razumikhin type theorems on general decay stability of stochastic functional differential equations with infinite delay to the best of the authors knowledge there are no results based on the so called razumikhin technique via a general decay stability for any type of stochastic differential equations in the present paper the razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay the obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given an example is presented to illustrate the usefulness of the theory

feedback control for linear time invariant systems with state and control bounds in the presence of disturbances the problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered the only information required about the disturbances is a finite convex polyhedral bound discrete and continuous time systems are considered the property of positive d invariance of a region is introduced and it is proved that a solution of the problem is achieved by the selection of a polyhedral set s and the computation of a feedback matrix k such that s is positively d invariant for the closed loop system it is shown that if polyhedral sets are considered the solution involves simple linear programming algorithms however the procedure suggested requires a great amount of computational work offline if the state space dimension is large because the feedback matrix k is obtained as a solution of a large set of linear inequalities all of the vertices of s are required

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

rational spl lscr sup 1 suboptimal compensators for continuous time systems the persistent disturbance rejection problem spl lscr sup 1 optimal control for continuous time systems leads to nonrational compensators even for single input single output systems as noted in dahleh and pearson 1987 the difficulty of physically implementing these controllers suggests that the most significant application of the continuous time spl lscr sup 1 theory is to furnish achievable performance bounds for rational controllers in this paper the authors use the theory of positively invariant sets to provide a design procedure based upon the use of the discrete euler approximating system for suboptimal rational spl lscr sup 1 controllers with a guaranteed cost the main results of the paper show that i the spl lscr sup 1 norm of a continuous time system is bounded above by the l sup 1 norm of an auxiliary discrete time system obtained by using the transformation z 1 rs and ii the proposed rational compensators yield spl lscr sup 1 cost arbitrarily close to the optimum even in cases where the design procedure proposed in the above mentioned paper fails due to the existence of plant zeros on the stability boundary

minimization of a regulated response to a fixed input the problem of minimizing a regulated output due to a specific bounded input is solved in the siso single input single output discrete time case it is shown that in most situations the optimal solution will not exist but given any epsilon 0 it is possible to find a suboptimal solution with performance within epsilon of the optimal performance the proposed approach is extended to the problem of shaping the error transient response it is shown how time domain templates can be used in this problem in the same way that frequency weighting functions are used in the h sup infinity and h sup 2 problems

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

semiparametric estimation of an accelerated failure time model with time dependent covariates summary a class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates a class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored these estimates are shown to be consistent and asymptotically normal with variances that can be consistently estimated it is also shown that estimators within this class achieve the semiparametric efficiency bound we consider an accelerated failure time model for time to event data in which the survival distribution is scaled by a factor which may be a function of time dependent covariates these models directly model the effect of covariates on the length of survival this is in contrast to the more commonly used proportional hazards model which models the hazard rate itself in some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion as compared to the concept that the hazard rate is changed for time independent covariates say z z1 zp the class of accelerated failure time models assumes that the survival distribution at time t given a set of covariates z z is given by f t i z f0 h z t the proportionality constant h z can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z often h z is taken to be log linear or h z exp b z in such cases if z 0 we can interpret fo t as the baseline survival distribution or the survival distribution for individuals with covariates all equal to zero a useful way of envisioning this model is to consider a hypothetical random variable u that corresponds to an individual s survival time if that individual had covariate values all equal to zero this baseline failure time u would be modified for values of the covariate different than zero for example if we denote the actual survival time by t then for an individual with covariate value z we have t e zu the parameters b in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates the assumption that u is independent of z in this hypothetical construct induces the probabilistic model

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

extended weighted log rank estimating functions in censored regression abstract in the censored regression model some regression estimators are introduced using weighted integrals of the log rank estimating functions their limiting covariance matrices do not involve the error density and can be reliably estimated inference can then be easily obtained some of these estimators have high asymptotic efficiency at some important submodels some lack of fit tests are derived that require little extra computing time these tests are asymptotically normal under the model and consistent against certain monotone or convex model misspecifications numerical studies show that for some weight functions the estimators and tests perform well implementation of the proposed procedures is discussed and illustrated in a real data example

