

locally efficient estimation of the quality adjusted lifetime distribution with right censored data and covariates summary zhao and tsiatis 1997 consider the problem of estimation of the distribution of the quality adjusted lifetime when the chronological survival time is subject to right censoring the quality adjusted lifetime is typically defined as a weighted sum of the times spent in certain states up until death or some other failure time they propose an estimator and establish the relevant asymptotics under the assumption of independent censoring in this paper we extend the data structure with a covariate process observed until the end of follow up and identify the optimal estimation problem because of the curse of dimensionality no globally efficient nonparametric estimators which have a good practical performance at moderate sample sizes exist given a correctly specified model for the hazard of censoring conditional on the observed quality of life and covariate processes we propose a closed form one step estimator of the distribution of the quality adjusted lifetime whose asymptotic variance attains the efficiency bound if we can correctly specify a lower dimensional working model for the conditional distribution of quality adjusted lifetime given the observed quality of life and covariate processes the estimator remains consistent and asymptotically normal even if this latter submodel is misspecified the practical performance of the estimators is illustrated with a simulation study we also extend our proposed one step estimator to the case where treatment assignment is confounded by observed risk factors so that this estimator can be used to test a treatment effect in an observational study

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

joint regression analysis of survival and quality adjusted survival summary in this paper a semiparametric bivariate linear regression model for survival and quality adjusted survival is investigated even with a parametric specification for the joint distribution maximum likelihood is not applicable because of induced informative censoring we propose inference procedures based on estimating functions the estimators are consistent and asymptotically normal hypothesis tests and confidence intervals may be constructed with easy to implement resampling techniques simultaneous regression modeling of survival and quality adjusted survival has not been studied formally our methodology gives parameter estimates that are highly interpretable in the context of a cost effectiveness analysis the usefulness of the proposal is illustrated with a breast cancer dataset

probabilistic study of the speed of approach to equilibrium for an inelastic kac model this paper deals with a one dimensional model for granular materials which boils down to an inelastic version of the kac kinetic equation with inelasticity parameter p 0 in particular the paper provides bounds for certain distances such as specific weighted distances and the kolmogorov distance between the solution of that equation and the limit it is assumed that the even part of the initial datum which determines the asymptotic properties of the solution belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent 2 1 p with such initial data it turns out that the limit exists and is just the aforementioned stable distribution a necessary condition for the relaxation to equilibrium is also proved some bounds are obtained without introducing any extra condition sharper bounds of an exponential type are exhibited in the presence of additional assumptions concerning either the behaviour close to the origin of the initial characteristic function or the behaviour at infinity of the initial probability distribution function

convergence rates in precise asymptotics let x1 x2 be i i d random variables with partial sums sn n 1 the now classical baum katz theorem provides necessary and sufficient moment conditions for the convergence of n 1 nr p 2p sn en1 p for fixed e 0 an equally classical paper by heyde in 1975 initiated what is now called precise asymptotics namely asymptotics for the same sum for the case r 2 and p 1 when instead e 0 in this paper we extend a result due to klesov 1994 in which he determined the convergence rate in heyde s theorem

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

distributed containment tracking of multiple stochastic nonlinear systems this paper investigates distributed containment tracking for multiple stochastic nonlinear systems with multiple dynamic leaders under directed network topology the control input of each agent can only use its local state and the states of its neighbors with the backstepping design method distributed tracking controllers are designed by using stochastic analysis and graph theory it is shown that the followers outputs will exponentially converge to the convex hull spanned by the dynamic leaders s outputs with tunable tracking errors while all the states of the closed loop system remain bounded in probability a numerical example is provided to illustrate the effectiveness of the theoretical results