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

efficient estimation for the accelerated failure time model the accelerated failure time model provides a natural formulation of the effects of covariates on potentially censored response variable the existing semiparametric estimators are computationally intractable and statistically inefficient in this article we propose an approximate nonparametric maximum likelihood method for the accelerated failure time model with possibly time dependent covariates we estimate the regression parameters by maximizing a kernel smoothed profile likelihood function the maximization can be achieved through conventional gradient based search algorithms the resulting estimators are consistent and asymptotically normal the limiting covariance matrix attains the semiparametric efficiency bound and can be consistently estimated we also provide a consistent estimator for the error distribution extensive simulation studies demonstrate that the asymptotic approximations are accurate in practical situations and the new estimators are considerably more efficient than the existing o

robust performance unknown disturbances and known fixed inputs this paper addresses the robust performance problem when the system under consideration is subjected to norm bounded time varying uncertainty different performance objectives are considered and computable bounds are obtained for the worst case performance in various norms in some important cases it is shown that these bounds are tight giving simple exact formulas for computing robust performance measures one of the important features of these formulas is that they enable the direct and exact calculation of a number of worst cast performance measures while avoiding entirely the iterations needed for computing these measures by existing methods that rely on repeated scalings and spectral radius bound evaluations

correspondence a comment on l optimal control of siso continuous time systems the paper l optimal control of siso continuous time systems by wang and sznaier wang sznaier 1997 automatica 33 1 85 90 studies the problem of designing a controller that optimally minimizes the peak absolute value of system output due to a fixed input signal with a newly defined function space a it was claimed that the set of all l bounded outputs could be parameterized and that the problem could be transformed to a minimal distance problem on l space we believe however their formulation has essential flaws

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

on constrained infinite time linear quadratic optimal control abstract this work presents a solution to the infinite time linear quadratic optimal control itlqoc problem with state and control constraints it is shown that a single finite dimensional convex program of known size can yield this solution properties of the resulting value function with respect to initial conditions are also established and are shoen to be useful in determining the aforementioned problem size an example illustrating the method is finally presented

learning and classification of complex dynamics standard exact techniques based on likelihood maximization are available for learning auto regressive process models of dynamical processes the uncertainty of observations obtained from real sensors means that dynamics can be observed only approximately learning can still be achieved via em k expectation maximization em based on kalman filtering this cannot handle more complex dynamics however involving multiple classes of motion a problem arises also in the case of dynamical processes observed visually background clutter arising for example in camouflage produces non gaussian observation noise even with a single dynamical class non gaussian observations put the learning problem beyond the scope of em k for those cases we show here how em c based on the condensation algorithm which propagates random particle sets can solve the learning problem here learning in clutter is studied experimentally using visual observations of a hand moving over a desktop the resulting learned dynamical model is shown to have considerable predictive value when used as a prior for estimation of motion the burden of computation in visual observation is significantly reduced multiclass dynamics are studied via visually observed juggling plausible dynamical models have been found to emerge from the learning process and accurate classification of motion has resulted in practice em c learning is computationally burdensome and the paper concludes with some discussion of computational complexity

small sample results for the kaplan meier estimator abstract whereas much is known about the asymptotic properties of the kaplan meier 1958 estimator kme of a survival function exact results for small samples have been difficult to obtain in this article we obtain an exact expression for the th moment 0 of the kme under a model of proportional hazards this enables us under proportional hazards to a study the bias of the kme and b compare the exact variance of the kme to its asymptotic variance

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

robust performance with fixed and worst case signals for uncertain time varying systems in this paper we focus our attention on the determination of upper bounds of the l norm of the output of a linear discrete time dynamic system driven by a step input in the presence of both persistent unknown but l bounded disturbances and memoryless time varying model uncertainty for the same type of systems we also analyze the transient behavior of the step response in terms of its overshoot the problem is solved in a constructive way by determining appropriate invariant sets contained in a given convex region finally we show how to extend these results to continuous time systems

rational suboptimal continuous time controller design we obtain rational suboptimal continuous time solutions to some optimal control problems specified via time domain performance criteria these include spl lscr sub 1 and spl lscr sub spl infin norms and peak overshoot the approach uses linear semi infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis the closed loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated

an algorithm for sampling subsets of h sub spl infin with applications to risk adjusted performance analysis and model in validation in spite of their potential to reduce computational complexity the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty since the problem of sampling causal bounded operators is largely open in this note we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of h sub spl infin as we show in the note samples taken from these sets can be used to carry out model in validation and robust performance analysis in the presence of structured dynamic linear time invariant uncertainty problems known to be np hard in the number of uncertainty blocks

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

design of l q regulators for state constrained continuous time systems a new methodology to the design of lq regulators for continuous time systems subject to linear state constraints is proposed consisting of two parts in the first one the positive invariance of the polyhedron defined by the constraints in the state space is imposed guaranteeing thereby that the constraints will not be violated furthermore the admissible constrained controllers are parameterized via the determination of the elements which are fixed in the state feedback matrix this parameterization enables in a second part the l q regulator to be obtained from the solution of a parameter optimization problem subject to linear constraints for which it is proposed a specialized feasible directions method

a set induced norm approach to the robust control of constrained systems most realistic control problems involve both some type of time domain constraints and model uncertainty however the majority of controller design procedures currently available focus only on one aspect of the problem with only a handful of methods capable of simultaneously addressing both issues recently it has been proposed to address this class of problems by using a constrained robustness measure generated by a constraint set induced operator norm to assess the stability properties of a family of systems in this paper the properties of this constrained robustness measure are explored and the theoretical framework is extended to include control as well as state constraints these results are applied to the problem of designing fixed order stabilizing feedback controllers for systems subject to structured parametric model uncertainty and time domain constraints

fundamental limitations on the time domain shaping of response to a fixed input in this paper we examine time domain limitation of performance problems in feedback control system design the main result is a theorem which gives a dual formulation to the problem of determining absolute limits on the time domain shaping of the response to a fixed input the duals that arise are particularly illuminating they have a simple interpretation as optimizing the impulse response of a transfer function whose poles are readily constructed from the data much insight is obtainable from the dual for example in helping to classify classes of plants with the same quantitative behavior new results on classical performance measures such as overshoot and undershoot are presented we also examine minimization of the difference between the maximum and minimum values of the error response a quantity we term fluctuation

active tracking of foveated feature clusters using affine structure we describe a novel method of obtaining a fixation point on a moving object for a real time gaze control system the method makes use of a real time implementation of a corner detector and tracker and reconstructs the image position of the desired fixation point from a cluster of corners detected on the object using the affine structure available from two or three views the method is fast reliable viewpoint invariant and insensitive to occlusion and or individual corner dropout or reappearance we compare two and three dimensional forms of the algorithm present results for the method in use with a high performance head eye platform and compare the results with two naive fixation methods

further results on rational approximations of spl lscr sup 1 optimal controllers the continuous time persistent disturbance rejection problem spl lscr sup 1 optimal control leads to nonrational compensators even for siso systems the difficulty of physically implementing these controllers suggests that the most significant applications of the continuous time spl lscr sup 1 theory is to furnish bounds for the achievable performance of the plant previously two different rational approximations of the optimal spl lscr sup 1 controller were developed by ohta et al 1992 and by blanchini and sznaier 1994 in this paper the authors explore the connections between these two approximations the main result of the paper shows that both approximations belong to the same subset spl omega sub t of the set of rational approximations and that the method proposed by blanchini and sznaier gives the best approximation in the sense of providing the tightest upper bound of the approximation error among the elements of this subset additionally the authors exploit the structure of the dual to the spl lscr sup 1 optimal control problem to obtain rational approximations with approximation error smaller than a prespecified bound

on the pth moment exponential stability criteria of neutral stochastic functional differential equations the paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the ito type this investigation can be very complicated even in many special cases by using usual methods based on lyapunov functionals in this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations

rational l sub spl infin suboptimal controllers for siso continuous time systems we study the problem of minimizing the weighted amplitude of the time response due to a given fixed input signal for single input single output siso continuous time systems and focus on obtaining rational suboptimal solutions an eas euler approximating system based method is proposed for designing a rational l sub spl infin suboptimal controller for siso systems it is shown that this rational approximation is the best one among a set of rational approximations in the sense of providing the tightest upper bound and that it can approximate the optimal cost arbitrarily close

goodness of fit analysis for the cox regression model based on a class of parameter estimators abstract in this article we propose a class of estimation functions for the vector of regression parameters in the cox proportional hazards model with possibly time dependent covariates by incorporating the weight functions commonly used in weighted log rank tests into the partial likelihood score function the resulting estimators behave much like the conventional maximum partial likelihood estimator in that they are consistent and asymptotically normal when the cox model is inappropriate however the estimators with different weight functions generally converge to nonidentical constant vectors for example the magnitude of the parameter estimator using the kaplan meier survival estimator as the weight function will be stochastically larger than that of the maximum partial likelihood estimator if covariate effects diminish over time such facts motivate us to develop goodness of fit methods for the cox regression model by comparing parameter estimators with different weight functions under the assume

on some stability problems of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract this paper covers the topic of both the p th moment p 2 and almost sure stability of impulsive stochastic cohen grossberg neural networks with mixed time delays we partially use a known result on exponential stability of impulsive stochastic functional differential systems based on the razumikhin type technique and extend it to the case of stochastic neural networks using the lyapunov function method and a gronwall type inequality additionally we consider the stability with respect to a general decay function which includes exponential but also more general lower rate decay functions as the polynomial and the logarithmic ones this fact gives us the opportunity to study general decay almost sure stability even when the exponential one cannot be discussed suitable examples which support the theory are also presented

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

l optimal control of siso continuous time systems abstract in this paper we study the problem of designing a controller that minimizes the weighted amplitude of the time response due to a given fixed input signal for siso continuous time systems the main result of the paper shows that this problem admits a minimizing solution in l and that the optimal closed loop system has a special structure a sum of delayed step functions all having the same amplitude thus the optimal controller has a non rational transfer function although in the general case finding this controller entails solving an infinite dimensional linear programming problem we show that in some special cases the optimal solutions have closed form expressions and can be found by solving a set of algebraic equations finally we address the issue of selecting time and frequency domain weighting functions this paper together with our paper rational l suboptimal controller for siso continuous time systems ieee trans autom control ac 41 1358 1363 1996 which deals with the design of rational l suboptimal controllers for general systems give a complete solution of the l control problem