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

a kernel bound for non symmetric stable distribution and its applications abstract we generalize an inequality in 20 to the non symmetric stable distribution case with 1 2 and apply it to study the error of stable clt in wasserstein 1 distance note that this inequality has a similar form as the classical esseen s inequality

on estimating the distribution function for quality of life in cancer clinical trials summary the analysis of quality of life data collected at periodic intervals in a cancer clinical trial must account for those patients data that are missing because of death or administrative censoring we examine estimates of the cumulative distribution function of an interpolated area under a quality of life curve as summaries of the quality of life experience of a treat ment group a proposed estimator although biased offers an improvement over a kaplan meier estimator that assumes incorrectly that the censoring is noninformative modalities may be an area in which quality of life measurements can be particularly infor mative because patient s self reported quality of life may not correspond to investigators perceptions e g see sugarbaker et al 1982 many of the statistical issues involved with assessing quality of life have been discussed by cox et al 1992 we focus in this paper on an unresolved issue pertinent to cancer clin ical trials estimating the distribution function of area under the curve auc quality of life scores for a treatment group to put the issue in context we note that in a typical cancer clinical trial both the proportion of patients who die on study as well as the proportion of patients whose data are censored because the patient is alive at the time of analysis are not small if quality of life is measured at fixed times after a patient is entered onto the trial then one must account for the data missing for both reasons it may be possible to score the quality of life measurements so that a score of zero for a patient who is not alive at that time point is reasonable we assume this throughout we also assume that the quality of life data at a given time point can usefully be summarized by a small set of scores corre

a consistent estimator for the distribution of quality adjusted survival time summary quality adjusted survival analysis is a new approach to therapy evaluation in clinical trials it has received much attention recently because of its ability to take patients quality of life into consideration in this paper we present a method that enables us to calculate the survival distribution of quality adjusted lifetime using martingale theory for counting processes we can show that our estimator is asymptotically consistent normally distributed and its asymptotic variance estimate can be obtained analytically simulation experiments are conducted to compare our estimator with the true underlying distribution for two cases that are of practical importance

approximation to stable law by the lindeberg principle abstract by the lindeberg principle we develop in this paper an approximation to one dimensional possibly asymmetric stable distributions with 0 2 in the smooth wasserstein distance it is the first time that the general stable central limit theorem is proved by the lindeberg principle and that this theorem with 0 1 is proved by a new method other than fourier analysis our main tools are a taylor like expansion and a kolmogorov forward equation

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

output tracking of stochastic high order nonlinear systems with markovian switching this technical note poses and solves the output tracking problem for a class of stochastic high order nonlinear systems with stationary markovian switching by introducing a ii operator and using dynkin formula for markovian switching systems a switching controller is constructed to ensure that the closed loop system has a unique solution and is bounded in probability also the tracking error converges to an arbitrarily small neighborhood of zero the efficiency of the tracking controller is demonstrated by a simulation example

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

on the rate of convergence of sums of extremes to a stable law letx1 x2 be a sequence of independent and identically distributed random variables in the domain of normal attraction of a nonnormal stabler law it is known that only the sum of thek n largest andk n smallest extreme values in thenth partial sum withk n andk n n 0 are responsible for the asymptotic stable distribution of the whole sum we investigate the rate at which such sums of extreme values converge to a stable law in conjunction with the rate at which the sums of the middle terms become asymptotically negligible in terms of rates of convergence our results provide in many cases a quantitative measure of exactly what portion of the sample is asymptotically stable

the two sample problem with induced dependent censorship summary induced dependent censorship is a general phenomenon in health service evaluation studies in which a measure such as quality adjusted survival time or lifetime medical cost is of interest we investigate the two sample problem and propose two classes of nonparametric tests based on consistent estimation of the survival function for each sample the two classes of test statistics examine the cumulative weighted difference in hazard functions and in survival functions we derive a unified asymptotic null distribution theory and inference procedure the tests are applied to trial v of the international breast cancer study group and show that long duration chemotherapy significantly improves time without symptoms of disease and toxicity of treatment as compared with the short duration treatment simulation studies demonstrate that the proposed tests with a wide range of weight choices perform well under moderate sample sizes

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

weighted sums of random variables attracted to stable laws on etudie des sommes ponderees de variables aleatoires en relation avec la loi des grands nombres et la loi du logarithme itere

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test