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

rational approximation of l sub 1 optimal controllers for siso systems the l sub 1 optimal control problem with rational controllers for continuous time systems is considered in which it is shown that the optimal l sub 1 performance index with rational controllers is equal to that of irrational controllers a sequence of rational controllers that approximates the optimal index is constructed convergence properties of such a sequence are studied that the corresponding sequence of objective transfer functions is shown to converge in weak topology in bv r sub in the time domain and uniformly in a wider sense in the frequency domain

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

l sub 1 analysis and design of sampled data systems the focus of this work is l sub 1 optimal control of sampled data systems a converging approximation procedure is derived to compute the l sub infinity induced norm of closed loop finite dimensional linear time invariant lti sampled data systems an approximation method is developed to synthesize l sub 1 optimal sampled data regulators finally an example is provided that illustrates the l sub 1 analysis and design techniques presented

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

further results on the optimal rejection of persistent bounded disturbances the problem of designing controllers that optimally reject persistent disturbances is studied the focus is on the case where the plant to be controlled has either zeros or poles on the stability boundary i e the unit circle in the discrete time case and the extended j omega axis in the continuous time case for the discrete time case the problem of minimizing a cost functional of the form f rg sub 1 where the transform g of g has some unit circle zeros is studied a previously published dual problem formulation is extended and it is shown that an optimal controller need not exist the construction of a sequence of suboptimal controllers whose performance approaches the unattainable infimum of the cost function is studied it is shown that two results which hold in the case of h sub infinity optimization do not hold in the presented situation specifically the introduction of unit circle zeros can increase the value of the infimum even when every unit circle zero of g is also a zero of f and a sequence of controllers constructed in an obvious fashion fails to be an optimizing sequence similar results are obtained for the continuous time case

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

stochastic stability of delayed neural networks with local impulsive effects in this paper the stability problem is studied for a class of stochastic neural networks nns with local impulsive effects the impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants hence the impulses here can encompass several typical impulses in nns the aim of this paper is to derive stability criteria such that stochastic nns with local impulsive effects are exponentially stable in mean square by means of the mathematical induction method several easy to check conditions are obtained to ensure the mean square stability of nns three examples are given to show the effectiveness of the proposed stability criterion

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

piecewise linear lq control for systems with input constraints abstract a piecewise linear control plc law based on lq theory is derived ths law raises an lq gain as the controlled error converges towards the origin it can be computed off line and it guarantees that input bounds are never exceeded without causing input saturation a succession of positively invariant sets are defined of diminishing size and associated with each is the corresponding highest lq gain possible in the presence of the input bounds the formulation gives rise to an iteration function whose solution is a fixed point fp the fp defines the optimal gain and the invariant set which comprise ellipsoids fp existence uniqueness and convergence properties are proven we explain the algorithms for the generation and subsequent implementation of the plc law the notion of a switching function is introduced consideration is given to the computational aspects of the fp the plc scheme is demonstrated for the linearized dynamics of the simple pendulum and the puma 560 robot a discrete time plc law can also be derived using the discrete time algebraic riccati equation

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

three step censored quantile regression and extramarital affairs this article suggests very simple three step estimators for censored quantile regression models with a separation restriction on the censoring probability the estimators are theoretically attractive i e asymptotically as efficient as the celebrated powell s censored least absolute deviation estimator at the same time they are conceptually simple and have trivial computational expenses they are especially useful in samples of small size or models with many regressors with desirable finite sample properties and small bias the separation restriction costs a small reduction of generality relative to the canonical censored regression quantile model yet its main plausible features remain intact the estimator can also be used to estimate a large class of traditional models including the normal amemiya tobin model and many accelerated failure and proportional hazard models we illustrate the approach with an extramarital affairs example and contrast our findings with those of fair

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

exponential stability of stochastic delayed hopfield neural networks the exponential stability for stochastic delayed hopfield neural networks hnns is considered the sufficient conditions to guarantee the almost surely exponential stability and exponential stability in mean square of an equilibrium solution are given one example is also given to demonstrate our results

h sub 2 control with time domain constraints theory and an application in this paper we study the problem of minimizing the h sub 2 norm of a given transfer function subject to time domain constraints on the time response of a different transfer function to a given test signal the main result of this paper shows that this problem admits a minimizing solution in r h sub 2 moreover rational solutions with performance arbitrarily close to optimal can be found by constructing families of approximating problems each one of these problems entails solving a finite dimensional quadratic programming problem whose dimension can be determined before hand these results are illustrated and experimentally validated by designing a controller for an active vision application

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem